Here are libraries that we’ll use.
library(vcd)## Loading required package: gridlibrary(vcdExtra)## Loading required package: gnmlibrary(MASS)var.values <- expand.grid(mstatus=c("divorce","married"),
ems=c("yes","no"),
pms=c("yes","no"),
gender=c("woman","man") )
counts <- c(17, 4, 54, 25, 36, 4, 214, 322,
28, 11, 60, 42, 17, 4, 68, 130)
df4 <- cbind(var.values,counts)
(df4 <- as.data.frame(df4) )## mstatus ems pms gender counts
## 1 divorce yes yes woman 17
## 2 married yes yes woman 4
## 3 divorce no yes woman 54
## 4 married no yes woman 25
## 5 divorce yes no woman 36
## 6 married yes no woman 4
## 7 divorce no no woman 214
## 8 married no no woman 322
## 9 divorce yes yes man 28
## 10 married yes yes man 11
## 11 divorce no yes man 60
## 12 married no yes man 42
## 13 divorce yes no man 17
## 14 married yes no man 4
## 15 divorce no no man 68
## 16 married no no man 130Split data into married and divorced and created variables needed in logit fit via GLM. This set up with make comparing loglinear and logit model results much easier that previous code.
m <- df4[which(df4$mstatus=="married"),]
m$freq.married <- m$counts
d <- df4[which(df4$mstatus=="divorce"),]
d$freq.divorced <- d$counts
wide.data <- cbind(m[,c(2,3,4,6)], d[,6])
names(wide.data) <- c("ems", "pms", "gender", "freq.married", "freq.divorced")
wide.data$ncases <- wide.data$freq.married + wide.data$freq.divorced
wide.data$p <- wide.data$freq.married/wide.data$ncasessummary(mod1 <- glm (counts ~ mstatus + pms + ems + gender + gender*pms
+ mstatus*ems + mstatus*pms + mstatus*pms*ems,
data=df4, family=poisson) )##
## Call:
## glm(formula = counts ~ mstatus + pms + ems + gender + gender *
## pms + mstatus * ems + mstatus * pms + mstatus * pms * ems,
## family = poisson, data = df4)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.12272 -0.60305 0.00924 0.62703 1.08468
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.9270 0.1675 17.470 < 2e-16 ***
## mstatusmarried -1.0986 0.2981 -3.685 0.000229 ***
## pmsno 0.7210 0.2178 3.311 0.000929 ***
## emsno 0.9295 0.1761 5.280 1.29e-07 ***
## genderman 0.3436 0.1307 2.628 0.008586 **
## pmsno:genderman -1.3106 0.1530 -8.569 < 2e-16 ***
## mstatusmarried:emsno 0.5671 0.3355 1.690 0.091002 .
## mstatusmarried:pmsno -0.7922 0.4824 -1.642 0.100564
## pmsno:emsno 0.7421 0.2311 3.211 0.001323 **
## mstatusmarried:pmsno:emsno 1.7955 0.5121 3.506 0.000454 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1333.8549 on 15 degrees of freedom
## Residual deviance: 8.1535 on 6 degrees of freedom
## AIC: 112.16
##
## Number of Fisher Scoring iterations: 41-pchisq(mod1$deviance,mod1$df.residual)## [1] 0.2270702We can do this in a number of ways.
