HurdleDMR.jl is a Julia implementation of the Hurdle Distributed Multinomial Regression (HDMR), as described in:
Bryan Kelly, Asaf Manela & Alan Moreira (2021). Text Selection, Journal of Business & Economic Statistics (ungated preprint).
It includes a Julia implementation of the Distributed Multinomial Regression (DMR) model of Taddy (2015).
This tutorial explains how to use this package from R via the JuliaCall package that is available on CRAN.
First, install Julia itself. The easiest way to do that is to get the latest stable release from the official download page. An alternative is to install JuliaPro.
Once installed, open julia in a terminal, press ] to activate package manager and add the following packages:
pkg> add RCall HurdleDMR GLM Lasso
Now, back to R
install.packages("JuliaCall")
Installing package into ‘/home/user/R/x86_64-pc-linux-gnu-library/3.6’ (as ‘lib’ is unspecified)
Load the JuliaCall library and setup julia
library(JuliaCall)
jl <- julia_setup(installJulia = TRUE)
Julia version 1.5.3 at location /home/user/packages/julias/julia-1.5.3/bin will be used. Loading setup script for JuliaCall... Finish loading setup script for JuliaCall.
jl
allows us to evaluate julia code.
The data should either be an n-by-p covars matrix or a DataFrame containing the covariates, and a (sparse) n-by-d counts matrix.
For illustration we'll analyse the State of the Union text that is roughly annual and relate it to stock market returns.
The sotu.jl
script compiles stock market execss returns and the State of the Union Address texts into a matching DataFrame covarsdf
and a sparse document-term matrix counts
.
julia_install_package_if_needed("HurdleDMR")
julia_install_package_if_needed("Lasso")
julia_install_package_if_needed("CSV")
julia_install_package_if_needed("DataDeps")
julia_install_package_if_needed("GLM")
julia_install_package_if_needed("DataFrames")
julia_install_package_if_needed("FamaFrenchData")
julia_install_package_if_needed("TextAnalysis")
julia_install_package_if_needed("SparseArrays")
julia_install_package_if_needed("PyCall")
# # if the above doesn't work, you can also try
# jl$command("import Pkg")
# jl$command("Pkg.add([\"Lasso\", \"CSV\", \"DataDeps\", \"DataFrames\", \"Pandas\", \"FamaFrenchData\", \"TextAnalysis\", \"SparseArrays\", \"PyCall\"])")
jl$call("include", "sotu.jl")
[[1]] Date Rem President 1 1927 29.47 Calvin Coolidge 2 1928 35.39 Calvin Coolidge 3 1929 -19.54 Herbert Hoover 4 1930 -31.23 Herbert Hoover 5 1931 -45.11 Herbert Hoover 6 1932 -9.39 Herbert Hoover 7 1934 3.02 Franklin D. Roosevelt 8 1935 44.96 Franklin D. Roosevelt 9 1936 32.07 Franklin D. Roosevelt 10 1937 -34.96 Franklin D. Roosevelt 11 1938 28.48 Franklin D. Roosevelt 12 1939 2.70 Franklin D. Roosevelt 13 1940 -7.14 Franklin D. Roosevelt 14 1941 -10.53 Franklin D. Roosevelt 15 1942 16.20 Franklin D. Roosevelt 16 1943 27.96 Franklin D. Roosevelt 17 1944 20.97 Franklin D. Roosevelt 18 1945 38.38 Franklin D. Roosevelt 19 1946 -6.73 Harry S. Truman 20 1947 2.95 Harry S. Truman 21 1948 1.07 Harry S. Truman 22 1949 19.12 Harry S. Truman 23 1950 28.82 Harry S. Truman 24 1951 19.22 Harry S. Truman 25 1952 11.80 Harry S. Truman 26 1953 -1.05 Dwight D. Eisenhower 27 1954 49.35 Dwight D. Eisenhower 28 1955 23.75 Dwight D. Eisenhower 29 1956 5.90 Dwight D. Eisenhower 30 1957 -13.16 Dwight D. Eisenhower 31 1958 43.45 Dwight D. Eisenhower 32 1959 9.76 Dwight D. Eisenhower 33 1960 -1.46 Dwight D. Eisenhower 34 1961 24.81 John F. Kennedy 35 1962 -12.90 John F. Kennedy 36 1963 17.84 John F. Kennedy 37 1964 12.54 Lyndon B. Johnson 38 1965 10.52 Lyndon B. Johnson 39 1966 -13.51 Lyndon B. Johnson 40 1967 24.49 Lyndon B. Johnson 41 1968 8.79 Lyndon B. Johnson 42 1969 -17.54 Lyndon B. Johnson 43 1970 -6.49 Richard Nixon 44 1971 11.78 Richard Nixon 45 1972 13.05 Richard Nixon 46 1973 -26.19 Richard Nixon 47 1974 -35.75 Richard Nixon 48 1975 32.44 Gerald R. Ford 49 1976 21.91 Gerald R. Ford 50 1977 -8.26 Gerald R. Ford 51 1978 1.03 Jimmy Carter 52 1979 13.09 Jimmy Carter 53 1980 22.13 Jimmy Carter 54 1981 -18.13 Jimmy Carter 55 1982 10.66 Ronald Reagan 56 1983 13.74 Ronald Reagan 57 1984 -6.05 Ronald Reagan 58 1985 24.91 Ronald Reagan 59 1986 10.12 Ronald Reagan 60 1987 -3.87 Ronald Reagan 61 1988 11.55 Ronald Reagan 62 1989 20.49 George H.W. Bush 63 1990 -13.95 George H.W. Bush 64 1991 29.18 George H.W. Bush 65 1992 6.23 George H.W. Bush 66 1993 8.21 William J. Clinton 67 1994 -4.10 William J. Clinton 68 1995 31.22 William J. Clinton 69 1996 15.96 William J. Clinton 70 1997 25.96 William J. Clinton 71 1998 19.46 William J. Clinton 72 1999 20.57 William J. Clinton 73 2000 -17.60 William J. Clinton 74 2001 -15.20 George W. Bush 75 2002 -22.76 George W. Bush 76 2003 30.75 George W. Bush 77 2004 10.72 George W. Bush 78 2005 3.09 George W. Bush 79 2006 10.60 George W. Bush 80 2007 1.04 George W. Bush 81 2008 -38.34 George W. Bush 82 2009 28.26 Barack Obama 83 2010 17.37 Barack Obama 84 2011 0.44 Barack Obama 85 2012 16.27 Barack Obama 86 2013 35.20 Barack Obama 87 2014 11.71 Barack Obama 88 2015 0.08 Barack Obama 89 2016 13.30 Barack Obama 90 2017 21.51 Donald J. Trump 91 2018 -6.93 Donald J. Trump 92 2019 28.28 Donald J. 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[34,] 0 0 0 2 0 0 0 0 0 0 [35,] 0 0 2 5 1 0 1 0 0 0 [36,] 0 0 0 3 0 0 0 0 0 0 [37,] 0 0 0 1 2 0 0 0 0 0 [38,] 0 0 0 2 0 0 0 0 0 0 [39,] 0 0 0 3 0 0 1 0 0 0 [40,] 1 0 1 2 1 1 1 0 0 0 [41,] 0 0 0 0 3 2 0 0 0 0 [42,] 0 0 1 0 0 2 1 0 0 0 [43,] 0 0 0 0 0 0 3 0 0 1 [44,] 0 0 0 0 0 0 0 0 1 3 [45,] 0 1 0 0 0 0 0 0 1 0 [46,] 0 0 0 0 0 0 0 0 0 0 [47,] 0 0 3 0 2 0 1 0 0 3 [48,] 0 0 0 0 1 0 1 0 0 0 [49,] 0 0 2 0 1 0 2 0 0 0 [50,] 0 0 1 0 1 3 0 0 0 0 [51,] 0 0 0 0 0 0 1 0 2 0 [52,] 0 0 1 0 0 0 0 0 0 0 [53,] 0 0 3 1 0 0 0 0 0 0 [54,] 0 0 0 6 14 3 3 0 7 4 [55,] 0 0 0 0 0 0 0 0 0 0 [56,] 0 0 0 0 0 0 0 0 0 0 [57,] 0 0 0 0 0 1 1 0 0 0 [58,] 0 0 0 0 0 0 0 0 0 0 [59,] 0 0 0 0 0 0 0 0 0 0 [60,] 0 0 1 0 0 0 0 0 2 1 [61,] 0 0 0 0 0 0 0 0 0 1 [62,] 0 0 1 0 1 1 0 0 0 0 [63,] 0 0 1 0 0 0 0 0 0 0 [64,] 0 0 2 3 0 0 1 0 0 0 [65,] 0 0 2 0 0 0 0 0 0 1 [66,] 0 0 0 0 0 0 0 1 1 1 [67,] 0 0 1 0 0 2 0 0 6 1 [68,] 0 0 0 0 0 1 0 0 4 1 [69,] 0 0 1 0 0 1 2 1 3 1 [70,] 0 1 0 1 0 3 0 0 3 1 [71,] 2 3 0 2 1 3 0 3 1 1 [72,] 3 0 0 1 0 2 0 0 0 0 [73,] 9 0 0 0 0 3 0 0 1 0 [74,] 0 0 3 0 0 0 0 0 0 0 [75,] 0 0 1 0 0 0 0 4 1 0 [76,] 2 0 2 6 2 0 0 4 0 0 [77,] 4 0 1 4 0 0 0 3 0 0 [78,] 1 0 0 1 2 0 0 2 0 0 [79,] 1 0 2 0 2 0 0 2 1 0 [80,] 1 0 1 2 0 1 0 0 0 0 [81,] 0 1 0 0 0 0 0 0 0 0 [82,] 0 0 3 0 0 1 0 0 0 0 [83,] 0 0 4 0 0 1 0 0 0 0 [84,] 0 1 2 0 0 0 0 0 0 0 [85,] 0 1 3 0 0 0 2 0 0 0 [86,] 3 0 3 0 2 0 0 0 0 0 [87,] 0 0 1 0 0 1 0 0 0 0 [88,] 0 0 3 0 1 1 1 0 0 0 [89,] 0 0 3 0 0 1 1 0 0 0 [90,] 0 0 1 0 0 0 0 0 0 0 [91,] 0 0 0 1 0 0 0 0 0 0 [92,] 0 0 0 0 0 0 1 0 0 0 [,158] [,159] [,160] [,161] [,162] [,163] [1,] 0 0 0 1 0 1 [2,] 0 1 0 0 0 4 [3,] 0 2 0 0 0 2 [4,] 0 1 0 0 0 0 [5,] 0 1 0 0 0 1 [6,] 0 1 0 1 0 0 [7,] 0 0 0 0 0 0 [8,] 0 0 0 0 0 0 [9,] 0 0 0 1 0 1 [10,] 0 0 0 0 0 1 [11,] 0 0 0 1 0 0 [12,] 0 0 0 2 0 0 [13,] 0 0 0 3 2 1 [14,] 0 0 0 0 0 1 [15,] 0 0 0 1 0 2 [16,] 0 0 0 0 0 7 [17,] 0 0 0 0 0 1 [18,] 2 0 1 1 1 1 [19,] 0 0 2 3 4 6 [20,] 0 0 0 1 1 4 [21,] 0 0 1 4 2 2 [22,] 0 0 0 1 0 0 [23,] 0 0 1 3 2 0 [24,] 2 0 0 0 0 2 [25,] 1 0 0 2 0 6 [26,] 3 0 0 1 1 0 [27,] 3 0 0 0 0 0 [28,] 1 1 1 1 0 0 [29,] 0 1 0 0 1 0 [30,] 1 0 0 0 0 0 [31,] 0 0 0 1 2 1 [32,] 1 0 0 0 0 1 [33,] 1 0 0 1 1 3 [34,] 0 0 0 2 0 0 [35,] 2 0 0 0 0 2 [36,] 1 0 0 2 1 1 [37,] 0 1 0 1 1 1 [38,] 0 2 0 0 0 0 [39,] 1 0 0 0 0 1 [40,] 2 0 0 0 0 1 [41,] 0 0 0 1 0 0 [42,] 1 1 0 1 1 1 [43,] 0 0 0 0 0 3 [44,] 0 0 0 0 0 0 [45,] 0 0 0 0 0 1 [46,] 0 1 0 1 0 0 [47,] 0 0 0 0 0 1 [48,] 0 2 0 0 1 1 [49,] 0 0 1 0 0 2 [50,] 1 2 0 0 0 0 [51,] 0 0 3 1 0 2 [52,] 0 0 0 2 0 0 [53,] 1 0 0 3 0 2 [54,] 6 12 2 2 0 3 [55,] 0 0 0 0 0 0 [56,] 0 0 2 0 0 0 [57,] 0 0 0 1 1 1 [58,] 0 0 0 1 0 0 [59,] 0 1 0 1 0 0 [60,] 0 0 0 0 0 0 [61,] 0 0 1 0 1 0 [62,] 0 0 0 0 0 0 [63,] 0 0 0 0 0 0 [64,] 0 0 0 1 1 1 [65,] 0 1 1 0 1 0 [66,] 0 3 0 0 2 0 [67,] 0 3 0 0 1 0 [68,] 0 1 0 0 1 0 [69,] 0 2 0 0 0 2 [70,] 0 1 1 0 0 0 [71,] 0 3 0 0 0 0 [72,] 0 2 1 0 0 1 [73,] 0 2 0 1 0 0 [74,] 0 1 0 0 1 0 [75,] 0 0 0 0 0 0 [76,] 0 0 0 1 0 0 [77,] 0 0 1 0 1 1 [78,] 0 0 0 0 0 0 [79,] 0 0 3 1 0 0 [80,] 0 0 0 0 0 0 [81,] 0 1 1 0 0 0 [82,] 0 0 0 0 0 0 [83,] 0 1 0 0 0 0 [84,] 0 1 0 0 0 0 [85,] 0 0 1 0 0 2 [86,] 0 0 0 0 0 0 [87,] 0 3 0 0 0 0 [88,] 0 0 0 0 0 1 [89,] 0 0 