Estimate probabilities in contingency table

multinomial(
x,
data = parent.frame(),
marginal = FALSE,
transform,
vcov = TRUE,
IC = TRUE,
...
)

## Arguments

x

Formula (or matrix or data.frame with observations, 1 or 2 columns)

data

Optional data.frame

marginal

If TRUE the marginals are estimated

transform

Optional transformation of parameters (e.g., logit)

vcov

Calculate asymptotic variance (default TRUE)

IC

Return ic decomposition (default TRUE)

...

Klaus K. Holst

## Examples

set.seed(1)
breaks <- c(-Inf,-1,0,Inf)
m <- lvm(); covariance(m,pairwise=TRUE) <- ~y1+y2+y3+y4
d <- transform(sim(m,5e2),
z1=cut(y1,breaks=breaks),
z2=cut(y2,breaks=breaks),
z3=cut(y3,breaks=breaks),
z4=cut(y4,breaks=breaks))

multinomial(d[,5])
#> Call: multinomial(x = d[, 5])
#>
#> Joint probabilities:
#> x
#> (-Inf,-1]    (-1,0]  (0, Inf]
#>     0.154     0.350     0.496
#>
#>    Estimate Std.Err   2.5%  97.5%    P-value
#> p1    0.154 0.01614 0.1224 0.1856  1.425e-21
#> p2    0.350 0.02133 0.3082 0.3918  1.669e-60
#> p3    0.496 0.02236 0.4522 0.5398 5.068e-109
(a1 <- multinomial(d[,5:6]))
#> Call: multinomial(x = d[, 5:6])
#>
#> Joint probabilities:
#>            z2
#> z1          (-Inf,-1] (-1,0] (0, Inf]
#>   (-Inf,-1]     0.064  0.062    0.028
#>   (-1,0]        0.066  0.146    0.138
#>   (0, Inf]      0.040  0.154    0.302
#>
#> Conditional probabilities:
#>            z2
#> z1           (-Inf,-1]     (-1,0]   (0, Inf]
#>   (-Inf,-1] 0.41558442 0.40259740 0.18181818
#>   (-1,0]    0.18857143 0.41714286 0.39428571
#>   (0, Inf]  0.08064516 0.31048387 0.60887097
#>
#>     Estimate  Std.Err    2.5%   97.5%   P-value
#> p11    0.064 0.010946 0.04255 0.08545 5.004e-09
#> p21    0.066 0.011104 0.04424 0.08776 2.780e-09
#> p31    0.040 0.008764 0.02282 0.05718 5.010e-06
#> p12    0.062 0.010785 0.04086 0.08314 8.986e-09
#> p22    0.146 0.015791 0.11505 0.17695 2.340e-20
#> p32    0.154 0.016142 0.12236 0.18564 1.425e-21
#> p13    0.028 0.007378 0.01354 0.04246 1.475e-04
#> p23    0.138 0.015424 0.10777 0.16823 3.657e-19
#> p33    0.302 0.020533 0.26176 0.34224 5.707e-49
(K1 <- kappa(a1)) ## Cohen's kappa
#>       Estimate Std.Err  2.5% 97.5%   P-value
#> kappa   0.2065 0.03547 0.137 0.276 5.805e-09

K2 <- kappa(d[,7:8])
## Testing difference K1-K2:
estimate(merge(K1,K2,id=TRUE),diff)
#>         Estimate Std.Err     2.5%  97.5% P-value
#> kappa.1  0.05756 0.04779 -0.03611 0.1512  0.2284

estimate(merge(K1,K2,id=FALSE),diff) ## Wrong std.err ignoring dependence
#>         Estimate Std.Err     2.5%  97.5% P-value
#> kappa.1  0.05756 0.04997 -0.04037 0.1555  0.2493
sqrt(vcov(K1)+vcov(K2))
#>            kappa
#> kappa 0.04996804

## Average of the two kappas:
estimate(merge(K1,K2,id=TRUE),function(x) mean(x))
#>    Estimate Std.Err   2.5%  97.5%  P-value
#> p1   0.2353 0.02603 0.1843 0.2863 1.57e-19
estimate(merge(K1,K2,id=FALSE),function(x) mean(x)) ## Independence
#>    Estimate Std.Err   2.5%  97.5%  P-value
#> p1   0.2353 0.02498 0.1863 0.2842 4.64e-21
##'
## Goodman-Kruskal's gamma
m2 <- lvm(); covariance(m2) <- y1~y2
breaks1 <- c(-Inf,-1,0,Inf)
breaks2 <- c(-Inf,0,Inf)
d2 <- transform(sim(m2,5e2),
z1=cut(y1,breaks=breaks1),
z2=cut(y2,breaks=breaks2))

(g1 <- gkgamma(d2[,3:4]))
#> Call: gkgamma(x = d2[, 3:4])
#> ────────────────────────────────────────────────────────────────────────────────
#> n = 500
#>
#>       Estimate  Std.Err    2.5%   97.5%   P-value
#> C      0.26654 0.013898 0.23931 0.29378 5.522e-82
#> D      0.06619 0.007974 0.05056 0.08182 1.033e-16
#> gamma  0.60214 0.053796 0.49670 0.70757 4.411e-29
## same as
if (FALSE) {
gkgamma(table(d2[,3:4]))
gkgamma(multinomial(d2[,3:4]))
}

##partial gamma
d2\$x <- rbinom(nrow(d2),2,0.5)
gkgamma(z1~z2|x,data=d2)
#> Call: gkgamma(x = z1 ~ z2 | x, data = d2)
#> ────────────────────────────────────────────────────────────────────────────────
#> Strata:
#>
#> 0 (n=112):
#>   Estimate Std.Err    2.5%   97.5%   P-value
#> C  0.29464 0.02999 0.23587 0.35342 8.758e-23
#> D  0.04624 0.01379 0.01921 0.07326 7.981e-04
#>
#> 1 (n=248):
#>   Estimate Std.Err    2.5%  97.5%   P-value
#> C  0.24340 0.01958 0.20502 0.2818 1.797e-35
#> D  0.08126 0.01256 0.05665 0.1059 9.786e-11
#>
#> 2 (n=140):
#>   Estimate Std.Err    2.5%  97.5%   P-value
#> C  0.28520 0.02604 0.23417 0.3362 6.415e-28
#> D  0.05806 0.01436 0.02992 0.0862 5.261e-05
#>
#> ────────────────────────────────────────────────────────────────────────────────
#>
#> n = 500
#>
#> Gamma coefficient:
#>
#>        Estimate Std.Err   2.5%  97.5%   P-value
#> γ:0      0.7287 0.09062 0.5511 0.9063 8.894e-16
#> γ:1      0.4994 0.08649 0.3299 0.6689 7.744e-09
#> γ:2      0.6617 0.09293 0.4796 0.8439 1.076e-12
#> pgamma   0.5663 0.06074 0.4473 0.6854 1.126e-20