Hauser (1979) Data on Social Mobility

Description

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

Hauser's data was first presented in 1979, and then published in 1980. The name of the dataset reflects the earliest use.

It reflects the "frequencies in a classification of son's first full-time civilian occupation by father's (or other family head's) occupation at son's sixteenth birthday among American men who were aged 20 to 64 in 1973 and were not currently enrolled in school".

As noted in Hauser's Table 1, "Counts are based on observations weighted to estimate population counts and compensate for departures of the sampling design from simple random sampling. Broad occupation groups are upper nonmanual: professional and kindred workers, managers and officials, and non-retail sales workers; lower nonmanual: proprietors, clerical and kindred workers, and retail sales workers; upper manual: craftsmen, foremen, and kindred workers; lower manual: service workers, operatives and kindred workers, and laborers (except farm); farm: farmers and farm managers, farm laborers, and foremen. density of mobility or immobility in the cells to which they refer."

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. Table 1.

References

Powers, D.A. and Xie, Y. (2008). Statistical Methods for Categorical Data Analysis, Bingley, UK: Emerald.

Examples

data(Hauser79)
str(Hauser79)

# display table
structable(~Father+Son, data=Hauser79)

#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-independence
hauser.quasi <-  update(hauser.indep, 
                        ~ . + Diag(Father,Son))
mosaic(hauser.quasi, ~Father+Son, 
       main="Quasi-independence model", 
       gp=shading_Friendly)

# Quasi-symmetry
hauser.qsymm <-  update(hauser.indep, 
                        ~ . + Diag(Father,Son) + Symm(Father,Son))

mosaic(hauser.qsymm, ~Father+Son, 
       main="Quasi-symmetry model", 
       gp=shading_Friendly)


# 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)

# uniform association
hauser.UA <- update(hauser.indep, ~ . + Fscore*Sscore)
LRstats(hauser.UA)

# uniform association, omitting diagonals
hauser.UAdiag <- update(hauser.indep, ~ . + Fscore*Sscore + Diag(Father,Son))
LRstats(hauser.UAdiag)

# 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)

# RC model
hauser.RC <- update(hauser.indep, ~ . + Mult(Father, Son), verbose=FALSE)
mosaic(hauser.RC, ~Father+Son, main="RC model", gp=shading_Friendly)
LRstats(hauser.RC)

# crossings models 
hauser.CR <- update(hauser.indep, ~ . + Crossings(Father,Son))
mosaic(hauser.topo, ~Father+Son, main="Crossings model", gp=shading_Friendly)
LRstats(hauser.CR)

hauser.CRdiag <- update(hauser.indep, ~ . + Crossings(Father,Son) + Diag(Father,Son))
LRstats(hauser.CRdiag)


# 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),]
# or, more simply
LRstats(modlist, sortby="AIC")

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)
	})