0 0 0 2 [90,] 0 1 0 0 2 0 [91,] 0 0 0 0 0 0 [92,] 0 0 0 0 0 2 [[3]] [1] "administration congress" "al qaeda" [3] "american families" "american family" [5] "american leadership" "american life" [7] "american people" "american workers" [9] "armed forces" "army navy" [11] "atomic energy" "balanced budget" [13] "billion dollars" "billions dollars" [15] "budget message" "business labor" [17] "care system" "child care" [19] "civil rights" "civil service" [21] "clean energy" "climate change" [23] "cold war" "collective bargaining" [25] "common sense" "congress act" [27] "congress enact" "congress pass" [29] "cost living" "country world" [31] "create jobs" "current fiscal" [33] "defense spending" "democrats republicans" [35] "district columbia" "dollars fiscal" [37] "economic development" "economic growth" [39] "economic recovery" "economic system" [41] "executive branch" "fair share" [43] "farm income" "federal budget" [45] "federal expenditures" "federal government" [47] "federal reserve" "federal spending" [49] "fellow americans" "fellow citizens" [51] "flood control" "foreign oil" [53] "foreign policy" "free enterprise" [55] "free nations" "free world" [57] "friends allies" "future generations" [59] "global economy" "god bless" [61] "government people" "government spending" [63] "growing economy" "health care" [65] "health education" "health insurance" [67] "health services" "help people" [69] "home abroad" "hope congress" [71] "human rights" "income tax" [73] "job training" "labor management" [75] "lasting peace" "latin america" [77] "law enforcement" "local government" [79] "local governments" "look forward" [81] "medical care" "meet challenge" [83] "middle class" "middle east" [85] "military forces" "military power" [87] "military strength" "million americans" [89] "million dollars" "million jobs" [91] "million people" "millions americans" [93] "millions people" "minimum wage" [95] "move forward" "nation earth" [97] "nation world" "national debt" [99] "national defense" "national government" [101] "national income" "national life" [103] "national security" "national service" [105] "nations world" "natural gas" [107] "natural resources" "north korea" [109] "nuclear weapons" "peace freedom" [111] "peace world" "people america" [113] "people united" "people world" [115] "persian gulf" "private enterprise" [117] "private sector" "public health" [119] "public private" "purchasing power" [121] "quality life" "recommend congress" [123] "republicans democrats" "research development" [125] "rest world" "saddam hussein" [127] "science technology" "security system" [129] "session congress" "social security" [131] "soviet union" "st century" [133] "standard living" "submitted congress" [135] "tax code" "tax credit" [137] "tax cut" "tax cuts" [139] "tax rates" "tax reduction" [141] "tax reductions" "tax relief" [143] "th congress" "thank god" [145] "throughout world" "time time" [147] "tonight im" "tonight propose" [149] "trade agreements" "united america" [151] "united nations" "urge congress" [153] "vice president" "war ii" [155] "weapons mass" "welfare reform" [157] "welfare system" "western europe" [159] "white house" "world economy" [161] "world peace" "world trade" [163] "world war" attr(,"class") [1] "JuliaTuple"
library(Matrix)
rcounts <- as(jl$eval("counts"), "sparseMatrix")
rcovarsdf <- jl$eval("covarsdf")
rcounts
92 x 163 sparse Matrix of class "dgCMatrix" [1,] 1 . . . . . . . . 1 . . . . . . . . . . . . . . . . 1 . . 1 . . . [2,] . . . . . . 1 . . 2 . . . . . . . . . 3 . . . . . . 1 1 . . . 2 . [3,] . . . . 1 . 2 . . 3 . . . . 1 . . . . 4 . . . . 1 . . . . 1 . 1 . [4,] . . . . . . . . . 1 . . 1 . 2 . . . . 1 . . . . . . . . 1 . . 3 . [5,] . . . . . . . . . 1 . . . . 1 . . . . . . . . . . . . . . . . . . [6,] . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . 1 . . . . [7,] . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . [8,] . . . . . . 2 . . . . . . 1 1 . . . . 1 . . . . 1 . . . . 1 . . . [9,] . . . . . . . . 1 . . 1 . . . . . . . . . . . . . . . . . . . . . [10,] . . . . . . . . . . . . . . . . . . . . . . . 2 . . . . . . . . . [11,] . . . . . . 1 . . . . 2 4 . . . . . . . . . . 2 . . . . . . . . . [12,] . . . . . 1 5 . 1 . . . 3 . . . . . . . . . . . 1 . . . . . . . . [13,] . . . . . . 2 . . 2 . . . . . . . . . . . . . . 2 . . . . . . . . [14,] . . . . . . 2 . . 1 . . . 1 1 1 . . . . . . . . . . . . . . . . . [15,] . . . . . . 3 . 4 . . . 1 . 1 . . . . . . . . . . . . . . . . . . [16,] . . . . . . 1 . 2 1 . . . . . . . . . . . . . . 1 . . . 1 . . . . [17,] . . . . . . 1 . 2 1 . . . . . . . . . . . . . . 2 . . . 1 . . . . [18,] 2 . . . 1 . 2 . 8 2 . . . . . 1 . . . . . . . . . . 1 . . . . . . [19,] . . 1 2 . . 2 . 15 3 2 1 80 2 2 3 . . . 1 . . . 3 . 1 1 . 4 . . 13 . [20,] . . . . . . 2 . 3 3 8 . 1 1 2 . . . 4 . . . . 7 . . . . . . . . . [21,] . . . 2 . . . . 2 . 1 . . . . 2 . . 2 . . . . 1 . 1 . 1 4 . . . . [22,] . . . . . . 2 . 2 . . . . . . . . . 2 . . . . 1 . . 3 . 1 . . . . [23,] . . . . . 1 . . . . 2 1 . . . . . . 1 . . . . 3 . . 2 . . . . . . [24,] . . . . . . 1 . . 1 1 . . . 1 . . . . . . . . . . . . . . . . . . [25,] . . . . . . 1 . 2 . . . . . 1 . . . 1 1 . . 1 . . . . . . . . . . [26,] . . . . . . 2 1 1 . . 1 4 . . . . . 2 . . . 1 2 1 . 1 . 1 . . 1 . [27,] . . . 1 . . 1 . 4 . 2 . 1 . 4 . . . . . . . . . . . 1 . . . . 2 . [28,] . . . . . . 1 . 5 . 1 1 3 1 1 . . . . . . . . . . 1 . . . . . 1 . [29,] . . . . . 1 2 1 2 . 3 4 6 . . . . . 3 1 . . . . . . . . 3 . . . . [30,] 1 . . . . . 1 . 1 . 3 . . . 2 1 . . 5 . . . . . . . 1 . 1 . . . . [31,] . . . . . . 5 1 2 . 2 . 2 . . . . . . . . . 2 . . . 1 . . . . . . [32,] . . . . . . . 1 3 . 1 1 5 . . 1 . . . . . . . 1 . . . . 1 . . 1 . [33,] . . . . . 1 2 . . . . 1 1 . . . . . 2 . . . . . . . 1 . . . . . . [34,] 1 . . 1 . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . [35,] . . . . . 1 1 . . . . 1 1 . . 1 . . 1 . . . 1 . 2 . . . . . . . . [36,] . . 1 . . 1 1 . . . . 1 1 1 . 1 . . . . . . 3 . . . . . . . 1 . . [37,] . . 1 1 . . . . . . . . . . . . . . 1 . . . . . . . . . . . 2 . . [38,] . . . . . 2 2 . . . . 1 . . . 2 . . 1 . . . 1 . . . . . . . . . . [39,] . . . . . 1 3 . 1 . . . 1 . . . . . 2 1 . . . . . . . . 1 . . . . [40,] . . 1 . . . 5 . . . . . . . . 1 . . 1 . . . 3 . . . . . . . . . . [41,] . . 1 1 . . 3 . . . . . . . . . . . 1 . . . . . . 2 1 1 . . . . . [42,] 1 . . 1 . 1 2 . . . . . . . . . . . 2 . . . . . . . . . . . . . . [43,] . . 2 . . 2 3 . . . . 3 . . . . . . . . . . . . . 1 . . 3 . . . . [44,] . . . 1 . . 3 . . . . . 1 . . . . . . . . . . . . . . . 1 . . . . [45,] . . . . . . 2 2 1 . . . . . . . . . . . . . . . . 1 1 . . . . . 1 [46,] . . . . . 1 . . . . . . . . . . . . . . . . . . 1 . . . 1 . . . . [47,] 1 . . . . . 7 1 . . . . . 1 . . 3 . . . . . . . . 2 . . 1 . 1 . . [48,] . . . 1 . . 6 . . . . . . 1 . . . . . 1 . . . . . 2 1 . . . 2 . . [49,] . . . . . 1 7 . 1 . . 1 . . . 1 . . . . . . . . 5 1 2 . 2 . 2 . . [50,] 1 . . . 2 . 3 . 2 . . . . . . . . . . . . . . . 2 . . 1 1 . . 1 2 [51,] . . . . . . 6 1 1 . . 1 . . . 1 . . . 1 . . . . . 1 . . . . . . . [52,] . . . 1 . . 4 4 . . . . . . 1 1 . . 1 1 . . . . 1 . . . . 2 . . . [53,] . . . . . . 2 . 1 . . . . . . . . . . . . . 1 . . 1 . . . . . . . [54,] 16 . 3 . . 2 6 1 3 . . . 1 1 . 1 4 . 7 6 . . . . 1 1 7 4 1 1 . . 9 [55,] 1 . . . . . 4 1 1 . . . 3 . . . . . 1 . . . . . . . . . . . 1 . . [56,] . . 1 . . . 5 1 1 . . 1 . . 1 1 . 1 1 . . . . . 1 . 1 . 1 . . . 2 [57,] . . . . . . 1 . . . . . 1 . . . . 1 . . . . . . 2 . . . . . . . 1 [58,] . . . . . . 3 . . . . 1 1 . . . . . 1 . . . . . . . . . . . . . 1 [59,] . . 1 . . . 6 . . . . 2 . 1 . . . . . . . . . . 1 . . . . . . . 1 [60,] . . . . . . 3 . . . . 1 . 1 . . . . . . . . . . . . . . . 1 . . . [61,] . . 1 . . . 1 . . . . 4 . 1 . . . . . . . . . . 1 . . 2 . . . . 1 [62,] . . 1 . 1 . . . 1 . 1 1 1 . . . . 4 . . . . . . 1 . 1 . . . 1 1 . [63,] . . . . . . 4 . 2 . . . 1 . . . 1 1 . . . . . . . . . . . . . . . [64,] . . . . 1 . 3 . . . . . . . . . . 1 1 . . . 1 . . . . . . . 2 . . [65,] . . . . . . 3 1 1 . . . . . . . 1 . . . . . 1 . . . 1 1 . 1 . . . [66,] . . 1 1 . . 15 . . . . . . 1 . 1 2 1 . . . . . . . . 1 1 1 1 3 . . [67,] . . . . . . 9 . 1 . . . . . . . 4 1 1 . . . 1 . . . . 2 . 1 8 . 2 [68,] . . . 1 . . 12 . 1 . . . . . . . . 1 . . . . 6 . 2 . . 1 . 3 1 . 1 [69,] . . 1 . 1 1 10 . . . . 1 . . . . . 1 . . . . 2 . . . . 3 . . 2 . . [70,] . . . 1 2 . 2 . . . . 5 . . . . . 1 . . . . 5 . . . . . . . 4 . . [71,] . . . 1 . . 5 1 . . . 3 . . . . . 8 . . . 1 . . . . . 2 . . . . . [72,] . . . . . 1 5 . . . . 7 . 1 . . . 2 . . 1 . 2 . . . . 1 . . . . 1 [73,] . . . . 1 . 2 . 2 . . 2 . . . . . 6 1 . . 1 . . . . . . . 2 . . . [74,] 1 . . . . . 3 . 1 . . . 1 . . . . . . . . . . . . . . . . . . . . [75,] . . . . . . 4 2 2 . . . 1 . . . . . . . . . . . . 1 1 . . 1 3 . 1 [76,] . . 2 . . . 5 . 1 . 2 1 . . . . 2 . . . . . . . . 1 . 1 . 2 . . . [77,] 1 . . . 1 1 4 1 . . . . . 1 . . 2 . . . . . . . 1 1 . . . . 1 . . [78,] . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 2 . . . . . [79,] . 3 1 . 1 . 3 1 . . . . . . . . . . . . 1 . . . . 2 . 1 . . . . . [80,] . 10 . . . . 4 . 2 . . . . . . . . . . . . 1 . . . . . . . . . . . [81,] . 8 3 . . . 3 1 . . . . . . . . . 1 . . 2 1 . . . . 1 4 . . . . . [82,] 1 1 1 . . . 5 . . . . . 1 1 . . . . . . 1 1 . . . . . . . . . . . [83,] 1 1 . . . . 11 . . . . . . . . . . 1 3 . 10 2 . . 1 . . . . . 5 . . [84,] . 3 . 2 2 . 3 1 . . . . . 1 . 1 . . . . 5 . . . . . . 1 . . 1 . 1 [85,] . 1 1 . 1 . 2 2 1 . . . . . . . . . . . 8 1 . . 2 . . . . . 4 . . [86,] . 4 . . . . 6 . 1 . . . . 1 . 1 . . . . 2 3 . . . 1 . 1 1 . 4 . . [87,] . 2 1 1 . . 4 . 1 . . 1 . . . . 1 . . . . 2 1 . . 1 . . . 1 6 . . [88,] . . 2 . 2 . 4 2 . . . . . . . . . . . . . 3 . . . . . 1 . 1 . . . [89,] . 3 . . 2 . 6 . . . . . . . . . 1 . 1 . 2 4 1 1 . . . . . . . . . [90,] . . . 1 1 . 3 . . . . . . 3 . . 1 1 2 . . . 1 . . . . . . . . . 1 [91,] . . 1 1 . 1 4 2 . . . . . 1 . . . . . . . . . . . . . 1 . . 1 . . [92,] . . . . . 1 1 2 . . . . . 1 . . . . 1 . . . . . . . . 2 . . . . 1 [1,] . . . . . . . . . . . . 12 . . . . 5 . . . . . . . . . . . . . . . [2,] . 1 . . . . . . . 1 . . 7 . . . . 3 . . . . . . . . . 1 . . . 1 . [3,] . 5 . . . . . . . 1 . . 10 1 . . . 2 . . . . . . . . . . . . . 1 . [4,] . 1 . . . . . . . . . . 1 . . . . 1 . . . . . . . . . . . . . . . [5,] . . . . . 2 1 . . . . . 5 7 . . . . . . . . . . . . . . . . . . . [6,] . . . . . 1 2 . . . 1 1 5 3 . . . . . . . . . . . . . 1 . . . . . [7,] . . . . . . . . . . . . . . . . . 1 . . . . . . . . . 1 . . . . . [8,] . . . . . . 1 . . . . . 4 . . . . . . . . . . . . . . . . . . . . [9,] . . . . . . . . . . . . 4 . . . . . . . . . . . . . . 1 . . . . . [10,] . . . . . 1 . 2 . . . . 1 . . . . . . . . . . . 1 . . . . . . . . [11,] . . . . . 1 2 . . . . 2 2 . . . . . . . . . . . . . . 1 . . . . . [12,] . . . . . . 1 . . . 1 . 2 . . . . 1 . . . . . . . . . . 1 . . . . [13,] . . . . . . 1 1 . . . . 1 . . . 1 . . . . . . . 1 . . . . . . 1 . [14,] . . . . . . . 1 . . . . . . . . . . . . . . 1 . 1 . . . . . . . . [15,] . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . [16,] . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . [17,] . . . . . . . . . . . . 1 . . . . . . 1 . . . . . . . . . . . . . [18,] . . . . . . . . . 1 . . 1 . . . . . . 1 . . . . 1 . . . . . . 1 . [19,] . 2 40 1 . 1 2 1 1 2 4 7 18 2 . . . 4 . 6 4 . . . . . . 1 . . . 1 1 [20,] . . . . . . . . . . 1 . 6 . . . . . . 1 1 . . . . . . . . . . 1 . [21,] . . . 1 . 2 5 . . . . 1 3 . . . . . . . 1 1 . . . . . . . . . 3 . [22,] . . . . 1 . 1 . 1 . 1 . 2 . . . . 1 . 4 3 . . . . . . . . . . 2 . [23,] . 1 . . 3 1 3 . 2 2 . 2 . . . . . . . 1 1 2 1 . . . . . . 1 . 1 . [24,] . . . 1 1 . . . . . . . . . . . . . . . . 16 6 1 . . . . . 1 . 1 . [25,] . 1 . . . . . 1 . . . . . . . . . . . 2 . 7 4 1 . . . 1 . . . . 1 [26,] . 2 . . . . 1 2 . 1 . 1 8 1 . . . . . 5 . 1 3 . . . . . . 1 . 1 . [27,] . 2 . . 4 . 1 . . . 1 . 12 . . . . 2 . 1 . 1 4 . . . . . . 3 . 1 . [28,] . 2 1 . 5 . . 2 . . 1 1 11 . . . 2 . . . . 9 2 . . . . . 1 1 . 1 2 [29,] . 3 . . 2 . 1 3 1 1 . . 3 . . . . . . 1 . 3 6 . . . . . 1 . . . 2 [30,] . . . . 1 . . . . 1 . . 4 . . . . 1 . . 2 3 5 . . . . . . . . 1 . [31,] . . . 2 1 . . . . . . . 1 . 1 . . . . 1 1 2 2 . . . . . . . . 1 . [32,] . . . 2 5 . . . . . 1 2 1 . 1 . . . . 1 . 1 2 . . . . . . 1 . 1 . [33,] . . . . 2 . . . . 1 . . 1 . . . . . . . . . 13 . . . . . . . . 1 . [34,] . . . . 5 . . 2 . 2 1 . . 1 . 1 1 . . . . . 2 . . . . . . . 1 . . [35,] . . . 1 3 . . . 1 . 1 . . . . . 1 . . 2 . 1 2 . . . . . . . 1 . 3 [36,] . . . . 1 1 . . . 1 . . . . 1 . . . . . . 4 5 . . . . . . . . . . [37,] 1 . . . . . . . . . . 1 . . . 2 1 . . . 2 1 1 . . . . . . 1 . . . [38,] . . . . 1 . . 1 . . . . . . . . . . . . . . . . . . . . . 1 1 . . [39,] . 1 . . . . . 1 . 1 2 . 2 . . 1 . . . . . . . . . . . . . . . 2 . [40,] . . . 1 1 . . 1 . . . 1 2 1 . 1 . . . 1 . . . . . . . . . . . . . [41,] 1 . . . . . . 2 1 . . 1 . . . . . . . . . . . . . . . . . . . . . [42,] . . . . . . . 2 . . . . . . 1 . 1 . . . . 1 . . . . . . . . . 1 . [43,] . 1 . . 2 . . . . . 1 . 6 . 1 . . . . 2 . . 1 . . . . . . . . 1 . [44,] . . . 1 . . . 2 . . 1 . 9 1 . . . . . 1 . . . . . . . 2 . 1 1 . . [45,] . 1 . . . . . 1 1 1 . . 2 . . . . . . 3 . . . . . . . . . . 3 . . [46,] . . . . 1 . . . . 1 . . 2 . 1 . . . . 1 . . . . . . . . 2 . . 1 . [47,] . . . 2 . . . . . 1 . . 2 . . . . . . . . . . . 1 . . . . . 6 . 1 [48,] . . . . . . 1 . . . 2 2 1 1 3 . . . 1 3 . . 1 . . . . . 1 . . . . [49,] . . . . 1 . 2 . . . 2 1 6 . 3 . . . 2 1 . . . . 3 . . . . . 2 . 3 [50,] . . . . 1 . . 1 . . . . 3 . . 1 1 . 2 2 . 1 . . . . 1 1 . . . . . [51,] . . . . 3 . 1 . . . 1 . . . 1 . . . 1 7 . . . . . . . 2 . . 1 . . [52,] . . . 1 . . 2 . . 2 1 . . . 1 . . . . . . . . . . . . 1 1 . 2 . . [53,] . . . . . . . . . . 1 . . . . . 1 . 2 . . . . . . . . . . . . 1 . [54,] . 2 . 16 4 1 . 1 . 2 1 1 26 . 2 . 2 1 3 9 1 . 1 7 1 1 . 1 2 . 17 1 3 [55,] . . . 1 2 2 . . . . 1 . 6 1 2 . . . . 3 2 . 1 . . . 2 . 5 . 1 . . [56,] . . . . 4 1 . . 1 . 1 . 1 . 2 . . . . 3 . . . 1 . . 1 . 1 . 1 . . [57,] . . . . 4 4 . . . . 1 . 1 . 2 . . . . . 1 . . . . . 3 . 2 . . . . [58,] . . . 1 2 . . . . . 1 . 4 1 . . 2 . . . 1 . 1 . . . 1 . 1 . 2 . . [59,] . . . . 1 . . . 1 . 3 . 3 . 1 . . . . . . 2 2 . . . 2 . . . . . . [60,] . . . . . . . . . . . . . . . . 1 . . . . 1 . . . . 2 . . . . . . [61,] . . . . 3 . . . . . 1 . 8 . . . . . . . . 2 1 . 1 1 1 2 1 . . . . [62,] . . . . 6 . . 2 . . 1 . 1 . 1 . . . 1 . . . . . . . 2 . . . . . . [63,] . . . . . . . . . . . . . . 2 . 1 . . . . 1 . . . . 3 . . . 3 . . [64,] . . . . 3 . . . . . . . 3 1 1 . . . . . . . . 2 2 . 1 . . . 1 . . [65,] . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . 1 . 3 . 4 [66,] 1 . . . 3 . . 1 . . 1 . 1 . 1 1 . . . . . . . . 1 3 1 . 1 . 18 . . [67,] 1 . . . 1 . . . . . . . . . . 4 . . . 1 . . . . . 2 2 . . . 29 . 5 [68,] . . . . 1 1 . . 1 . . . 2 . . 3 2 . . 1 . . . . . 3 1 1 . . 7 . 3 [69,] . . . . . . . . . . . . 5 . . 3 2 . . 1 . . . . . . 2 . . . 5 . 2 [70,] . . . . 1 . . . . . 1 . 1 . . 3 1 . . 1 . . . . . 3 2 . . 1 2 . 3 [71,] . 1 . . 1 . . . . . . . . . . 1 3 . . . . . . . . 3 2 . . . 1 . 2 [72,] . . . . 2 . . . . 1 . . . . . 2 . . . . . . . . 1 2 . . . 1 2 . 3 [73,] . . . 1 4 . . . . . . . . . . 3 1 . . . . . . . . . 2 . . . 9 . 2 [74,] . . . . . . . . . . . . . . . 2 2 . . . . . . . . . 1 . . . . . . [75,] . . . . . . . . . . . . . . . 1 . . 1 . . . . 2 . . 1 . . . 1 . . [76,] . . . . 1 . . . . . . . 1 . 1 . 3 . . . . 1 . 2 . . . . . 1 6 . . [77,] . . . . 2 . . . . . . . . . . . 1 . . . . . . 1 . . . . . 1 9 . 3 [78,] . . . . . . . . . . . . 1 . . . 2 . . . . 1 . . 2 . 1 . . 1 3 . . [79,] . . . . 1 . . . . . 2 . 2 . . . 5 . . . . . . 1 . 1 1 . 1 1 2 . 1 [80,] . . . . . . . . . . 2 . 1 . . 1 2 . 2 1 . . . . 1 . 1 . . 1 5 . 10 [81,] . . . . 2 . . . . . . . 4 . . 2 2 . . 1 . . . 1 . . . . . . 2 . 1 [82,] 3 . . . 1 1 . . . . 1 . 2 . . . . . . . . . . 1 1 2 2 1 . . 16 . 2 [83,] 3 . . . 1 . . . . . . . 1 . . . . . . . . . . . . 1 2 . 3 . 7 . 3 [84,] 6 . . . . . . . . . . . 1 . . . . . . . 1 . . . 2 . 2 . . . 4 . 2 [85,] 1 . . . . . . 1 4 . . . . . . . 1 . 1 . . . . . . . 2 1 1 . 2 . 1 [86,] 3 . . . 3 . . . 1 . . . . . . 1 . . 1 . 1 . . . 3 1 2 . . 1 5 . . [87,] 2 . . . 2 . . . . . . . 1 . . 2 . . 2 . . 1 . . 2 2 3 . . . 4 . 4 [88,] 4 . . . 1 . . . 2 . . . . . . 1 . . 2 . . . . . 2 . 2 . . 2 4 . 1 [89,] 1 . . . . . . . . . . . . . . 2 1 . 1 1 . . . . . 1 2 1 . 1 3 . . [90,] 2 . . . . . . 1 1 . . . . . . . . . . 2 . 1 . 1 . . 2 . . . 3 . 4 [91,] 2 . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . [92,] 1 . . . . . . . 1 . . . . . . . 2 . . 1 . . . . . . 2 . . . . . . [1,] . . . . . . . . . . . . 1 . 1 . . . . 1 . . . . . . . . . . . 1 4 6 [2,] . . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 3 [3,] . . 1 . . 1 . . . . 6 1 1 . 