exp(coef(mod1))## (Intercept) mstatusmarried
## 18.6721992 0.3333333
## pmsno emsno
## 2.0565333 2.5333333
## genderman pmsno:genderman
## 1.4100000 0.2696513
## mstatusmarried:emsno mstatusmarried:pmsno
## 1.7631579 0.4528302
## pmsno:emsno mstatusmarried:pmsno:emsno
## 2.1002979 6.0225998exp(confint(mod1)) ## Waiting for profiling to be done...## 2.5 % 97.5 %
## (Intercept) 13.2623287 25.6048005
## mstatusmarried 0.1797506 0.5836535
## pmsno 1.3445827 3.1641322
## emsno 1.8079908 3.6115977
## genderman 1.0929295 1.8258637
## pmsno:genderman 0.1993896 0.3633231
## mstatusmarried:emsno 0.9302023 3.4919961
## mstatusmarried:pmsno 0.1685466 1.1412597
## pmsno:emsno 1.3328079 3.3037901
## mstatusmarried:pmsno:emsno 2.2513211 17.0681176df4$fit1 <- mod1$fitted
# This give the covariance matrix of estimated coefficients
covb <- vcov(mod1)
sub_covb <- c(covb[7,7],covb[7,10],covb[10,7],covb[10,10])
sub.covb <- matrix(sub_covb,nrow=2,ncol=2)
# --- you have to figure out linear combination of parameter
# estimates to give the odds ratio that your interested in The easy way to 95% ci for odds ratios
exp(coef(mod1))## (Intercept) mstatusmarried
## 18.6721992 0.3333333
## pmsno emsno
## 2.0565333 2.5333333
## genderman pmsno:genderman
## 1.4100000 0.2696513
## mstatusmarried:emsno mstatusmarried:pmsno
## 1.7631579 0.4528302
## pmsno:emsno mstatusmarried:pmsno:emsno
## 2.1002979 6.0225998exp(confint(mod1)) ## Waiting for profiling to be done...## 2.5 % 97.5 %
## (Intercept) 13.2623287 25.6048005
## mstatusmarried 0.1797506 0.5836535
## pmsno 1.3445827 3.1641322
## emsno 1.8079908 3.6115977
## genderman 1.0929295 1.8258637
## pmsno:genderman 0.1993896 0.3633231
## mstatusmarried:emsno 0.9302023 3.4919961
## mstatusmarried:pmsno 0.1685466 1.1412597
## pmsno:emsno 1.3328079 3.3037901
## mstatusmarried:pmsno:emsno 2.2513211 17.0681176summary(logit1 <- glm(p ~ ems + pms + gender, data=wide.data, weights=ncases, family=binomial))##
## Call:
## glm(formula = p ~ ems + pms + gender, family = binomial, data = wide.data,
## weights = ncases)
##
## Deviance Residuals:
## 2 4 6 8 10 12 14 16
## 1.10324 -0.96777 -2.12076 0.66225 2.26247 -0.61508 -1.01946 -0.05336
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.1046 0.2746 -7.664 1.80e-14 ***
## emsno 1.5655 0.2466 6.349 2.17e-10 ***
## pmsno 0.8894 0.1666 5.339 9.37e-08 ***
## genderman 0.3057 0.1445 2.116 0.0344 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 107.956 on 7 degrees of freedom
## Residual deviance: 13.629 on 4 degrees of freedom
## AIC: 56.893
##
## Number of Fisher Scoring iterations: 4summary(loglin1 <- glm(counts ~ mstatus + mstatus*ems + mstatus*pms + ems + pms + gender + ems*pms + ems*gender + pms*gender + ems*pms*gender + mstatus*gender, data=df4, family=poisson) )##
## Call:
## glm(formula = counts ~ mstatus + mstatus * ems + mstatus * pms +
## ems + pms + gender + ems * pms + ems * gender + pms * gender +
## ems * pms * gender + mstatus * gender, family = poisson,
## data = df4)
##
## Deviance Residuals:
## 1 2 3 4 5 6 7 8
## -0.40347 1.02681 0.57326 -0.77971 0.90329 -1.91878 -0.50928 0.42333
## 9 10 11 12 13 14 15 16
## -0.97188 2.04309 0.40420 -0.46363 0.51324 -0.88084 0.04328 -0.03122
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.92950 0.22025 13.301 < 2e-16 ***
## mstatusmarried -2.10456 0.27459 -7.664 1.80e-14 ***
## emsno 0.98045 0.25151 3.898 9.69e-05 ***
## pmsno 0.49960 0.27207 1.836 0.066313 .
## genderman 0.58092 0.27134 2.141 0.032282 *
## mstatusmarried:emsno 1.56549 0.24658 6.349 2.17e-10 ***
## mstatusmarried:pmsno 0.88936 0.16659 5.339 9.37e-08 ***
## emsno:pmsno 0.99105 0.29996 3.304 0.000954 ***
## emsno:genderman -0.44916 0.31224 -1.439 0.150288
## pmsno:genderman -1.30392 0.38263 -3.408 0.000655 ***
## mstatusmarried:genderman 0.30574 0.14451 2.116 0.034372 *
## emsno:pmsno:genderman -0.01418 0.41893 -0.034 0.973006
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1333.855 on 15 degrees of freedom
## Residual deviance: 13.629 on 4 degrees of freedom
## AIC: 121.63
##
## Number of Fisher Scoring iterations: 5Notice that the residual deviance for both models are equivalent (i.e., \(G^2=14.629\), \(df=4\)). Also that parameters match up; that is,
| logit | Loglinear | ASE |
|---|---|---|
| int =-2.1046 | M (married) = -2.1046 | 0.2746 |
| Ems (no)= 1.5655 | ME = 1.5655 | 0.2466 |
| Pms (no)= 0.8894 | MP = 0.8894 | 0.1666 |
| Gender (man)=0.3057 | MG =0.3057 | 0.1445 |
summary( logit2 <- glm(p ~ ems + pms + gender + gender*pms, weights=ncases, data=wide.data, family=binomial) )##
## Call:
## glm(formula = p ~ ems + pms + gender + gender * pms, family = binomial,
## data = wide.data, weights = ncases)
##
## Deviance Residuals:
## 2 4 6 8 10 12 14 16
## 1.2924 -0.4672 -2.1530 0.4614 2.0789 -1.0152 -0.9152 0.2691
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.2277 0.3177 -7.012 2.35e-12 ***
## emsno 1.5699 0.2467 6.365 1.95e-10 ***
## pmsno 1.0258 0.2417 4.243 2.20e-05 ***
## genderman 0.5044 0.2903 1.738 0.0823 .
## pmsno:genderman -0.2645 0.3341 -0.792 0.4286
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 107.96 on 7 degrees of freedom
## Residual deviance: 13.00 on 3 degrees of freedom
## AIC: 58.263
##
## Number of Fisher Scoring iterations: 4summary(loglin2 <- glm (counts ~ mstatus + mstatus*ems + mstatus*pms + mstatus*gender + mstatus*gender*pms + ems + pms + gender + gender*pms + gender*ems + pms*ems + gender*pms*ems, data=df4, family=poisson) ) ##
## Call:
## glm(formula = counts ~ mstatus + mstatus * ems + mstatus * pms +
## mstatus * gender + mstatus * gender * pms + ems + pms + gender +
## gender * pms + gender * ems + pms * ems + gender * pms *
## ems, family = poisson, data = df4)
##
## Deviance Residuals:
## 1 2 3 4 5 6 7 8
## -0.4576 1.2087 0.2696 -0.3816 0.9207 -1.9462 -0.3557 0.2939
## 9 10 11 12 13 14 15 16
## -0.9098 1.8693 0.6772 -0.7563 0.4545 -0.7944 -0.2171 0.1591
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.94217 0.22040 13.349 < 2e-16 ***
## mstatusmarried -2.22772 0.31771 -7.012 2.35e-12 ***
## emsno 1.00990 0.25336 3.986 6.72e-05 ***
## pmsno 0.48388 0.27301 1.772 0.07633 .
## genderman 0.55718 0.27311 2.040 0.04134 *
## mstatusmarried:emsno 1.56989 0.24665 6.365 1.96e-10 ***
## mstatusmarried:pmsno 1.02577 0.24174 4.243 2.20e-05 ***
## mstatusmarried:genderman 0.50435 0.29027 1.738 0.08229 .
## pmsno:genderman -1.26231 0.38608 -3.270 0.00108 **
## emsno:genderman -0.50363 0.31991 -1.574 0.11542
## emsno:pmsno 0.95424 0.30356 3.144 0.00167 **
## mstatusmarried:pmsno:genderman -0.26446 0.33406 -0.792 0.42857
## emsno:pmsno:genderman 0.06429 0.43039 0.149 0.88126
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1333.9 on 15 degrees of freedom
## Residual deviance: 13.0 on 3 degrees of freedom
## AIC: 123
##
## Number of Fisher Scoring iterations: 5summary( logit3 <- glm(p ~ ems + pms + gender + gender*ems, weights=ncases, data=wide.data, family=binomial) )##
## Call:
## glm(formula = p ~ ems + pms + gender + gender * ems, family = binomial,
## data = wide.data, weights = ncases)
##
## Deviance Residuals:
## 2 4 6 8 10 12 14 16
## 1.7532 -1.0348 -1.1269 0.3867 1.4109 -0.3428 -1.7345 0.2550
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.5432 0.4044 -6.288 3.21e-10 ***
## emsno 2.0199 0.3913 5.162 2.44e-07 ***
## pmsno 0.8978 0.1666 5.390 7.05e-08 ***
## genderman 1.0856 0.4917 2.208 0.0272 *
## emsno:genderman -0.8501 0.5097 -1.668 0.0954 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 107.956 on 7 degrees of freedom
## Residual deviance: 10.746 on 3 degrees of freedom
## AIC: 56.009
##
## Number of Fisher Scoring iterations: 4summary(loglin3 <-glm (counts ~ mstatus + mstatus*ems + mstatus*pms + mstatus*gender+ mstatus*gender*ems
+ ems + pms + gender + gender*pms +gender*ems + pms*ems + gender*pms*ems,
data=df4, family=poisson) ) ##
## Call:
## glm(formula = counts ~ mstatus + mstatus * ems + mstatus * pms +
## mstatus * gender + mstatus * gender * ems + ems + pms + gender +
## gender * pms + gender * ems + pms * ems + gender * pms *
## ems, family = poisson, data = df4)
##
## Deviance Residuals:
## 1 2 3 4 5 6 7 8
## -0.5722 1.6572 0.6151 -0.8321 0.4214 -1.0452 -0.2984 0.2460
## 9 10 11 12 13 14 15 16
## -0.6594 1.2473 0.2229 -0.2604 0.9538 -1.4487 -0.2057 0.1507
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.9688 0.2202 13.482 < 2e-16 ***
## mstatusmarried -2.5432 0.4045 -6.288 3.22e-10 ***
## emsno 0.9353 0.2529 3.697 0.000218 ***
## pmsno 0.5436 0.2720 1.998 0.045682 *
## genderman 0.4854 0.2781 1.745 0.080908 .
## mstatusmarried:emsno 2.0199 0.3913 5.162 2.44e-07 ***
## mstatusmarried:pmsno 0.8978 0.1666 5.390 7.05e-08 ***
## mstatusmarried:genderman 1.0856 0.4917 2.208 0.027252 *
## emsno:genderman -0.3241 0.3217 -1.007 0.313743
## pmsno:genderman -1.4053 0.3885 -3.618 0.000297 ***
## emsno:pmsno 0.9386 0.3021 3.107 0.001891 **
## mstatusmarried:emsno:genderman -0.8501 0.5097 -1.668 0.095360 .
## emsno:pmsno:genderman 0.1020 0.4248 0.240 0.810240
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1333.855 on 15 degrees of freedom
## Residual deviance: 10.746 on 3 degrees of freedom
## AIC: 120.75
##
## Number of Fisher Scoring iterations: 5summary( logit4<- glm(p ~ ems + pms + gender + pms*ems, weights=ncases, data=wide.data, family=binomial) )##
## Call:
## glm(formula = p ~ ems + pms + gender + pms * ems, family = binomial,
## data = wide.data, weights = ncases)
##
## Deviance Residuals:
## 2 4 6 8 10 12 14 16
## -0.2594 -0.2549 -0.3737 0.2015 0.1725 0.2141 0.4373 -0.3443
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.3049 0.3150 -4.142 3.44e-05 ***
## emsno 0.5962 0.3366 1.771 0.07651 .
## pmsno -0.7004 0.4850 -1.444 0.14874
## genderman 0.3089 0.1458 2.118 0.03415 *
## emsno:pmsno 1.7999 0.5130 3.509 0.00045 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 107.95608 on 7 degrees of freedom
## Residual deviance: 0.69784 on 3 degrees of freedom
## AIC: 45.961
##
## Number of Fisher Scoring iterations: 4summary(loglin4 <- glm (counts ~ mstatus + mstatus*ems + mstatus*pms + mstatus*gender+mstatus*pms*ems
+ ems + pms + gender + gender*pms +gender*ems + pms*ems + gender*pms*ems ,
data=df4, family=poisson) ) ##
## Call:
## glm(formula = counts ~ mstatus + mstatus * ems + mstatus * pms +
## mstatus * gender + mstatus * pms * ems + ems + pms + gender +
## gender * pms + gender * ems + pms * ems + gender * pms *
## ems, family = poisson, data = df4)
##
## Deviance Residuals:
## 1 2 3 4 5 6 7 8
## 0.11762 -0.23118 0.14538 -0.20932 0.12524 -0.35213 -0.15584 0.12780
## 9 10 11 12 13 14 15 16
## -0.09026 0.14699 -0.13621 0.16516 -0.17840 0.39920 0.28061 -0.19949
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.8046 0.2283 12.283 < 2e-16 ***
## mstatusmarried -1.3049 0.3150 -4.142 3.44e-05 ***
## emsno 1.1646 0.2588 4.500 6.80e-06 ***
## pmsno 0.7580 0.2809 2.698 0.00697 **
## genderman 0.5447 0.2733 1.993 0.04625 *
## mstatusmarried:emsno 0.5962 0.3366 1.771 0.07651 .
## mstatusmarried:pmsno -0.7004 0.4850 -1.444 0.14874
## mstatusmarried:genderman 0.3089 0.1458 2.118 0.03415 *
## emsno:pmsno 0.6495 0.3130 2.075 0.03798 *
## pmsno:genderman -1.2311 0.3828 -3.216 0.00130 **
## emsno:genderman -0.4019 0.3106 -1.294 0.19568
## mstatusmarried:emsno:pmsno 1.7999 0.5130 3.509 0.00045 ***
## emsno:pmsno:genderman -0.1030 0.4230 -0.243 0.80763
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1333.85486 on 15 degrees of freedom
## Residual deviance: 0.69784 on 3 degrees of freedom
## AIC: 110.7
##
## Number of Fisher Scoring iterations: 4summary(logit5<- glm(p ~ ems + pms + gender + gender*ems + gender*pms,
weights=ncases, data=wide.data, family=binomial) )##
## Call:
## glm(formula = p ~ ems + pms + gender + gender * ems + gender *
## pms, family = binomial, data = wide.data, weights = ncases)
##
## Deviance Residuals:
## 2 4 6 8 10 12 14 16
## 1.8791 -0.6166 -1.1765 0.2284 1.2938 -0.6716 -1.6157 0.4993
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.6335 0.4306 -6.116 9.58e-10 ***
## emsno 2.0113 0.3921 5.130 2.90e-07 ***
## pmsno 1.0107 0.2438 4.145 3.39e-05 ***
## genderman 1.2212 0.5358 2.279 0.0227 *
## emsno:genderman -0.8210 0.5115 -1.605 0.1085
## pmsno:genderman -0.2151 0.3351 -0.642 0.5210
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 107.956 on 7 degrees of freedom
## Residual deviance: 10.332 on 2 degrees of freedom
## AIC: 57.596
##
## Number of Fisher Scoring iterations: 4summary(loglin5 <- glm (counts ~ mstatus + mstatus*ems + mstatus*pms + mstatus*gender + mstatus*gender*ems + mstatus*gender*pms + ems + pms + gender + gender*pms +gender*ems + pms*ems + gender*pms*ems,
data=df4, family=poisson) ) ##
## Call:
## glm(formula = counts ~ mstatus + mstatus * ems + mstatus * pms +
## mstatus * gender + mstatus * gender * ems + mstatus * gender *
## pms + ems + pms + gender + gender * pms + gender * ems +
## pms * ems + gender * pms * ems, family = poisson, data = df4)
##
## Deviance Residuals:
## 1 2 3 4 5 6 7 8
## -0.5994 1.7809 0.3586 -0.5016 0.4430 -1.0900 -0.1765 0.1449
## 9 10 11 12 13 14 15 16
## -0.6114 1.1402 0.4423 -0.5054 0.8761 -1.3576 -0.4011 0.2974
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.9752 0.2201 13.516 < 2e-16 ***
