
Hauser (1979) Data on Social Mobility
Hauser79.Rd
Hauser (1979) presented this two-way frequency table, cross-classifying occupational categories of sons and fathers in the United States.
It is a good example for exploring a variety of models for square tables: quasi-independence, quasi-symmetry, row/column effects, uniform association, etc., using the facilities of the gnm.
Usage
data(Hauser79)
Format
A frequency data frame with 25 observations on the following 3 variables, representing the cross-classification of 19912 individuals by father's occupation and son's first occupation.
Son
a factor with levels
UpNM
LoNM
UpM
LoM
Farm
Father
a factor with levels
UpNM
LoNM
UpM
LoM
Farm
Freq
a numeric vector
Details
The table levels for Son
and Father
have been arranged in order of decreasing status
as is common for mobility tables.
Source
R.M. Hauser (1979), Some exploratory methods for modeling mobility tables and other cross-classified data. In: K.F. Schuessler (Ed.), Sociological Methodology, 1980, Jossey-Bass, San Francisco, pp. 413-458.
References
Powers, D.A. and Xie, Y. (2008). Statistical Methods for Categorical Data Analysis, Bingley, UK: Emerald.
Examples
data(Hauser79)
str(Hauser79)
#> 'data.frame': 25 obs. of 3 variables:
#> $ Son : Factor w/ 5 levels "UpNM","LoNM",..: 1 2 3 4 5 1 2 3 4 5 ...
#> $ Father: Factor w/ 5 levels "UpNM","LoNM",..: 1 1 1 1 1 2 2 2 2 2 ...
#> $ Freq : num 1414 521 302 643 40 ...
# display table
structable(~Father+Son, data=Hauser79)
#> Son UpNM LoNM UpM LoM Farm
#> Father
#> UpNM 1414 521 302 643 40
#> LoNM 724 524 254 703 48
#> UpM 798 648 856 1676 108
#> LoM 756 914 771 3325 237
#> Farm 409 357 441 1611 1832
#Examples from Powers & Xie, Table 4.15
# independence model
mosaic(Freq ~ Father + Son, data=Hauser79, shade=TRUE)
hauser.indep <- gnm(Freq ~ Father + Son,
data=Hauser79,
family=poisson)
mosaic(hauser.indep, ~Father+Son, main="Independence model", gp=shading_Friendly)
# Quasi-symmetry
hauser.quasi <- update(hauser.indep, ~ . + Diag(Father,Son))
mosaic(hauser.quasi, ~Father+Son, main="Quasi-independence model", gp=shading_Friendly)
hauser.qsymm <- update(hauser.indep, ~ . + Diag(Father,Son) + Symm(Father,Son))
mosaic(hauser.qsymm, ~Father+Son, main="Quasi-symmetry model", gp=shading_Friendly)
#mosaic(hauser.qsymm, ~Father+Son, main="Quasi-symmetry model")
# numeric scores for row/column effects
Sscore <- as.numeric(Hauser79$Son)
Fscore <- as.numeric(Hauser79$Father)
# row effects model
hauser.roweff <- update(hauser.indep, ~ . + Father*Sscore)
LRstats(hauser.roweff)
#> Likelihood summary table:
#> AIC BIC LR Chisq Df Pr(>Chisq)
#> hauser.roweff 2308.9 2324.7 2080.2 12 < 2.2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# uniform association
hauser.UA <- update(hauser.indep, ~ . + Fscore*Sscore)
LRstats(hauser.UA)
#> Likelihood summary table:
#> AIC BIC LR Chisq Df Pr(>Chisq)
#> hauser.UA 2503.4 2515.6 2280.7 15 < 2.2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# uniform association, omitting diagonals
hauser.UAdiag <- update(hauser.indep, ~ . + Fscore*Sscore + Diag(Father,Son))
LRstats(hauser.UAdiag)
