Minnesota High School Graduates
Hoyt.RdMinnesota high school graduates of June 1930 were classified with respect to
(a) Rank by thirds in their graduating class, (b) post-high school Status in April 1939 (4 levels), (c) Sex,
(d) father's Occupational status (7 levels, from 1=High to 7=Low).
The data were first presented by Hoyt et al. (1959) and have been analyzed by Fienberg(1980), Plackett(1974) and others.
Usage
data(Hoyt)Format
A 4-dimensional array resulting from cross-tabulating 4 variables for 13968 observations. The variable names and their levels are:
| No | Name | Levels |
| 1 | Status | "College", "School", "Job", "Other" |
| 2 | Rank | "Low", "Middle", "High" |
| 3 | Occupation | "1", "2", "3", "4", "5", "6", "7" |
| 4 | Sex | "Male", "Female" |
Details
Post high-school Status is natural to consider as the response.
Rank and father's Occupation are ordinal variables.
Source
Fienberg, S. E. (1980). The Analysis of Cross-Classified Categorical Data. Cambridge, MA: MIT Press, p. 91-92.
R. L. Plackett, (1974). The Analysis of Categorical Data. London: Griffin.
References
Hoyt, C. J., Krishnaiah, P. R. and Torrance, E. P. (1959) Analysis of complex contingency tables, Journal of Experimental Education 27, 187-194.
See also
minn38 provides the same data as a data frame.
Examples
data(Hoyt)
# display the table
structable(Status + Sex ~ Rank + Occupation, data=Hoyt)
#> Status College School Job Other
#> Sex Male Female Male Female Male Female Male Female
#> Rank Occupation
#> Low 1 87 53 3 7 17 13 105 76
#> 2 72 36 6 16 18 11 209 111
#> 3 52 52 17 28 14 49 541 521
#> 4 88 48 9 18 14 29 328 191
#> 5 32 12 1 5 12 10 124 101
#> 6 14 9 2 1 5 15 148 130
#> 7 20 3 3 1 4 6 109 88
#> Middle 1 216 163 4 30 14 28 118 118
#> 2 159 116 14 41 28 53 227 214
#> 3 119 162 13 64 44 129 578 708
#> 4 158 130 15 47 36 62 304 305
#> 5 43 35 5 11 7 37 119 152
#> 6 24 19 6 13 15 22 131 174
#> 7 41 25 5 9 13 15 88 158
#> High 1 256 309 2 17 10 38 53 89
#> 2 176 225 8 49 22 68 95 210
#> 3 119 243 10 79 33 184 257 448
#> 4 144 237 12 57 20 63 115 219
#> 5 42 72 2 20 7 21 56 95
#> 6 24 42 2 10 4 19 61 105
#> 7 32 36 2 14 4 19 41 93
# mosaic for independence model
plot(Hoyt, shade=TRUE)
# examine all pairwise mosaics
pairs(Hoyt, shade=TRUE)
# collapse Status to College vs. Non-College
Hoyt1 <- collapse.table(Hoyt, Status=c("College", rep("Non-College",3)))
plot(Hoyt1, shade=TRUE)
#################################################
# fitting models with loglm, plotting with mosaic
#################################################
# fit baseline log-linear model for Status as response
require(MASS)
hoyt.mod0 <- loglm(~ Status + (Sex*Rank*Occupation),
data=Hoyt1)
hoyt.mod0
#> Call:
#> loglm(formula = ~Status + (Sex * Rank * Occupation), data = Hoyt1)
#>
#> Statistics:
#> X^2 df P(> X^2)
#> Likelihood Ratio 2080.359 41 0
#> Pearson 2090.750 41 0
mosaic(hoyt.mod0,
gp=shading_Friendly,
main="Baseline model: Status + (Sex*Rank*Occ)")
#> Error in loglm(formula = ~Status + (Sex * Rank * Occupation), data = