assoc.twocat.by.RdCross-tabulation and measures of association between two categorical variables, for each category of a group variable
assoc.twocat.by(x, y, by, weights = NULL, na.rm = FALSE, na.value = "NA",
nperm = NULL, distrib = "asympt")factor : the first categorical variable
factor : the second categorical variable
factor : the group variable
numeric vector of weights. If NULL (default), uniform weights (i.e. all equal to 1) are used.
logical, indicating whether NA values should be silently removed before the computation proceeds. If FALSE (default), an additional level is added to the variables (see na.value argument).
character. Name of the level for NA category. Default is "NA". Only used if na.rm = FALSE.
numeric. Number of permutations for the permutation test of independence. If NULL (default), no permutation test is performed.
the null distribution of permutation test of independence can be approximated by its asymptotic distribution (asympt, default) or via Monte Carlo resampling (approx).
A list of items, one for each category of the group variable. Each item is a list of lists with the following elements :
tables list :
cross-tabulation frequencies
percentages
row percentages
column percentages
expected values
global list :
chi-squared value
Cramer's V between the two variables
p-value from a permutation (i.e. non-parametric) test of independence
global PEM
Goodman and Kruskal tau (forward association, i.e. x is the predictor and y is the response)
Goodman and Kruskal tau (backward association, i.e. y is the predictor and x is the respons)
local list :
the table of standardized (i.e.Pearson) residuals.
the table of adjusted standardized residuals.
the table of p-values of adjusted standardized residuals.
the table of odds ratios.
the table of local PEM
the table of the phi coefficients for each pair of levels
the table of permutation p-values for each pair of levels
gather : a data frame gathering informations, with one row per cell of the cross-tabulation.
The adjusted standardized residuals are strictly equivalent to test-values for nominal variables as proposed by Lebart et al (1984).
Agresti, A. (2007). An Introduction to Categorical Data Analysis, 2nd ed. New York: John Wiley & Sons.
Rakotomalala R., Comprendre la taille d'effet (effect size), http://eric.univ-lyon2.fr/~ricco/cours/slides/effect_size.pdf
Lebart L., Morineau A. and Warwick K., 1984, *Multivariate Descriptive Statistical Analysis*, John Wiley and sons, New-York.
data(Movies)
assoc.twocat.by(Movies$Country, Movies$ArtHouse, Movies$Festival, nperm=100)
#> $tables
#> $tables$freq
#> $tables$freq$No
#> No Yes Sum
#> Europe 38 27 65
#> France 212 344 556
#> Other 6 18 24
#> USA 249 29 278
#> Sum 505 418 923
#>
#> $tables$freq$Yes
#> No Yes Sum
#> Europe 1 6 7
#> France 0 49 49
#> Other 0 2 2
#> USA 8 11 19
#> Sum 9 68 77
#>
#>
#> $tables$prop
#> $tables$prop$No
#> No Yes Sum
#> Europe 4.1170098 2.9252438 7.0422535
#> France 22.9685807 37.2697725 60.2383532
#> Other 0.6500542 1.9501625 2.6002167
#> USA 26.9772481 3.1419285 30.1191766
#> Sum 54.7128927 45.2871073 100.0000000
#>
#> $tables$prop$Yes
#> No Yes Sum
#> Europe 1.298701 7.792208 9.090909
#> France 0.000000 63.636364 63.636364
#> Other 0.000000 2.597403 2.597403
#> USA 10.389610 14.285714 24.675325
#> Sum 11.688312 88.311688 100.000000
#>
#>
#> $tables$rprop
#> $tables$rprop$No
#> No Yes Sum
#> Europe 58.46154 41.53846 100
#> France 38.12950 61.87050 100
#> Other 25.00000 75.00000 100