1 . . . . . . . . . . . . . . . . . 2 . [4,] . . . . . 2 . . . . 1 . . . . . . . . . . . . . . . . . . . . . 1 . [5,] . . 1 . . . . . . . 1 1 3 . . . . . . . . . . . . . . . . . . 2 1 1 [6,] 1 . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . 1 . [7,] . . . . . . . . . . . . . 1 . . . . . . . . 1 . . . 1 . . . . . . 2 [8,] . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . 1 [9,] . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . 1 1 . . [10,] . . . . . . . . . . . . . 2 . . . . . . . . . . . 1 . . 1 . . . . 2 [11,] . . . . . 1 . . . . . 2 . . . . . . 1 . . . . . . . . 1 . . . . . 3 [12,] . . . . . 1 . . . . . . . . 1 . . . . . . . 1 . . . . . . . . . 2 . [13,] . . . . . . . . . . . . . . . . . . . . . 1 . . 1 . . . . . 1 . 3 . [14,] . . . . 1 . . . . 1 . . . 1 1 . . . . . . 1 . . . . . . . . . . 1 . [15,] . . . . . . . . . . . . . . . . . . . . 1 . . . . . 1 . . . . . 1 . [16,] . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . 2 . . . [17,] . . 1 1 . . . . 2 . . . . . 1 . . . . . . . . . 1 . . . 1 . 1 . . . [18,] . . . . . . . . . . . . 1 . 1 . . . . . . . . . . . . . . . . . . . [19,] 4 . 1 3 . . . 5 2 . . 2 9 2 8 1 . . . . . . 119 . . 1 . 8 2 . . 1 19 1 [20,] . . 1 1 . . . 9 1 . 1 . . . 1 . . . . . 1 . . . . . . 1 . . . . 3 . [21,] . . . . 3 1 . 1 . . . . 1 1 4 . . 1 . . . . . . 1 . . 2 3 . . . . . [22,] . . 1 . . . . . . . . . . . 3 . . . . . . . . . . . . 1 . . . 1 . . [23,] 1 . 1 1 1 . . . . . . . . . 1 1 . . . . 1 . . . . . . . 1 . . . . . [24,] . 1 . . . . . . . . . . . . 1 2 . . 2 1 1 . . . . . . . . . . . . . [25,] 2 . . 1 1 . . . . . . . . 2 1 1 . 2 2 1 1 . . . 1 . 1 . . . . . . . [26,] . . . . . . . 4 . . . . 1 . . . . . . 2 1 . . . . . . . . . . 2 . . [27,] . . 1 . . 1 . 1 1 . . . 1 . 1 . . 1 . 1 1 . . . 1 . 1 . . . . . . . [28,] 3 1 . . . . . 2 . . . 1 2 1 4 . . 1 1 2 3 . . . 1 . . 2 . . . . . . [29,] . . . . . . . 2 1 1 . 1 . 1 2 . . 2 . 2 2 1 . . . . . 1 . . . 2 . . [30,] . . 1 . . . . 1 . . . . . . . . . 3 . 1 1 . . . 1 . . . . . . . . . [31,] . . . . . . . . 1 . . . 1 . . . . . 1 3 6 . 1 . . 1 2 . . . 1 1 . . [32,] . . . . . . . 1 . 1 1 . . 1 . . . . . 1 1 . . . . . . . . . . . . . [33,] . 1 . . . . . . . . . . . 1 . 1 . . . . . . 1 . 1 . . . . . . 1 . . [34,] . . 1 . . . . . . 3 . . . . . . . . . . . 2 . . . . . . . . . . 1 1 [35,] 1 1 . . 1 1 . . . 4 . 1 . . . . . 1 . 1 2 2 . 1 . . . . . . . . . . [36,] . . 1 . . . . . . 2 . . . . . . . 1 . . . 4 . 1 . . 1 . . . . . . . [37,] . . 1 . . . . . 1 . . . . . 1 . . . . 1 . . . 1 . . . 1 . 1 . . . . [38,] . . . . . 1 . . . 2 1 . . . . . . . . 1 . . . . . . . 1 . . 1 . . 1 [39,] . 1 . . . . . . . 1 1 . . . 1 . . . . . . . . 1 . . . 1 . 2 . . . . [40,] . . . 1 . . . . . 2 2 . 4 1 1 . . 1 . . . 5 . . . . . 1 . . . . . 1 [41,] 1 . 1 . . 1 1 . . 1 3 1 . . 1 1 . 1 . . . 2 . 1 . . . . . . . . . 2 [42,] . . . 1 . . 1 . . . 1 . 2 . 1 . . 2 . . . 1 . . . . . . . . 2 . . . [43,] . 1 . . 1 . 1 . . 1 3 . 1 . . . . . . . . . . . 1 2 1 . . . 3 . . . [44,] 1 . . . . . 1 1 . . . 3 3 . 4 2 . . . . . . . . . 1 1 . . . 2 . 1 . [45,] 1 . . . . . . . . . . . 1 . . . . . . . . . . . . 1 . . . . 1 . . . [46,] . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . 1 . . . [47,] . . 1 . . . . . 2 1 . . 1 2 . . . 3 1 . 3 . . 1 1 3 . . . . 4 . 1 . [48,] . . . . . . . . . . . 1 1 . . . . 2 1 . 2 2 . . . 1 . . 1 . 1 1 1 . [49,] 1 . 1 . . 1 1 . . 1 2 . 3 . . 2 . 1 2 1 . 2 . 1 . 1 . . . . . . . . [50,] . . . 1 . 1 . . . 1 . . 1 1 . . . 3 1 . 1 . 1 1 1 . . . . . . . 3 . [51,] . . 1 . 5 1 . . . 1 . . . . . . . 1 1 . . . . 1 . . 1 . . . . . . . [52,] . . 1 . 5 . . . 1 1 . . . 1 . . . 2 . 1 . . . . . 1 . . . . 2 . . . [53,] . . . . 3 . . . . . . . . . . 1 . 7 2 4 . . . . . . . . . . . . . . [54,] 4 . . 5 25 . 1 . . 3 2 3 9 2 . . . 11 2 5 2 . . 2 3 . 2 2 1 1 2 . . . [55,] . 1 . . 1 1 1 . . . . 1 4 1 . . . 1 3 . . . . . . . . . . . . . 1 1 [56,] . 1 1 . . . 1 1 . 2 . . 1 1 . 1 . 3 . . 1 1 . . . . . . . . . 2 1 . [57,] . . 1 . . 1 . . . . . . . . . . . 1 . . . 1 . . . . . . 3 . . 1 1 . [58,] . 1 . 1 . 1 1 . . . . . . . . . . . . . 1 . . 1 . . . . . . . . . . [59,] . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 2 . [60,] . . . 1 1 . . . . 2 . . . . . . . 1 1 . . . . 2 . . . . . . 1 . . . [61,] . . . . 1 . . . . . . . . . . . . . . . . . . . . 2 . . . . . . 1 . [62,] 1 . . . . . . . . . 1 . . 1 . . . . . . . 2 . . . . . . 1 . . . . . [63,] . . 3 . . . . . . . . . . . . 2 . . 1 . . . . . . . 1 . 1 . . 1 . . [64,] . . 1 . . . . . 1 1 . . . . . . . . . . . . . 1 . . . . . 1 . . . . [65,] . 1 . . . . 1 . . . . . . . . . 1 . . . . . . . . 1 . . . 3 . . . . [66,] . 1 . . . 1 1 . . . . 1 . . . 1 2 . 1 . . . . 1 . 1 1 . . 1 . 1 2 . [67,] . . . 2 2 3 2 . 1 . . . . . 1 . 5 2 . . . 2 . . 1 2 1 . . . . 1 . . [68,] . 1 3 1 . . . . . 1 . . . . 1 . 4 4 . . . 2 1 2 . 2 . 5 . . . . . . [69,] . 1 2 . . 1 . . . . 1 . 1 . . 1 . 1 . . . 2 . 1 2 1 . 3 . . . . . . [70,] . 1 . . 1 . . . . 2 . . . . . 1 . 1 . . . 1 . 1 2 2 . . . . 1 . . . [71,] . . . . . 1 1 . . 1 1 . . . . . 1 1 . . . 1 . 1 1 2 . 1 2 . . . . . [72,] . 1 1 . . . . . 1 . . 1 . . 1 . 1 2 . . . 3 . 1 . 1 2 1 . . . . . 1 [73,] . 1 . . 1 1 . . . . 2 . . 1 . 1 . 1 . . . 3 . 1 1 2 . 1 . . . 2 . 1 [74,] . . . . . . . . . 2 2 . 1 . . . . 1 . . . . . . . 1 . . . . . . . . [75,] . . . . . . . . 1 1 1 . . . . . . . . . . . . . . . . . . . . . . . [76,] . 1 . . 2 . . . . . 1 . . . 1 . . 3 . . . 1 . . 3 . 2 . . . 1 . . . [77,] . . . . . . 2 . . . 7 . . . 1 . . 4 . . . . . . . 1 . . 1 . . . . . [78,] . 1 . . 1 . 1 . . . . . . . . . . 6 . . . 1 . 1 . . . . 1 . . . . . [79,] . 1 . . . . . . 1 . 1 . . . . . . 5 . . 1 1 . 1 . . . . 1 . . . . . [80,] . . . . . . . . . . 1 . . . . 1 . 6 . . . . . 1 . 1 . . . . . . . . [81,] . . . . . . . . . . 1 . . 1 1 . . 2 . . . . . . 1 . . . . 2 . . . 1 [82,] . . . . . . . . 1 . . . . . . . . . . . . 2 . 1 . 1 . . 1 . . . . . [83,] . 1 . . 1 . . . . . . . . . . . . . . . . 3 . 3 1 2 . . 1 . . 1 . . [84,] . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . 3 2 . . . . [85,] . 1 . . . . . . . . . . . . . . 1 1 . . . 2 1 3 . 2 . . 1 . 1 . . . [86,] . . . . . . 1 . 1 . 1 . . . . . 6 2 . . . . . 2 . 1 . 6 . 2 . . . . [87,] . . . . . 1 . . 1 . 1 . . . . . 2 . . . . 2 . 2 1 2 . 3 . 3 . . . . [88,] . . . . . . 1 . . . 1 . . . . . 7 2 . 1 . . . 1 . 1 . 1 . 1 1 . . . [89,] . . . . . . . . 1 1 . . . . . . . 2 . 1 . . . 1 . . . 1 . 1 . . . . [90,] . . 1 . . . . . . . 2 . . . . . 3 2 . . . 2 . . 1 . . . . . . . 1 . [91,] . . . . . . 1 . . . . . 1 . . . 1 . . . . . . 1 . 1 . . . . . . . . [92,] . . . . . . . . . . 3 . . . . . 2 3 . . . 1 . 1 . . 1 . . . . . . . [1,] . . . . . . . . . . 1 . . . . 3 . . 1 3 . . . . 1 . . . . . . . [2,] 1 . . . 1 . 1 . . . 1 . . . . 4 . 2 . 1 . . . . . . . . 2 . . . [3,] . . 1 . 1 . . . . . 1 . . . . 2 . 7 . . . 7 . . . . . . 1 . . . [4,] . . . . . . 3 . . . . . . . . . . . 1 . . 3 . . . . . . . . . . [5,] . . . . . . 1 . . . 1 . . . . . . 3 1 . . 2 . . 1 . . . 1 . . . [6,] . 1 1 . . . . . . . 1 . . . . . . 3 . . . 1 . . . . . . 5 . . . [7,] . 2 . . 1 . 2 . . . . . . . . . . . . 1 . . . . . . . . 1 . . . [8,] 1 . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . [9,] 4 1 . . . . . . . . 1 . 2 2 . . . . . . . 1 . . 1 . . . . 1 . . [10,] . . . . . . . . . . . . 1 . . 1 . . . . . . . . 1 . . 1 . 1 . . [11,] . 1 . . 1 . . . . . . . 2 . . . . . . 10 . . . . . . . . . . . . [12,] 6 . . . 1 . . . . . . . . . . . . . 1 1 . . . . 1 . . . . 1 . . [13,] 1 . . . 1 . 1 . . 1 . . 1 . . . . . . . . . . . 4 . . . . 1 . . [14,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [15,] 2 . . . . . . . . . . . . 2 . . . . . . . . . . . . . . . . . . [16,] . 1 . . . . . . . . 1 . . . . . . . . . . . . . 1 . . . . . . . [17,] . . 1 10 . . . . . . 2 . . . . . . . . 1 . 1 . . . . . . . 1 . . [18,] 1 1 . 5 . . 1 . . . . . . . . 3 . . . 2 . 1 . . 1 . . 1 . 2 . . [19,] 7 . 1 1 2 . 3 . . 1 1 . 3 3 . 5 . 1 2 8 . 1 . . . . . 3 . 16 3 . [20,] 1 . 4 1 1 . 2 . . . 1 . . 1 . 5 . . 1 1 . 1 . . . . . 1 . 1 3 . [21,] 2 . 2 . . . 2 . . . 1 . 2 . . 1 . . 1 1 . . . . 1 . . . . 3 . . [22,] . 1 1 . 1 . 1 . . . 2 . 3 . . 2 . . . 1 . 2 . . . . . . . 6 . . [23,] 1 2 . . 1 . 5 . . 1 1 . 1 . . . . 1 1 1 . 2 . . . . . 1 2 1 . . [24,] . . 1 . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 7 . [25,] . . . . 1 . 1 . . 1 1 . . 1 . . . 1 . . . . . . 2 . . . . 1 3 . [26,] . . 2 . 1 . 1 . . . 1 . . . . . . . 1 1 . 2 . . 1 . . 1 . 1 . . [27,] . . 3 . 1 . 1 . 2 . . . . . . . . . 1 . . 4 . 1 . . . 1 . 1 1 . [28,] . 2 2 . . . . . 2 2 . . . . . . . . . . . 2 . 1 . . . 1 1 2 . . [29,] 2 2 2 . 1 . 1 . . . . . 1 . . . . . . . . 1 . . . . . 1 . 1 . . [30,] . 2 1 . 2 . 2 . 1 . . . 1 . . 1 . . . 2 . 1 . 1 . . . . . 1 . . [31,] . . 1 . 1 . . . . . . . 2 3 . . . . . . . . . 2 . . . . . . 2 . [32,] . 1 1 . . . . . . . . . 1 . . 3 . 1 1 . . 1 . 1 . . . . . . . . [33,] . . . . 1 . . . 1 . . . . 1 . . . . . . . . . 1 . . . . . . 3 . [34,] . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . 1 . . 1 4 . [35,] . 1 1 . . . 1 . . . . . . . . . . . . 1 . . . . . . . 1 . 3 1 . [36,] 1 . . . . . . . 2 3 . . . . . . . . . 2 . . . . . . . 1 . 1 1 . [37,] . . . 1 . . . . . . . . . . . . . . . 1 . . . . . . . . 2 2 . . [38,] . . . . . . . . . . . . . . . . . . 1 . 1 . . . . . . . . 1 2 . [39,] . . . . . . . . 1 . . . 1 . . 1 . . 1 . 1 . . . 1 . . . . . 1 . [40,] . . . . . 1 . 1 1 . . . . . . 1 . . . . 2 1 1 . . . . . . 3 7 . [41,] . . . . 1 . . . 1 . 2 . . . . . . . . . . . . . . . . . . 2 2 . [42,] . . . . 2 . . . 1 . 1 . . . . . . 1 . . . . . . . . . . . 2 2 . [43,] . . . . 2 . . . . 1 . . 2 4 . . . . . . 4 . 1 . . . . . 1 . 1 . [44,] . . . . . . 2 . . . . 4 . . . . . . . . 1 . . . . . . . . . . . [45,] . . . . 1 . . . . . 1 1 1 . . . . . . . 2 . . 1 . . . . 4 . 2 . [46,] . . . . . . 3 . . . . . . . . . . . . . . . . . . . 1 . . . . . [47,] . . . . 2 . . . . . 6 2 1 . . 2 . . . . . . . 1 . . . . 2 . 3 1 [48,] . . . . 1 3 . . . . . . . . . . 1 . . . . . . 1 1 . . . . 1 2 . [49,] . . . . . 1 . . . . . . . . . . . . . 1 . . . . . . . 1 . 6 . . [50,] . . 2 . . 2 . . 1 1 1 . . . . . . . . . 1 . . . . . . . . . 2 . [51,] . . 2 . 1 . . . 2 . 1 . . . . . . . . . . . . . 1 . . . . . 2 . [52,] . . 2 . . . 2 . 1 . 1 . 1 . . . 1 . . . 1 . . . . . . . . . 6 1 [53,] . . . . 2 . . . 3 . 2 . . . 4 . . . . . . . . . . . . . . . 13 . [54,] . 2 12 . 3 6 4 . 7 2 1 . . 2 11 1 18 2 1 . 2 1 . 3 . . 10 7 . 17 19 . [55,] . . 1 . . . . . . 1 1 . . . . . 2 . . . . . . . 1 . . . . 1 1 . [56,] 1 . . . . . . . . 4 1 2 . . . . 3 . . . 1 . 1 1 1 . . 1 . 6 3 1 [57,] . . . . . . 1 . 1 1 1 . 1 . . . 3 . . 1 . . 1 . . . 1 . . . 3 . [58,] . . 1 . . 1 1 . 1 . . . . . . . 2 . . . . . . 1 . . . . . . 1 . [59,] . . 2 . 1 . . . 1 . . . . . . . 1 . . . . . . . . . . . . 1 . 1 [60,] . . 1 . . . . . . 1 . . . . . . . . . . . . . . . . 1 . 1 . 3 2 [61,] . . 2 . . . . . 1 2 1 . . . . . 1 . . . . . . . . . . . . . . . [62,] . . 3 . . . . . 3 . 1 1 . . . . 1 . . . . . . 1 . . . . . 1 1 . [63,] . . . . . . . . . . . . . 2 . . . . . . . . . 1 . . . . . 3 1 . [64,] . . . . 1 . . . . . 1 . . . 4 . . . . . . . . 1 . 1 . . . . 1 1 [65,] . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . 1 1 . [66,] 1 . . 4 . . . . . . . . . 1 . . 4 . 3 . . . 2 1 . . . . . 5 . 2 [67,] . . 1 2 . . . . 1 . 1 1 . . . . 3 . . . . . 1 . 2 . . . 1 . . . [68,] . . . 1 . . . 1 . 2 . . . . . . 2 . . . 1 . 2 . . . . . . 2 . 1 [69,] . . . 1 . . . 2 2 1 . 1 . 2 1 . . . . 1 . . 2 . . . . . . 3 . . [70,] . . 1 1 . . . 2 1 1 1 . . 1 . . 3 . . . . . . . . . 1 . . 3 . 9 [71,] . . . . . . . . . . . . . . . 1 . 1 . . 1 . 1 1 . 3 1 2 . 6 . 14 [72,] . . . 1 1 . . . 1 . . . . . . 1 3 . . . 1 . . . . 1 . . . 23 . 23 [73,] . . 1 . . . . 1 1 1 . . 1 . . . 2 . . . 1 . . . . . 5 . . 3 . 9 [74,] . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . [75,] . . 1 . . . . 1 2 . 1 . . . . . . 1 . . . . 2 . . . . . . 2 . . [76,] . . . . . . . 1 5 . 2 . 1 . 1 . . . . . . . . . . 19 . . 1 2 1 . [77,] . . 1 . . . . 1 2 . 1 1 . 1 . . 1 . . . . . . . . 2 . 1 . 2 . 1 [78,] . . . . . . . 1 1 1 . . . . . . . . . . . . . . . 1 . 2 . 18 . 1 [79,] . . . . 1 . . 1 1 . 1 . 1 1 . . . . 1 . 1 . . 1 . . . . . 3 . . [80,] . . . . . . . . 2 . . 1 . . . . . . . . . . . . . . . . . 2 . . [81,] . . . . . . . . . . 1 . . . 1 . . . . . . . 1 . . . . . . 1 . 1 [82,] . . . 1 . . . . . . . . . . . 2 1 . . . . . . . 1 . 1 . . 2 . 2 [83,] . . 3 . . . . 1 1 . . . . . . . . 1 . . . . . . . . . . . 2 . 2 [84,] . . . . . 1 . 1 2 . . . . . . . 1 . . . 1 . 2 1 1 . 1 . . 1 . 2 [85,] . . . . . 4 . . . . . 1 . . . . 1 . . . . . . . . . 1 . . 1 . . [86,] . . 1 . . 3 . 1 . . . . . 1 . . . . . . . . . 1 . . 1 . . 1 . . [87,] . . 1 . . 4 . . . . . . . . . . . . . . . . 1 . 2 . 1 . . 1 1 1 [88,] . . 2 . . . . . . . . 1 . 1 . . . . . . . . 2 1 . . 1 . . 1 . . [89,] . . 1 . 1 . . . . . . 1 . 1 . . 1 . . . . . . 1 2 . . . . 1 . 2 [90,] . . . . 2 . . . . . . 1 . . . . . . 2 . . . 1 . . . . . . . . . [91,] . . . . . . . 4 1 . . 1 . . . . 1 . . . . . 1 . . . . . . . . 1 [92,] . . 1 . 1 1 . 1 1 . . . . . . . . . . . 1 . 1 . . . . . . . . 1 [1,] 1 . . . . . . 4 1 . . . . . . . . . . . . . . . . . . . 1 . 1 [2,] . 1 . . . . 2 1 1 . . . . 1 . . . . 1 1 . . . . . . 1 . . . 4 [3,] . . . . . . 2 2 . 1 . . . 2 . . . . . . . . . . . . 2 . . . 2 [4,] . . . . . . . 3 . . . . . . . . . . . . . . . . . . 1 . . . . [5,] . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . 1 [6,] . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . [7,] . . . . . . . . . . . . . 1 . . 1 . . . . . . . . . . . . . . [8,] . . . . . . . . . . . . 2 2 . . . . . . . . . . . . . . . . . [9,] . . . . . . . . . . 1 . . 1 . . . . . . . . . . . . . . 1 . 1 [10,] . . . . . . . . . . 1 . . . . . . 1 . . . . . . . . . . . . 1 [11,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . [12,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . . [13,] . . . . . . . . . . . . . . . . 4 2 . . . . . . . . . . 3 2 1 [14,] 1 . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . 1 [15,] . . . . . . . . . . . . . . . . . . 7 . . . . . . . . . 1 . 2 [16,] . . . . . . . . . . . . . . . . . . 10 . . . . . . . . . . . 7 [17,] 6 . . . . . . . . . . . . 1 . . . . 1 . . . . . . . . . . . 1 [18,] . . . . . . . 1 . . . . 2 . . . . . 7 . . . . . . 2 . 1 1 1 1 [19,] 5 . . . . . 1 3 4 . . . 2 2 . . 1 . 27 6 . 1 . . . . . 2 3 4 6 [20,] 1 2 . . . . 1 . . . . . 1 . . . . . 2 3 . 1 . . . . . . 1 1 4 [21,] 4 1 . 2 . . . 1 . 1 . . 1 . . . 1 . 1 2 . 1 . . . . . 1 4 2 2 [22,] 1 . . . . . . . . . 1 . 1 . . . 1 1 1 . . . . . . . . . 1 . . [23,] 2 . . . . . . 1 . . . . 1 . . . . . 6 3 . . 1 . . . . 1 3 2 . [24,] . . . . . . . . . . . . 1 . . . . . 7 . . 2 . . . 2 . . . . 2 [25,] . . . . . . . . . . . . 3 . . . . . 6 . . 2 . . . 1 . . 2 . 6 [26,] . . . . . . 1 . . . . . 1 . . . 1 . 5 . . . . . . 3 . . 1 1 . [27,] 2 1 . . . . . . 2 . . . . 2 . . . . 3 4 . . . . . 3 . . . . . [28,] . 1 . . 2 1 . . 1 . 2 . 2 . . . . . 7 3 . . . . . 1 1 1 1 . . [29,] . 6 . . 4 . . . . . . . . 1 . . 2 . 5 2 . . . . . . 1 . . 1 . [30,] . . . . . . . . . . 2 . . 1 . . . 1 2 2 . . . . . 1 . . . . . [31,] 1 . . . . . . . . . 1 . 1 1 . . 1 . 3 . . 1 . . . . . . 1 2 1 [32,] . 1 . . . . . . 1 . . . 3 . . . . . 1 . . 1 . . . 1 . . . . 1 [33,] . . . . . . . . . . . . . . . . . . 2 2 . 3 . . . 1 . . 1 1 3 [34,] . . . . . . . . . . . . . . . . . . 2 . . . . . . . . . 2 . . [35,] 1 . . 1 . . 2 . . . . . . . . . . 2 5 1 . 1 . . . 2 . . . . 2 [36,] . . . . 2 . 3 4 . . . . . . . . . . 3 . . . . . . 1 . . 2 1 1 [37,] 1 1 . . 2 . . 1 . . . . . 1 . . . . 1 2 . . . . . . 1 . 1 1 1 [38,] . . . . . 1 . . . . . . . . . . . . 2 . . . . . . . 2 . . . . [39,] . . . . . . . . 1 . 1 . 1 . . . . . 3 . . 1 . . . 1 . . . . 1 [40,] . . . . 1 . 2 . . . 5 . 1 . . 1 . 1 2 1 1 1 . . . 2 . . . . 1 [41,] . 1 . . . . . 1 . . . . . . . . . . . 3 2 . . . . . . . 1 . . [42,] . . . . . . . . . . . . 2 . . . . 1 . . 2 1 . . . 1 1 . 1 1 1 [43,] . . . . . . . . . . . . . . . . . . . . . 3 . . 1 . . . . . 3 [44,] . 1 . . . . . . . . 1 . . . . . . . . . . . . 1 3 . . . . . . [45,] . . . . . . 1 . . . 2 . . . . . 1 . . . . . . 1 . . . . . . 1 [46,] . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . . [47,] . 1 . . . . . . . . . . . . . . . 3 . 2 . 1 . . 3 . . . . . 1 [48,] . 1 . 3 4 . 1 1 . . . . 1 . . . . . . 1 . 1 . . . . 2 . . 1 1 [49,] . 1 . . 1 1 . 3 1 . . . . . . . . 2 . 1 . 2 . . . . . 1 . . 2 [50,] . 1 . . . . . 1 . . . . . . . . . 1 . 1 3 . . . . 1 2 . . . . [51,] 1 . . 1 1 2 1 1 1 . . . . . . . . . . . . 1 . 2 . . . 3 1 . 2 [52,] . . . . . . . . . . 1 . . . . . . 1 . . . . . . . . . . 2 . . [53,] . . . . . . . . . . . . 2 . . . . 3 1 . . . . . . 1 . . 3 . 2 [54,] 1 4 . 2 . 1 . 1 5 . 6 . 5 . . . . . 6 14 3 3 . 7 4 6 12 2 2 . 3 [55,] . . . . . . 1 . 2 1 . . . . 1 . . . . . . . . . . . . . . . . [56,] . . 1 . . 2 . . . . . 1 2 . 1 . . . . . . . . . . . . 2 . . . [57,] . . 1 . . 1 2 1 . . . 1 1 1 . . . . . . 1 1 . . . . . . 1 1 1 [58,] . . 1 . . . 5 . . . . 1 . . . . . . . . . . . . . . . . 1 . . [59,] . . . . 1 . 1 . . . . . . . . . . . . . . . . . . . 1 . 1 . . [60,] . . . . . . . . . . 4 1 . 1 . . . 1 . . . . . 2 1 . . . . . . [61,] . . . . . . 1 . . . . 1 . . . . . . . . . . . . 1 . . 1 . 1 . [62,] . . . 2 . . 1 . . . . 1 . . 3 . . 1 . 1 1 . . . . . . . . . . [63,] . . . . . . . . . . . . . . 1 . . 1 . . . . . . . . . . . . . [64,] . . . 1 . . . . . . . . . . 1 . . 2 3 . . 1 . . . . . . 1 1 1 [65,] . . . 3 . . 1 . . . . . . . . . . 2 . . . . . . 1 . 1 1 . 1 . [66,] . . 1 3 1 . 1 . . . . 1 . . . . . . . . . . 1 1 1 . 3 . . 2 . [67,] . . . 1 . 2 1 . . 1 . 1 . . . . . 1 . . 2 . . 6 1 . 3 . . 1 . [68,] . . . . 4 4 . . 1 2 1 1 2 2 . . . . . . 1 . . 4 1 . 1 . . 1 . [69,] . . . 2 2 . . . . 1 . 1 1 . . . . 1 . . 1 2 1 3 1 . 2 . . . 2 [70,] . . . 1 . . . . . 1 . 1 . . 1 . 1 . 1 . 3 . . 3 1 . 1 1 . . . [71,] . . . 1 1 6 1 . . . . . . . . 2 3 . 2 1 3 . 3 1 1 . 3 . . . . [72,] . . . 2 1 . 1 . . . . . . 1 . 3 . . 1 . 2 . . . . . 2 1 . . 1 [73,] . . . 10 . 2 . . . 1 . 1 . . . 9 . . . . 3 . . 1 . . 2 . 1 . . [74,] . . . . . . . . . . . . 1 . . . . 3 . . . . . . . . 1 . . 1 . [75,] . . . . . 1 1 . . 3 . 1 3 . . . . 1 . . . . 4 1 . . . . . . . [76,] . . . . . . . . . 3 . . . . 1 2 . 2 6 2 . . 4 . . . . . 1 . . [77,] . . . 2 . 1 . . 1 2 . . . . . 4 . 1 4 . . . 3 . . . . 1 . 1 1 [78,] . . 3 . . . . . . 2 . 1 . . . 1 . . 1 2 . . 2 . . . . . . . . [79,] 1 . . 1 . 1 . . . 3 . . . . . 1 . 2 . 2 . . 2 1 . . . 3 1 . . [80,] . . 1 . . . . . . . . . . . . 1 . 1 2 . 1 . . . . . . . . . . [81,] . . 1 . . . . . . 4 1 . . . . . 1 . . . . . . . . . 1 1 . . . [82,] . . 1 1 4 . . . . . . 1 . . . . . 3 . . 1 . . . . . . . . . . [83,] . . . 4 . 6 . . . . . 1 . 1 3 . . 4 . . 1 . . . . . 1 . . . . [84,] . . 2 1 . 2 1 . . . 1 1 . . 2 . 1 2 . . . . . . . . 1 . . . . [85,] . . 3 1 2 1 2 . . 1 . 1 . . 4 . 1 3 . . . 2 . . . . . 1 . . 2 [86,] . . 3 . . . 2 . . 1 . 1 1 . 3 3 . 3 . 2 . . . . . . . . . . . [87,] . . 2 1 . . 1 . . . . . . . 1 . . 1 . . 1 . . . . . 3 . . . . [88,] . . 2 . 1 . . . . . . 1 . . 2 . . 3 . 1 1 1 . . . . . . . . 1 [89,] 1 . . . . 2 . . . . . 1 . . 1 . . 3 . . 1 1 . . . . . . . . 2 [90,] . . . 1 . . . . . 1 . 1 1 . . . . 1 . . . . . . . . 1 . . 2 . [91,] . . . 1 2 4 1 . . . . 1 . . . . . . 1 . . . . . . . . . . . . [92,] 2 . . 1 1 . . . . . . 1 . . . . . . . . . 1 . . . . . . . . 2
rcovarsdf
Date | Rem | President | |
---|---|---|---|
<int> | <dbl> | <chr> | |
1 | 1927 | 29.47 | Calvin Coolidge |
2 | 1928 | 35.39 | Calvin Coolidge |
3 | 1929 | -19.54 | Herbert Hoover |
4 | 1930 | -31.23 | Herbert Hoover |
5 | 1931 | -45.11 | Herbert Hoover |
6 | 1932 | -9.39 | Herbert Hoover |
7 | 1934 | 3.02 | Franklin D. Roosevelt |
8 | 1935 | 44.96 | Franklin D. Roosevelt |
9 | 1936 | 32.07 | Franklin D. Roosevelt |
10 | 1937 | -34.96 | Franklin D. Roosevelt |
11 | 1938 | 28.48 | Franklin D. Roosevelt |
12 | 1939 | 2.70 | Franklin D. Roosevelt |
13 | 1940 | -7.14 | Franklin D. Roosevelt |
14 | 1941 | -10.53 | Franklin D. Roosevelt |
15 | 1942 | 16.20 | Franklin D. Roosevelt |
16 | 1943 | 27.96 | Franklin D. Roosevelt |
17 | 1944 | 20.97 | Franklin D. Roosevelt |
18 | 1945 | 38.38 | Franklin D. Roosevelt |
19 | 1946 | -6.73 | Harry S. Truman |
20 | 1947 | 2.95 | Harry S. Truman |
21 | 1948 | 1.07 | Harry S. Truman |
22 | 1949 | 19.12 | Harry S. Truman |
23 | 1950 | 28.82 | Harry S. Truman |
24 | 1951 | 19.22 | Harry S. Truman |
25 | 1952 | 11.80 | Harry S. Truman |
26 | 1953 | -1.05 | Dwight D. Eisenhower |
27 | 1954 | 49.35 | Dwight D. Eisenhower |
28 | 1955 | 23.75 | Dwight D. Eisenhower |
29 | 1956 | 5.90 | Dwight D. Eisenhower |
30 | 1957 | -13.16 | Dwight D. Eisenhower |
⋮ | ⋮ | ⋮ | ⋮ |
63 | 1990 | -13.95 | George H.W. Bush |
64 | 1991 | 29.18 | George H.W. Bush |
65 | 1992 | 6.23 | George H.W. Bush |
66 | 1993 | 8.21 | William J. Clinton |
67 | 1994 | -4.10 | William J. Clinton |
68 | 1995 | 31.22 | William J. Clinton |
69 | 1996 | 15.96 | William J. Clinton |
70 | 1997 | 25.96 | William J. Clinton |
71 | 1998 | 19.46 | William J. Clinton |
72 | 1999 | 20.57 | William J. Clinton |
73 | 2000 | -17.60 | William J. Clinton |
74 | 2001 | -15.20 | George W. Bush |
75 | 2002 | -22.76 | George W. Bush |
76 | 2003 | 30.75 | George W. Bush |
77 | 2004 | 10.72 | George W. Bush |
78 | 2005 | 3.09 | George W. Bush |
79 | 2006 | 10.60 | George W. Bush |
80 | 2007 | 1.04 | George W. Bush |
81 | 2008 | -38.34 | George W. Bush |
82 | 2009 | 28.26 | Barack Obama |
83 | 2010 | 17.37 | Barack Obama |
84 | 2011 | 0.44 | Barack Obama |
85 | 2012 | 16.27 | Barack Obama |
86 | 2013 | 35.20 | Barack Obama |
87 | 2014 | 11.71 | Barack Obama |
88 | 2015 | 0.08 | Barack Obama |
89 | 2016 | 13.30 | Barack Obama |
90 | 2017 | 21.51 | Donald J. Trump |
91 | 2018 | -6.93 | Donald J. Trump |
92 | 2019 | 28.28 | Donald J. Trump |
jl$command("using Distributed")
jl$command("addprocs(4)")
julia_library("HurdleDMR")
jl$command("@everywhere using HurdleDMR")
First we need to convert the R sparseMatrix to julia. We do this in pieces because if we materialize the entire dense matrix representation it may require more memory than we have.
A <- as(rcounts, "TsparseMatrix")
jl$assign("i", A@i + 1)
jl$assign("j", A@j + 1)
jl$assign("v", A@x)
jl$assign("m", dim(A)[1])
jl$assign("n", dim(A)[2])
jl$command("jcounts = sparse(i, j, v, m, n);")
# Note: jcounts is now a julia object accessible to julia not R
# # uncomment the following line to make sure the matrices are the same (DO NOT TRY WITH BIG DATA)
# all(jl$eval("jcounts") == rcounts)
The Distributed Multinomial Regression (DMR) model of Taddy (2015) is a highly scalable
approximation to the Multinomial using distributed (independent, parallel)
Poisson regressions, one for each of the d categories (columns) of a large counts
matrix,
on the covarsdf
.
To fit a DMR:
jl$assign("jcovars", as.matrix(rcovarsdf[['Rem']]))
jl$command("m = dmr(jcovars, jcounts)")
or with a dataframe and formula, by first converting the pandas dataframe to julia
jl$assign("jcovarsdf", rcovarsdf) # assign to julia dataframe
jl$command("mf = @model(c ~ Rem)") # model formula
jl$command("m = fit(DMR, mf, jcovarsdf, jcounts)")
We can get the coefficients matrix for each variable + intercept as usual with
jl$eval("coef(m)")
-5.43397777 | -5.16903423 | -5.483462 | -5.87732380 | -5.873792642 | -5.771144 | -3.235432812 | -5.38168 | -4.410759806 | -5.678937911 | ⋯ | -5.232148 | -5.829416147 | -5.289306 | -5.76087053 | -5.414535e+00 | -4.72731232 | -5.64625805 | -4.924965597 | -5.378998270 | -4.430372689 |
-0.03460506 | -0.01747071 | 0.000000 | 0.01188229 | 0.006711126 | 0.000000 | 0.007545783 | 0.00000 | 0.009774115 | -0.008737706 | ⋯ | 0.000000 | 0.007185718 | 0.000000 | -0.02318809 | 9.579289e-06 | -0.01967833 | 0.00122726 | 0.007426632 | 0.007352226 | 0.004405577 |
By default we only return the AICc maximizing coefficients. To also get back the entire regulatrization paths, run
jl$command("paths = dmrpaths(jcovars, jcounts)")
We can now select, for example the coefficients that minimize 10-fold CV mse (takes a little longer)
jl$command("using Lasso: MinCVmse;")
jl$command("segselect = MinCVKfold{MinCVmse}(10);")
jl$eval("coef(paths, segselect)")
-5.448371e+00 | -5.232148 | -5.43167163 | -5.771144e+00 | -5.819935e+00 | -5.771144 | -3.173760e+00 | -5.38168 | -4.327030e+00 | -5.724624e+00 | ⋯ | -5.232148 | -5.771144e+00 | -5.289306 | -5.76087053 | -5.414469e+00 | -4.72731232 | -5.637613e+00 | -4.924965597 | -5.319159e+00 | -4.396826e+00 |
-5.117028e-14 | 0.000000 | -0.01060117 | 1.036714e-09 | 2.086696e-08 | 0.000000 | 1.182784e-14 | 0.00000 | 2.361194e-09 | -9.887320e-13 | ⋯ | 0.000000 | 8.493204e-12 | 0.000000 | -0.02318809 | 6.425219e-09 | -0.01967833 | 2.782913e-09 | 0.007426632 | 7.622884e-10 | 7.830152e-10 |
For highly sparse counts, as is often the case with text that is selected for
various reasons, the Hurdle Distributed Multinomial Regression (HDMR) model of
Kelly, Manela, and Moreira (2021), may be superior to the DMR. It approximates
a higher dispersion Multinomial using distributed (independent, parallel)
Hurdle regressions, one for each of the d categories (columns) of a large counts
matrix,
on the covars
. It allows a potentially different sets of covariates to explain
category inclusion ($h=1{c>0}$), and repetition ($c>0$) using the optional inpos
and inzero
keyword arguments.