## mstatusmarried -2.6335 0.4306 -6.116 9.59e-10 ***
## emsno 0.9646 0.2560 3.767 0.000165 ***
## pmsno 0.5336 0.2729 1.956 0.050518 .
## genderman 0.4704 0.2793 1.684 0.092100 .
## mstatusmarried:emsno 2.0113 0.3921 5.129 2.91e-07 ***
## mstatusmarried:pmsno 1.0107 0.2438 4.145 3.39e-05 ***
## mstatusmarried:genderman 1.2212 0.5358 2.279 0.022657 *
## emsno:genderman -0.3735 0.3308 -1.129 0.258884
## pmsno:genderman -1.3663 0.3926 -3.480 0.000501 ***
## emsno:pmsno 0.9046 0.3067 2.949 0.003185 **
## mstatusmarried:emsno:genderman -0.8210 0.5115 -1.605 0.108511
## mstatusmarried:pmsno:genderman -0.2151 0.3351 -0.642 0.521044
## emsno:pmsno:genderman 0.1591 0.4333 0.367 0.713504
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1333.855 on 15 degrees of freedom
## Residual deviance: 10.332 on 2 degrees of freedom
## AIC: 122.34
##
## Number of Fisher Scoring iterations: 5summary(logit6<- glm(p ~ ems + pms + gender + gender*pms + ems*pms,
weights=ncases, data=wide.data, family=binomial) )##
## Call:
## glm(formula = p ~ ems + pms + gender + gender * pms + ems * pms,
## family = binomial, data = wide.data, weights = ncases)
##
## Deviance Residuals:
## 2 4 6 8 10 12 14 16
## -0.10282 0.04534 -0.40883 0.07229 0.06684 -0.03764 0.48337 -0.12296
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.3901 0.3591 -3.871 0.000108 ***
## emsno 0.6090 0.3383 1.800 0.071788 .
## pmsno -0.5976 0.5267 -1.134 0.256590
## genderman 0.4320 0.2837 1.523 0.127778
## pmsno:genderman -0.1677 0.3306 -0.507 0.611932
## emsno:pmsno 1.7809 0.5146 3.460 0.000539 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 107.95608 on 7 degrees of freedom
## Residual deviance: 0.43965 on 2 degrees of freedom
## AIC: 47.703
##
## Number of Fisher Scoring iterations: 4summary(loglin6 <-glm (counts ~ mstatus + mstatus*ems + mstatus*pms + mstatus*gender+ mstatus*ems*gender + mstatus*gender*pms + ems + pms + gender + gender*pms +gender*ems + pms*ems + gender*pms*ems,
data=df4, family=poisson) ) ##
## Call:
## glm(formula = counts ~ mstatus + mstatus * ems + mstatus * pms +
## mstatus * gender + mstatus * ems * gender + mstatus * gender *
## pms + ems + pms + gender + gender * pms + gender * ems +
## pms * ems + gender * pms * ems, family = poisson, data = df4)
##
## Deviance Residuals:
## 1 2 3 4 5 6 7 8
## -0.5994 1.7809 0.3586 -0.5016 0.4430 -1.0900 -0.1765 0.1449
## 9 10 11 12 13 14 15 16
## -0.6114 1.1402 0.4423 -0.5054 0.8761 -1.3576 -0.4011 0.2974
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.9752 0.2201 13.516 < 2e-16 ***