#> USA 89.56835 10.43165 100
#> Sum 54.71289 45.28711 100
#>
#> $tables$rprop$Yes
#> No Yes Sum
#> Europe 14.28571 85.71429 100
#> France 0.00000 100.00000 100
#> Other 0.00000 100.00000 100
#> USA 42.10526 57.89474 100
#> Sum 11.68831 88.31169 100
#>
#>
#> $tables$cprop
#> $tables$cprop$No
#> No Yes Sum
#> Europe 7.524752 6.459330 7.042254
#> France 41.980198 82.296651 60.238353
#> Other 1.188119 4.306220 2.600217
#> USA 49.306931 6.937799 30.119177
#> Sum 100.000000 100.000000 100.000000
#>
#> $tables$cprop$Yes
#> No Yes Sum
#> Europe 11.11111 8.823529 9.090909
#> France 0.00000 72.058824 63.636364
#> Other 0.00000 2.941176 2.597403
#> USA 88.88889 16.176471 24.675325
#> Sum 100.00000 100.000000 100.000000
#>
#>
#> $tables$expected
#> $tables$expected$No
#> No Yes
#> Europe 35.56338 29.43662
#> France 304.20368 251.79632
#> Other 13.13109 10.86891
#> USA 152.10184 125.89816
#>
#> $tables$expected$Yes
#> No Yes
#> Europe 0.8181818 6.1818182
#> France 5.7272727 43.2727273
#> Other 0.2337662 1.7662338
#> USA 2.2207792 16.7792208
#>
#>
#>
#> $global
#> $global$chi.squared
#> $global$chi.squared$No
#> [1] 206.9385
#>
#> $global$chi.squared$Yes
#> [1] 23.82577
#>
#>
#> $global$cramer.v
#> $global$cramer.v$No
#> [1] 0.4734998
#>
#> $global$cramer.v$Yes
#> [1] 0.5562603
#>
#>
#> $global$permutation.pvalue
#> $global$permutation.pvalue$No
#> [1] 0
#>
#> $global$permutation.pvalue$Yes
#> [1] 2.44592e-10
#>
#>
#> $global$global.pem
#> $global$global.pem$No
#> [1] 60.11803
#>
#> $global$global.pem$Yes
#> [1] 96.42857
#>
#>
#> $global$GK.tau.xy
#> $global$GK.tau.xy$No
#> [1] 0.2242021
#>
#> $global$GK.tau.xy$Yes
#> [1] 0.3094255
#>
#>
#> $global$GK.tau.yx
#> $global$GK.tau.yx$No
#> [1] 0.1572228
#>
#> $global$GK.tau.yx$Yes
#> [1] 0.2062297
#>
#>
#>
#> $local
#> $local$std.residuals
#> $local$std.residuals$No
#> No Yes
#> Europe 0.4085886 -0.4491008
#> France -5.2864732 5.8106349
#> Other -1.9679122 2.1630336
#> USA 7.8568468 -8.6358648
#>
#> $local$std.residuals$Yes
#> No Yes
#> Europe 0.20100756 -0.07312724
#> France -2.39317211 0.87064424
#> Other -0.48349378 0.17589670
#> USA 3.87807848 -1.41085828
#>
#>
#> $local$adj.residuals
#> $local$adj.residuals$No
#> No Yes
#> Europe 0.6297326 -0.6297326
#> France -12.4579495 12.4579495
#> Other -2.9630531 2.9630531
#> USA 13.9663200 -13.9663200
#>
#> $local$adj.residuals$Yes
#> No Yes
#> Europe 0.2243363 -0.2243363
#> France -4.2230982 4.2230982
#> Other -0.5213106 0.5213106
#> USA 4.7548724 -4.7548724
#>
#>
#> $local$adj.res.pval
#> $local$adj.res.pval$No
#> No Yes
#> Europe 0.52886957 0.52886957
#> France 0.00000000 0.00000000
#> Other 0.00304604 0.00304604
#> USA 0.00000000 0.00000000
#>
#> $local$adj.res.pval$Yes
#> No Yes
#> Europe 8.224956e-01 8.224956e-01
#> France 2.409667e-05 2.409667e-05
#> Other 6.021504e-01 6.021504e-01
#> USA 1.985718e-06 1.985718e-06
#>
#>
#> $local$odss.ratios
#> $local$odss.ratios$No
#> NULL
#>
#> $local$odss.ratios$Yes
#> NULL
#>
#>
#> $local$local.pem
#> $local$local.pem$No
#> y
#> x No Yes
#> Europe 8.277512 -8.277512
#> France -55.476318 55.476318
#> Other -54.306931 54.306931
#> USA 76.965509 -76.965509
#>
#> $local$local.pem$Yes
#> y
#> x No Yes
#> Europe 2.941176 -2.941176
#> France -100.000000 100.000000
#> Other -100.000000 100.000000
#> USA 85.249042 -85.249042
#>
#>
#> $local$phi
#> $local$phi$No
#> No Yes
#> Europe 0.02072790 -0.02072790
#> France -0.41005840 0.41005840
#> Other -0.09753008 0.09753008
#> USA 0.45970702 -0.45970702
#>