Both the model for zeroes and for positive counts are regularized by default,
using GammaLassoPath
, picking the AICc optimal segment of the regularization
path.
HDMR can be fitted:
jl$assign("jcovars", as.matrix(rcovarsdf[['Rem']]))
jl$command("m = hdmr(jcovars, jcounts)")
We can get the coefficients matrix for each variable + intercept as usual though now there is a set of coefficients for the model for repetitions and for inclusions
cm <- jl$eval("coef(m)")
coefspos <- cm[1] # repetition
coefszero <- cm[2] # inclusion
coefspos
-4.10095408 | -2.46311402 | -5.69913212 | -5.811141 | -4.562263 | -5.653145346 | -2.8389103 | -4.7322153 | -3.87792475 | -4.441343 | ⋯ | -4.917323 | -3.01996764 | -3.81827965 | -5.19695206 | -4.20262645 | -3.974637 | -5.28172697 | -4.68035784 | -4.97128452 | -3.99263610 |
-0.02713336 | -0.03288065 | -0.05020055 | 0.000000 | 0.000000 | -0.006017206 | 0.0133696 | 0.0326247 | 0.02040813 | 0.000000 | ⋯ | 0.000000 | -0.03340693 | 0.01541684 | -0.03889998 | 0.01138997 | 0.000000 | 0.01084449 | 0.02035161 | 0.01634997 | 0.02509239 |
coefszero
-0.5918418 | -0.931126067 | 0.033016312 | -0.37745848 | -0.478606926 | -0.06758676 | 3.204239 | 0.20563006 | 0.96301244 | -0.5918418 | ⋯ | 0.331805533 | -1.12500898 | -0.501823 | -0.5918418 | -0.243609690 | 0.72372502 | -0.297698794 | 0.707424066 | 0.154299606 | 1.194453996 |
0.0000000 | 0.003297792 | -0.001667455 | 0.01815652 | 0.006536081 | -0.01706256 | 0.000000 | -0.01729066 | 0.00736779 | 0.0000000 | ⋯ | -0.008679934 | 0.01034119 | 0.000000 | 0.0000000 | -0.001827842 | -0.02699193 | 0.004191436 | 0.008971672 | 0.005415282 | -0.003363608 |
By default we only return the AICc maximizing coefficients. To get the coefficients that minimize say the BIC criterion, run
jl$command("paths = hdmrpaths(jcovars, jcounts)")
cm <- jl$eval("coef(paths, MinBIC())")
coefspos <- cm[1] # repetition
coefszero <- cm[2] # inclusion
coefspos
-4.10095408 | -2.46311402 | -5.69913212 | -5.811141 | -4.562263 | -5.653145346 | -2.8389103 | -4.7322153 | -3.87792475 | -4.441343 | ⋯ | -4.917323 | -3.01996764 | -3.81827965 | -5.19695206 | -4.20262645 | -3.974637 | -5.28172697 | -4.68035784 | -4.97128452 | -3.99263610 |
-0.02713336 | -0.03288065 | -0.05020055 | 0.000000 | 0.000000 | -0.006017206 | 0.0133696 | 0.0326247 | 0.02040813 | 0.000000 | ⋯ | 0.000000 | -0.03340693 | 0.01541684 | -0.03889998 | 0.01138997 | 0.000000 | 0.01084449 | 0.02035161 | 0.01634997 | 0.02509239 |
coefszero
-0.5918418 | -0.931126067 | 0.033016312 | -0.37745848 | -0.478606926 | -0.06758676 | 3.204239 | 0.20563006 | 0.96301244 | -0.5918418 | ⋯ | 0.331805533 | -1.12500898 | -0.501823 | -0.5918418 | -0.243609690 | 0.72372502 | -0.297698794 | 0.707424066 | 0.154299606 | 1.194453996 |
0.0000000 | 0.003297792 | -0.001667455 | 0.01815652 | 0.006536081 | -0.01706256 | 0.000000 | -0.01729066 | 0.00736779 | 0.0000000 | ⋯ | -0.008679934 | 0.01034119 | 0.000000 | 0.0000000 | -0.001827842 | -0.02699193 | 0.004191436 | 0.008971672 | 0.005415282 | -0.003363608 |
A sufficient reduction projection summarizes the counts, much like a sufficient
statistic, and is useful for reducing the d dimensional counts in a potentially
much lower dimension matrix z
.
To get a sufficient reduction projection in direction of Rem
for the above
example
jl$eval("srproj(m,jcounts,1,1)")
0.028175143 | -0.0001159315 | 30 | 22 |
0.016418996 | -0.0008058789 | 28 | 33 |
-0.001015670 | -0.0059385017 | 44 | 34 |
-0.002358679 | -0.0115558569 | 10 | 17 |
-0.047935776 | -0.0097930356 | 17 | 22 |
-0.023847399 | -0.0040984682 | 13 | 20 |
0.018328712 | 0.0008254937 | 5 | 14 |
0.011159980 | 0.0022287515 | 6 | 14 |
0.015826070 | 0.0016236662 | 8 | 19 |
0.012626627 | -0.0069825601 | 4 | 17 |
0.029240021 | 0.0018497984 | 21 | 19 |
0.010661262 | 0.0001764243 | 14 | 21 |
0.010915089 | -0.0024769141 | 15 | 25 |
0.013369599 | -0.0031232606 | 1 | 17 |
0.018721772 | 0.0032890459 | 14 | 13 |
0.018202062 | 0.0015602281 | 17 | 13 |
0.043963981 | 0.0034730108 | 18 | 24 |
0.024591449 | 0.0031551677 | 26 | 32 |
-0.060960485 | 0.0012849889 | 467 | 83 |
0.008602795 | 0.0023754687 | 54 | 47 |
0.008782844 | 0.0004553420 | 40 | 51 |
0.007795954 | 0.0020575147 | 24 | 36 |
0.012140871 | 0.0031816988 | 30 | 50 |
0.012850854 | 0.0057735008 | 37 | 25 |
0.010568510 | 0.0003276491 | 32 | 41 |
0.006026514 | 0.0012054207 | 34 | 46 |
0.013311252 | 0.0047344318 | 45 | 47 |
0.011280431 | 0.0025087390 | 61 | 57 |
0.010743699 | 0.0023009237 | 54 | 51 |
0.006289642 | 0.0014774549 | 26 | 40 |
⋮ | ⋮ | ⋮ | ⋮ |
0.0135140685 | 0.0019994300 | 15 | 22 |
0.0085551916 | 0.0046663049 | 15 | 34 |
0.0102688777 | 0.0013368689 | 12 | 27 |
0.0102517243 | 0.0021114087 | 59 | 56 |
0.0019550838 | 0.0014165380 | 82 | 51 |
0.0219413600 | 0.0049928442 | 64 | 55 |
0.0110403022 | 0.0014620922 | 44 | 51 |
0.0181575257 | 0.0044670146 | 41 | 50 |
0.0181104138 | 0.0012899225 | 58 | 50 |
0.0122410893 | 0.0064235663 | 73 | 49 |
-0.0076051917 | -0.0008017496 | 65 | 48 |
0.0077726939 | -0.0056456992 | 8 | 17 |
-0.0022009776 | -0.0025361075 | 18 | 32 |
0.0661417043 | 0.0035892465 | 59 | 43 |
0.0068813566 | 0.0025056753 | 38 | 44 |
0.0008039077 | 0.0046059752 | 33 | 30 |
0.0010300373 | 0.0026443469 | 25 | 48 |
0.0033736123 | 0.0018389497 | 37 | 28 |
-0.0145189670 | -0.0030228707 | 27 | 35 |
0.0102762951 | 0.0041270793 | 34 | 38 |
0.0084724868 | 0.0018046980 | 61 | 39 |
0.0042099290 | 0.0007256417 | 31 | 42 |
0.0131395362 | 0.0034877352 | 36 | 47 |
0.0086154073 | 0.0045672347 | 50 | 47 |
0.0109674929 | 0.0025615845 | 39 | 48 |
0.0078692064 | 0.0022333633 | 32 | 43 |
0.0065210215 | 0.0044729721 | 23 | 43 |
0.0070370863 | 0.0009275432 | 21 | 36 |
0.0186969325 | 0.0033253048 | 12 | 27 |
0.0094056181 | 0.0032048917 | 11 | 32 |
Here, the first column is the SR projection from the model for positive counts, the second is the the SR projection from the model for hurdle crossing (zeros), and the third is the total count for each observation.
Counts inverse regression allows us to predict a covariate with the counts and other covariates. Here we use hdmr for the backward regression and another model for the forward regression. This can be accomplished with a single command, by fitting a CIR{HDMR,FM} where the forward model is FM <: RegressionModel.
jl$command("using GLM: LinearModel") # loading up the GLM model for the forward regression
jl$command("spec = CIR{HDMR,LinearModel}") # model class specification
jl$command("mf = @model(h ~ President + Rem, c ~ President + Rem)") # model formula
jl$eval("cir = fit(spec, mf, jcovarsdf, jcounts, :Rem, nocounts=true)")
Julia Object of type TableCountsRegressionModel{CIR{HDMR,LinearModel},DataFrame,SparseMatrixCSC{Float64,Int64}}. TableCountsRegressionModel{CIR{HDMR,LinearModel},DataFrame,SparseMatrixCSC{Float64,Int64}} 2-part model: [h ~ President + Rem, c ~ President + Rem] Forward model coefficients for predicting Rem: ───────────────────────────────────────────────────────────────────────────────────────────────────────── Coef. Std. Error t Pr(>|t|) Lower 95% Upper 95% ───────────────────────────────────────────────────────────────────────────────────────────────────────── (Intercept) 17.4837 11.3688 1.54 0.1285 -5.17963 40.147 President: Calvin Coolidge 13.0088 13.4688 0.97 0.3374 -13.8407 39.8584 President: Donald J. Trump -2.14014 11.22 -0.19 0.8493 -24.5069 20.2266 President: Dwight D. Eisenhower -10.4126 8.31052 -1.25 0.2143 -26.9793 6.15409 President: Franklin D. Roosevelt -6.29263 9.24355 -0.68 0.4982 -24.7193 12.134 President: George H.W. Bush -22.2441 11.175 -1.99 0.0503 -44.5211 0.0329016 President: George W. Bush -20.2675 8.51922 -2.38 0.0200 -37.2502 -3.28473 President: Gerald R. Ford -5.36949 11.0539 -0.49 0.6286 -27.4051 16.6662 President: Harry S. Truman -9.36385 8.82709 -1.06 0.2923 -26.9603 8.23263 President: Herbert Hoover -36.1278 10.9276 -3.31 0.0015 -57.9116 -14.3439 President: Jimmy Carter -14.2189 10.3702 -1.37 0.1746 -34.8916 6.45379 President: John F. Kennedy -18.4067 11.4176 -1.61 0.1113 -41.1672 4.35383 President: Lyndon B. Johnson -18.0297 9.02763 -2.00 0.0496 -36.026 -0.0335 President: Richard Nixon -33.7795 9.89593 -3.41 0.0011 -53.5067 -14.0523 President: Ronald Reagan -16.7344 8.7381 -1.92 0.0595 -34.1535 0.684648 President: William J. Clinton -3.09842 8.2069 -0.38 0.7069 -19.4586 13.2617 zpos 477.131 327.085 1.46 0.1490 -174.901 1129.16 zzero 9002.65 2147.99 4.19 <1e-4 4720.72 13284.6 m -0.0506128 0.0478887 -1.06 0.2941 -0.146077 0.0448514 ℓ 0.0367347 0.257807 0.14 0.8871 -0.477194 0.550663 ─────────────────────────────────────────────────────────────────────────────────────────────────────────
where the nocounts=True
means we also fit a benchmark model without counts.
The last few coefficients are due to text data.
zpos
is the SR projection summarizing the information in repeated use of terms.
zzero
is the SR projection summarizing the information in term inclusion.
m
is the total number of excess counts.
ℓ
is the total number of nonzero counts.