## mstatusmarried -2.6335 0.4306 -6.116 9.59e-10 ***
## emsno 0.9646 0.2560 3.767 0.000165 ***
## pmsno 0.5336 0.2729 1.956 0.050518 .
## genderman 0.4704 0.2793 1.684 0.092100 .
## mstatusmarried:emsno 2.0113 0.3921 5.129 2.91e-07 ***
## mstatusmarried:pmsno 1.0107 0.2438 4.145 3.39e-05 ***
## mstatusmarried:genderman 1.2212 0.5358 2.279 0.022657 *
## emsno:genderman -0.3735 0.3308 -1.129 0.258884
## pmsno:genderman -1.3663 0.3926 -3.480 0.000501 ***
## emsno:pmsno 0.9046 0.3067 2.949 0.003185 **
## mstatusmarried:emsno:genderman -0.8210 0.5115 -1.605 0.108511
## mstatusmarried:pmsno:genderman -0.2151 0.3351 -0.642 0.521044
## emsno:pmsno:genderman 0.1591 0.4333 0.367 0.713504
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1333.855 on 15 degrees of freedom
## Residual deviance: 10.332 on 2 degrees of freedom
## AIC: 122.34
##
## Number of Fisher Scoring iterations: 5summary( logit7 <- glm(p ~ ems + pms + gender + gender*ems + ems*pms,
weights= ncases, data=wide.data, family=binomial) )##
## Call:
## glm(formula = p ~ ems + pms + gender + gender * ems + ems * pms,
## family = binomial, data = wide.data, weights = ncases)
##
## Deviance Residuals:
## 2 4 6 8 10 12 14 16
## 0.13038 -0.32409 -0.11978 0.11917 -0.08189 0.27297 0.13038 -0.20302
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.5199 0.4716 -3.223 0.00127 **
## emsno 0.8279 0.5041 1.642 0.10053
## pmsno -0.6147 0.5043 -1.219 0.22290
## genderman 0.6147 0.5043 1.219 0.22290
## emsno:genderman -0.3343 0.5268 -0.635 0.52570
## emsno:pmsno 1.7048 0.5352 3.186 0.00144 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 107.95608 on 7 degrees of freedom
## Residual deviance: 0.29001 on 2 degrees of freedom
## AIC: 47.553
##
## Number of Fisher Scoring iterations: 3summary(loglin7 <- glm (counts ~ mstatus + ems + pms + gender + gender*pms +gender*ems
+ pms*ems + gender*pms*ems + mstatus*ems + mstatus*pms + mstatus*gender
+ mstatus*gender*ems + mstatus*ems*pms,
data=df4, family=poisson) ) ##
## Call:
## glm(formula = counts ~ mstatus + ems + pms + gender + gender *
## pms + gender * ems + pms * ems + gender * pms * ems + mstatus *
## ems + mstatus * pms + mstatus * gender + mstatus * gender *
## ems + mstatus * ems * pms, family = poisson, data = df4)
##
## Deviance Residuals:
## 1 2 3 4 5 6 7 8
## -0.05579 0.11784 0.18556 -0.26570 0.03860 -0.11339 -0.09224 0.07546
## 9 10 11 12 13 14 15 16
## 0.04379 -0.06919 -0.17327 0.21093 -0.05579 0.11784 0.16507 -0.11818
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.8467 0.2341 12.162 < 2e-16 ***
## mstatusmarried -1.5199 0.4716 -3.223 0.00127 **
## emsno 1.1169 0.2664 4.193 2.76e-05 ***
## pmsno 0.7304 0.2808 2.601 0.00930 **
## genderman 0.4772 0.2924 1.632 0.10270
## pmsno:genderman -1.2076 0.3857 -3.131 0.00174 **
## emsno:genderman -0.3242 0.3333 -0.973 0.33071
## emsno:pmsno 0.6783 0.3133 2.165 0.03037 *
## mstatusmarried:emsno 0.8279 0.5041 1.642 0.10053
## mstatusmarried:pmsno -0.6147 0.5043 -1.219 0.22290
## mstatusmarried:genderman 0.6147 0.5043 1.219 0.22290
## emsno:pmsno:genderman -0.1183 0.4244 -0.279 