#> $local$phi$Yes
#> No Yes
#> Europe 0.02556550 -0.02556550
#> France -0.48126671 0.48126671
#> Other -0.05940885 0.05940885
#> USA 0.54186800 -0.54186800
#>
#>
#> $local$phi.perm.pval
#> $local$phi.perm.pval$No
#> No Yes
#> Europe 2.510009e-01 2.510009e-01
#> France 1.883333e-33 0.000000e+00
#> Other 2.547376e-03 2.547376e-03
#> USA 0.000000e+00 7.698796e-41
#>
#> $local$phi.perm.pval$Yes
#> No Yes
#> Europe 4.249291e-01 4.249291e-01
#> France 2.212897e-05 2.212897e-05
#> Other 3.085375e-01 3.085375e-01
#> USA 1.117872e-06 1.117872e-06
#>
#>
#>
#> $gather
#> $gather$No
#> var.y var.x freq prop rprop cprop expected std.residuals
#> 1 No Europe 38 0.041170098 0.5846154 0.07524752 35.56338 0.4085886
#> 2 No France 212 0.229685807 0.3812950 0.41980198 304.20368 -5.2864732
#> 3 No Other 6 0.006500542 0.2500000 0.01188119 13.13109 -1.9679122
#> 4 No USA 249 0.269772481 0.8956835 0.49306931 152.10184 7.8568468
#> 5 Yes Europe 27 0.029252438 0.4153846 0.06459330 29.43662 -0.4491008
#> 6 Yes France 344 0.372697725 0.6187050 0.82296651 251.79632 5.8106349
#> 7 Yes Other 18 0.019501625 0.7500000 0.04306220 10.86891 2.1630336
#> 8 Yes USA 29 0.031419285 0.1043165 0.06937799 125.89816 -8.6358648
#> adj.residuals or pem phi perm.pval freq.x freq.y
#> 1 0.6297326 1.17836466 8.277512 0.02072790 2.510009e-01 65 505
#> 2 -12.4579495 0.15564727 -55.476318 -0.41005840 1.883333e-33 556 505
#> 3 -2.9630531 0.26720107 -54.306931 -0.09753008 2.547376e-03 24 505
#> 4 13.9663200 13.04700970 76.965509 0.45970702 0.000000e+00 278 505
#> 5 -0.6297326 0.84863373 -8.277512 -0.02072790 2.510009e-01 65 418
#> 6 12.4579495 6.42478327 55.476318 0.41005840 0.000000e+00 556 418
#> 7 2.9630531 3.74250000 54.306931 0.09753008 2.547376e-03 24 418
#> 8 -13.9663200 0.07664592 -76.965509 -0.45970702 7.698796e-41 278 418
#> prop.x prop.y
#> 1 0.07042254 0.5471289
#> 2 0.60238353 0.5471289
#> 3 0.02600217 0.5471289
#> 4 0.30119177 0.5471289
#> 5 0.07042254 0.4528711
#> 6 0.60238353 0.4528711
#> 7 0.02600217 0.4528711
#> 8 0.30119177 0.4528711
#>
#> $gather$Yes
#> var.y var.x freq prop rprop cprop expected std.residuals
#> 1 No Europe 1 0.01298701 0.1428571 0.11111111 0.8181818 0.20100756
#> 2 No France 0 0.00000000 0.0000000 0.00000000 5.7272727 -2.39317211
#> 3 No Other 0 0.00000000 0.0000000 0.00000000 0.2337662 -0.48349378
#> 4 No USA 8 0.10389610 0.4210526 0.88888889 2.2207792 3.87807848
#> 5 Yes Europe 6 0.07792208 0.8571429 0.08823529 6.1818182 -0.07312724
#> 6 Yes France 49 0.63636364 1.0000000 0.72058824 43.2727273 0.87064424
#> 7 Yes Other 2 0.02597403 1.0000000 0.02941176 1.7662338 0.17589670
#> 8 Yes USA 11 0.14285714 0.5789474 0.16176471 16.7792208 -1.41085828
#> adj.residuals or pem phi perm.pval freq.x freq.y
#> 1 0.2243363 1.29166667 2.941176 0.02556550 4.249291e-01 7 9
#> 2 -4.2230982 0.00000000 -100.000000 -0.48126671 2.212897e-05 49 9
#> 3 -0.5213106 0.00000000 -100.000000 -0.05940885 3.085375e-01 2 9
#> 4 4.7548724 41.45454545 85.249042 0.54186800 1.117872e-06 19 9
#> 5 -0.2243363 0.77419355 -2.941176 -0.02556550 4.249291e-01 7 68
#> 6 4.2230982 Inf 100.000000 0.48126671 2.212897e-05 49 68
#> 7 0.5213106 Inf 100.000000 0.05940885 3.085375e-01 2 68
#> 8 -4.7548724 0.02412281 -85.249042 -0.54186800 1.117872e-06 19 68
#> prop.x prop.y
#> 1 0.09090909 0.1168831
#> 2 0.63636364 0.1168831
#> 3 0.02597403 0.1168831
#> 4 0.24675325 0.1168831
#> 5 0.09090909 0.8831169
#> 6 0.63636364 0.8831169
#> 7 0.02597403 0.8831169
#> 8 0.24675325 0.8831169
#>
#>