We can get the forward and backward model coefficients with
jl$eval("coeffwd(cir)")
jl$eval("coefbwd(cir)")
[[1]] [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] -7.505779 -3.282723 -5.62136487 -5.652125 -4.648856 0 -2.339185684 [2,] 0.000000 0.000000 0.00000000 0.000000 0.000000 0 -1.392722095 [3,] 0.000000 0.000000 0.00000000 0.000000 0.000000 0 0.000000000 [4,] 0.000000 0.000000 0.00000000 0.000000 0.000000 0 -1.161731770 [5,] 4.133066 0.000000 0.00000000 0.000000 0.000000 0 0.000000000 [6,] 0.000000 0.000000 0.00000000 0.000000 0.000000 0 0.384143438 [7,] 0.000000 1.548887 1.86918130 0.000000 0.000000 0 -0.155145281 [8,] 0.000000 0.000000 0.00000000 0.000000 1.152582 0 0.319885626 [9,] 0.000000 0.000000 -1.98595262 0.000000 0.000000 0 -2.622315710 [10,] 0.000000 0.000000 0.00000000 0.000000 0.000000 0 -0.728698645 [11,] 4.261420 0.000000 0.00000000 0.000000 0.000000 0 -1.092640287 [12,] 0.000000 0.000000 0.00000000 0.000000 0.000000 0 -1.687828035 [13,] 0.000000 0.000000 0.00000000 0.000000 0.000000 0 0.210020981 [14,] 0.000000 0.000000 1.73365836 0.000000 0.000000 0 0.000000000 [15,] 0.000000 0.000000 0.00000000 0.000000 0.000000 0 0.108919475 [16,] 0.000000 0.000000 0.00000000 -1.089354 0.000000 0 0.060834783 [17,] 0.000000 0.000000 -0.02408756 0.000000 0.000000 0 0.001485679 [,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16] [1,] -4.803314 0 -3.8617954 -4.219357 0 0 0 -4.9505610 0 [2,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [3,] 1.807744 0 0.0000000 0.000000 0 0 0 0.0000000 0 [4,] 0.000000 0 0.0000000 0.509528 0 0 0 1.2634779 0 [5,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [6,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [7,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [8,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [9,] 0.000000 0 -0.9218806 0.000000 0 0 0 -0.4537237 0 [10,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [11,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [12,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [13,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [14,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [15,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [16,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [17,] 0.000000 0 0.0000000 0.000000 0 0 0 0.0000000 0 [,17] [,18] [,19] [,20] [,21] [,22] [,23] [1,] -4.253677 0 -4.0167735 -4.602895 -1.59466607 -3.472972 0 [2,] 0.000000 0 0.0000000 1.685378 0.00000000 0.000000 0 [3,] 0.000000 0 0.0000000 0.000000 0.00000000 0.000000 0 [4,] 0.000000 0 0.7619655 0.000000 0.00000000 0.000000 0 [5,] 0.000000 0 0.0000000 0.000000 0.00000000 0.000000 0 [6,] 0.000000 0 0.0000000 0.000000 0.00000000 0.000000 0 [7,] 0.000000 0 0.0000000 0.000000 -3.48095656 -2.137882 0 [8,] 0.000000 0 0.0000000 0.000000 0.00000000 0.000000 0 [9,] 0.000000 0 0.0000000 -1.732907 0.00000000 0.000000 0 [10,] 0.000000 0 0.0000000 1.455482 0.00000000 0.000000 0 [11,] 0.000000 0 0.0000000 0.000000 0.00000000 0.000000 0 [12,] 0.000000 0 0.0000000 0.000000 0.00000000 0.000000 0 [13,] 0.000000 0 0.0000000 0.000000 0.00000000 0.000000 0 [14,] 0.000000 0 0.0000000 0.000000 0.00000000 0.000000 0 [15,] 0.000000 0 0.0000000 0.000000 0.00000000 0.000000 0 [16,] 0.000000 0 0.0000000 0.000000 -4.83384879 -2.791211 0 [17,] 0.000000 0 0.0000000 0.000000 -0.04507891 0.000000 0 [,24] [,25] [,26] [,27] [,28] [,29] [,30] [,31] [1,] -4.0528218 -4.385440 0 0 0 0 -5.224671 -3.134215 [2,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [3,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [4,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [5,] 0.8633202 0.000000 0 0 0 0 0.000000 0.000000 [6,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [7,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [8,] 0.0000000 1.679027 0 0 0 0 0.000000 0.000000 [9,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [10,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [11,] 0.0000000 -1.804907 0 0 0 0 0.000000 0.000000 [12,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [13,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [14,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [15,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [16,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [17,] 0.0000000 0.000000 0 0 0 0 0.000000 0.000000 [,32] [,33] [,34] [,35] [,36] [,37] [1,] -3.7346761 -4.6822966 -3.147161 -6.070552 -2.605535e+00 -5.002686 [2,] 0.0000000 0.0000000 0.000000 0.000000 0.000000e+00 0.000000 [3,] 0.0000000 0.0000000 0.000000 0.000000 0.000000e+00 0.000000 [4,] -0.6375095 0.0000000 0.000000 2.360939 0.000000e+00 1.483285 [5,] 0.0000000 0.0000000 0.000000 0.000000 0.000000e+00 0.000000 [6,] 0.0000000 0.0000000 0.000000 0.000000 0.000000e+00 0.000000 [7,] 0.0000000 0.0000000 0.000000 0.000000 0.000000e+00 0.000000 [8,] 0.0000000 0.0000000 0.000000 0.000000 0.000000e+00 0.000000 [9,] 0.0000000 0.0000000 0.000000 0.000000 1.265823e-09 -1.718555 [10,] 0.0000000 0.0000000 0.000000 3.421690 0.000000e+00 0.000000 [11,] 0.0000000 0.6855419 0.000000 0.000000 0.000000e+00 1.667727 [12,] 0.0000000 0.0000000 0.000000 0.000000 0.000000e+00 0.000000 [13,] 0.0000000 0.0000000 0.000000 0.000000 0.000000e+00 0.000000 [14,] 0.0000000 0.0000000 0.000000 0.000000 0.000000e+00 0.000000 [15,] 0.0000000 0.0000000 0.000000 0.000000 0.000000e+00 0.000000 [16,] 0.0000000 0.0000000 -1.746490 0.000000 0.000000e+00 0.000000 [17,] 0.0000000 0.0000000 0.000000 0.000000 0.000000e+00 0.000000 [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [1,] -4.11040157 -5.690131 -4.3619723 0 -4.665016 0 0 -4.442229 [2,] 0.00000000 0.000000 0.0000000 0 0.000000 0 0 0.000000 [3,] 0.00000000 0.000000 0.0000000 0 0.000000 0 0 0.000000 [4,] 1.08228703 0.000000 -0.3205167 0 0.000000 0 0 0.000000 [5,] 0.00000000 0.000000 0.0000000 0 0.000000 0 0 0.000000 [6,] 2.47876098 0.000000 0.0000000 0 0.000000 0 0 0.000000 [7,] 0.00000000 0.000000 0.0000000 0 0.000000 0 0 0.000000 [8,] -0.79409280 0.000000 0.0000000 0 0.000000 0 0 0.000000 [9,] 0.00000000 0.000000 0.0000000 0 -1.132761 0 0 0.000000 [10,] 0.00000000 0.000000 0.0000000 0 0.000000 0 0 0.000000 [11,] -0.19047745 0.000000 0.0000000 0 0.000000 0 0 -2.149369 [12,] 1.64538275 0.000000 0.0000000 0 0.000000 0 0 0.000000 [13,] 0.00000000 0.000000 0.0000000 0 0.000000 0 0 0.000000 [14,] 0.00000000 0.000000 0.0000000 0 0.000000 0 0 0.000000 [15,] 1.52733690 2.173267 0.0000000 0 0.000000 0 0 0.000000 [16,] -0.07096524 0.000000 0.0000000 0 0.000000 0 0 0.000000 [17,] 0.00000000 0.000000 0.0000000 0 0.000000 0 0 0.000000 [,46] [,47] [,48] [,49] [,50] [,51] [,52] [,53] [1,] -3.97781901 -6.64333684 0 -4.0030239 0 -4.879824 -4.4899802 0 [2,] 2.37910193 0.00000000 0 0.0000000 0 2.535290 0.0000000 0 [3,] 0.00000000 0.00000000 0 0.0000000 0 0.000000 0.0000000 0 [4,] 1.58792655 0.00000000 0 0.0000000 0 0.000000 0.0000000 0 [5,] 1.04737338 0.00000000 0 0.0000000 0 0.000000 0.0000000 0 [6,] 0.80042083 0.00000000 0 0.0000000 0 0.000000 0.0000000 0 [7,] 0.00000000 0.00000000 0 0.0000000 0 0.000000 0.0000000 0 [8,] 1.19519243 0.00000000 0 0.0000000 0 0.000000 0.0000000 0 [9,] 0.86053644 0.00000000 0 0.0000000 0 0.000000 0.0000000 0 [10,] 2.63596516 2.41284694 0 0.0000000 0 0.000000 0.0000000 0 [11,] 1.44460160 0.00000000 0 0.0000000 0 -1.557078 -0.1887058 0 [12,] 0.00000000 0.00000000 0 0.0000000 0 0.000000 0.0000000 0 [13,] 0.64131038 0.00000000 0 0.0000000 0 0.000000 0.0000000 0 [14,] 2.06083503 0.00000000 0 0.0000000 0 0.000000 0.0000000 0 [15,] 1.86184359 0.00000000 0 0.0000000 0 0.000000 0.0000000 0 [16,] 0.00000000 0.00000000 0 0.2304902 0 0.000000 0.0000000 0 [17,] 0.01122679 -0.06744592 0 0.0000000 0 0.000000 0.0000000 0 [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [1,] -4.757180 0 0 0 -4.335847 -4.739275 -3.5551345 0 [2,] 0.000000 0 0 0 0.000000 0.000000 0.0000000 0 [3,] 0.000000 0 0 0 0.000000 0.000000 0.0000000 0 [4,] 0.000000 0 0 0 0.000000 0.000000 0.0000000 0 [5,] 0.000000 0 0 0 0.000000 0.000000 0.0000000 0 [6,] 0.000000 0 0 0 0.000000 0.000000 0.4309116 0 [7,] 0.000000 0 0 0 0.000000 0.000000 -1.0345630 0 [8,] 0.000000 0 0 0 0.000000 0.000000 0.0000000 0 [9,] 0.000000 0 0 0 0.000000 0.000000 0.0000000 0 [10,] 0.000000 0 0 0 0.000000 0.000000 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[,151] [,152] [,153] [,154] [,155] [,156] [,157] [,158] [1,] 0 0 0.3001665 -0.3158611 0.2223889 0 0 0 0 [2,] 0 0 0.0000000 0.0000000 0.0000000 0 0 0 0 [3,] 0 0 0.0000000 0.0000000 0.0000000 0 0 0 0 [4,] 0 0 0.0000000 -0.7198381 0.0000000 0 0 0 0 [5,] 0 0 0.0000000 0.0000000 0.0000000 0 0 0 0 [6,] 0 0 0.0000000 0.0000000 0.0000000 0 0 0 0 [7,] 0 0 0.0000000 0.0000000 0.0000000 0 0 0 0 [8,] 0 0 0.4738358 0.0000000 0.0000000 0 0 0 0 [9,] 0 0 0.0000000 -0.7786509 0.4402478 0 0 0 0 [10,] 0 0 0.0000000 0.0000000 0.0000000 0 0 0 0 [11,] 0 0 0.0000000 0.0000000 0.0000000 0 0 0 0 [12,] 0 0 0.0000000 0.0000000 0.0000000 0 0 0 0 [13,] 0 0 0.0000000 1.0937860 0.0000000 0 0 0 0 [14,] 0 0 0.0000000 0.0000000 0.0000000 0 0 0 0 [15,] 0 0 0.0000000 0.0000000 0.0000000 0 0 0 0 [16,] 0 0 0.0000000 2.2377061 0.0000000 0 0 0 0 [17,] 0 0 0.0000000 0.0000000 0.0000000 0 0 0 0 [,159] [,160] [,161] [,162] [,163] [1,] 0.3098994 -0.2710405 0 0 1.1827939 [2,] 1.0325666 0.0000000 0 0 0.9190527 [3,] 0.0000000 0.0000000 0 0 0.0000000 [4,] 0.0000000 0.0000000 0 0 0.0000000 [5,] -0.7204098 0.0000000 0 0 0.9620101 [6,] 0.0000000 0.0000000 0 0 0.0000000 [7,] 0.0000000 0.1346900 0 0 -0.6620037 [8,] 0.9185864 0.0000000 0 0 0.0000000 [9,] -1.6442036 0.0000000 0 0 0.0000000 [10,] 3.0932194 0.0000000 0 0 0.0000000 [11,] 0.0000000 0.0000000 0 0 0.0000000 [12,] -0.7029568 0.0000000 0 0 0.0000000 [13,] 0.6795241 0.0000000 0 0 0.0000000 [14,] 0.0000000 0.0000000 0 0 0.0000000 [15,] -0.1047310 0.0000000 0 0 -0.5793430 [16,] 3.0264889 0.0000000 0 0 -0.6656456 [17,] -0.0151613 0.0000000 0 0 0.0000000 attr(,"class") [1] "JuliaTuple"
The fitted model can be used to predict vy with new data
jl$assign("jcovarsnewdata", rcovarsdf[1:10,]) # assign new covariates data to julia dataframe
# convert sparse counts matrix for new data
A <- as(rcounts[1:10,], "TsparseMatrix")
jl$assign("i", A@i + 1)
jl$assign("j", A@j + 1)
jl$assign("v", A@x)
jl$assign("m", dim(A)[1])
jl$assign("n", dim(A)[2])
jl$command("jcountsnewdata = sparse(i, j, v, m, n);")
jl$eval("HurdleDMR.predict(cir, jcovarsnewdata, jcountsnewdata)")
We can also predict only with the other covariates, which in this case is just a linear regression
jl$eval("HurdleDMR.predict(cir, jcovarsnewdata, jcountsnewdata; nocounts=true)")
Kelly, Manela, and Moreira (2021) show that the differences between DMR and HDMR can be substantial in some cases, especially when the counts data is highly sparse.
Please reference the paper for additional details and example applications.