0.78048
## mstatusmarried:emsno:genderman -0.3343 0.5268 -0.635 0.52570
## mstatusmarried:emsno:pmsno 1.7048 0.5352 3.186 0.00144 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1333.85486 on 15 degrees of freedom
## Residual deviance: 0.29001 on 2 degrees of freedom
## AIC: 112.29
##
## Number of Fisher Scoring iterations: 3summary( logit8 <- glm(p ~ ems + pms + gender + gender*ems + ems*pms + pms*gender,
weights=ncases, data=wide.data ,family=binomial) )##
## Call:
## glm(formula = p ~ ems + pms + gender + gender * ems + ems * pms +
## pms * gender, family = binomial, data = wide.data, weights = ncases)
##
## Deviance Residuals:
## 2 4 6 8 10 12 14 16
## 0.20163 -0.08550 -0.18209 0.03124 -0.12528 0.07135 0.20163 -0.05307
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.5603 0.4880 -3.197 0.00139 **
## emsno 0.8108 0.5104 1.589 0.11215
## pmsno -0.5422 0.5419 -1.000 0.31708
## genderman 0.6704 0.5282 1.269 0.20437
## emsno:genderman -0.2920 0.5411 -0.540 0.58942
## emsno:pmsno 1.6974 0.5383 3.154 0.00161 **
## pmsno:genderman -0.1283 0.3387 -0.379 0.70495
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 107.95608 on 7 degrees of freedom
## Residual deviance: 0.14636 on 1 degrees of freedom
## AIC: 49.41
##
## Number of Fisher Scoring iterations: 3summary(loglin8 <- glm (counts ~ mstatus + mstatus*ems + mstatus*pms + mstatus*gender
+ mstatus*ems*pms + mstatus*ems*gender + mstatus*pms*gender
+ ems + pms + gender + gender*pms +gender*ems + pms*ems + gender*pms*ems ,
data=df4, family=poisson) ) ##
## Call:
## glm(formula = counts ~ mstatus + mstatus * ems + mstatus * pms +
## mstatus * gender + mstatus * ems * pms + mstatus * ems *
## gender + mstatus * pms * gender + ems + pms + gender + gender *
## pms + gender * ems + pms * ems + gender * pms * ems, family = poisson,
## data = df4)
##
## Deviance Residuals:
## 1 2 3 4 5 6 7 8
## -0.08535 0.18268 0.04832 -0.07053 0.05925 -0.17218 -0.02421 0.01975
## 9 10 11 12 13 14 15 16
## 0.06724 -0.10570 -0.04565 0.05483 -0.08535 0.18268 0.04304 -0.03105
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.85384 0.23409 12.191 < 2e-16 ***
## mstatusmarried -1.56030 0.48799 -3.197 0.00139 **
## emsno 1.12856 0.26704 4.226 2.38e-05 ***
## pmsno 0.71979 0.28183 2.554 0.01065 *
## genderman 0.46563 0.29378 1.585 0.11297
## mstatusmarried:emsno 0.81085 0.51041 1.589 0.11215
## mstatusmarried:pmsno -0.54216 0.54191 -1.000 0.31708
## mstatusmarried:genderman 0.67043 0.52822 1.269 0.20437
## emsno:pmsno 0.66544 0.31444 2.116 0.03432 *
## emsno:genderman -0.34780 0.33888 -1.026 0.30474
## pmsno:genderman -1.18541 0.38994 -3.040 0.00237 **
## mstatusmarried:emsno:pmsno 1.69743 0.53825 3.154 0.00161 **
## mstatusmarried:emsno:genderman -0.29201 0.54108 -0.540 0.58942
## mstatusmarried:pmsno:genderman -0.12826 0.33875 -0.379 0.70495
## emsno:pmsno:genderman -0.08576 0.43297 -0.198 0.84298
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1333.85486 on 15 degrees of freedom
## Residual deviance: 0.14636 on 1 degrees of freedom
## AIC: 114.15
##
## Number of Fisher Scoring iterations: 3