#> Likelihood summary table:
#> AIC BIC LR Chisq Df Pr(>Chisq)
#> hauser.UAdiag 305.72 324 73.007 10 1.161e-11 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Levels for Hauser 5-level model
levels <- matrix(c(
2, 4, 5, 5, 5,
3, 4, 5, 5, 5,
5, 5, 5, 5, 5,
5, 5, 5, 4, 4,
5, 5, 5, 4, 1
), 5, 5, byrow=TRUE)
hauser.topo <- update(hauser.indep, ~ . + Topo(Father, Son, spec=levels))
mosaic(hauser.topo, ~Father+Son, main="Topological model", gp=shading_Friendly)
hauser.RC <- update(hauser.indep, ~ . + Mult(Father, Son), verbose=FALSE)
mosaic(hauser.RC, ~Father+Son, main="RC model", gp=shading_Friendly)
LRstats(hauser.RC)
#> Likelihood summary table:
#> AIC BIC LR Chisq Df Pr(>Chisq)
#> hauser.RC 920.16 939.66 685.45 9 < 2.2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# crossings models
hauser.CR <- update(hauser.indep, ~ . + Crossings(Father,Son))
mosaic(hauser.topo, ~Father+Son, main="Crossings model", gp=shading_Friendly)
LRstats(hauser.CR)
#> Likelihood summary table:
#> AIC BIC LR Chisq Df Pr(>Chisq)
#> hauser.CR 318.63 334.47 89.914 12 5.131e-14 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
hauser.CRdiag <- update(hauser.indep, ~ . + Crossings(Father,Son) + Diag(Father,Son))
LRstats(hauser.CRdiag)
#> Likelihood summary table:
#> AIC BIC LR Chisq Df Pr(>Chisq)
#> hauser.CRdiag 298.95 318.45 64.237 9 2.03e-10 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# compare model fit statistics
modlist <- glmlist(hauser.indep, hauser.roweff, hauser.UA, hauser.UAdiag,
hauser.quasi, hauser.qsymm, hauser.topo,
hauser.RC, hauser.CR, hauser.CRdiag)
sumry <- LRstats(modlist)
sumry[order(sumry$AIC, decreasing=TRUE),]
#> Likelihood summary table:
#> AIC BIC LR Chisq Df Pr(>Chisq)
#> hauser.indep 6390.8 6401.8 6170.1 16 < 2.2e-16 ***
#> hauser.UA 2503.4 2515.6 2280.7 15 < 2.2e-16 ***
#> hauser.roweff 2308.9 2324.7 2080.2 12 < 2.2e-16 ***
#> hauser.RC 920.2 939.7 685.4 9 < 2.2e-16 ***
#> hauser.quasi 914.1 931.1 683.3 11 < 2.2e-16 ***
#> hauser.CR 318.6 334.5 89.9 12 5.131e-14 ***
#> hauser.UAdiag 305.7 324.0 73.0 10 1.161e-11 ***
#> hauser.CRdiag 298.9 318.5 64.2 9 2.030e-10 ***
#> hauser.topo 295.3 311.1 66.6 12 1.397e-09 ***
#> hauser.qsymm 268.2 291.3 27.4 6 0.0001193 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# or, more simply
LRstats(modlist, sortby="AIC")
#> Likelihood summary table:
#> AIC BIC LR Chisq Df Pr(>Chisq)
#> hauser.indep 6390.8 6401.8 6170.1 16 < 2.2e-16 ***
#> hauser.UA 2503.4 2515.6 2280.7 15 < 2.2e-16 ***
#> hauser.roweff 2308.9 2324.7 2080.2 12 < 2.2e-16 ***
#> hauser.RC 920.2 939.7 685.4 9 < 2.2e-16 ***
#> hauser.quasi 914.1 931.1 683.3 11 < 2.2e-16 ***
#> hauser.CR 318.6 334.5 89.9 12 5.131e-14 ***
#> hauser.UAdiag 305.7 324.0 73.0 10 1.161e-11 ***
#> hauser.CRdiag 298.9 318.5 64.2 9 2.030e-10 ***
#> hauser.topo 295.3 311.1 66.6 12 1.397e-09 ***
#> hauser.qsymm 268.2 291.3 27.4 6 0.0001193 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
mods <- substring(rownames(sumry),8)
with(sumry,
{plot(Df, AIC, cex=1.3, pch=19, xlab='Degrees of freedom', ylab='AIC')
text(Df, AIC, mods, adj=c(0.5,-.5), col='red', xpd=TRUE)
})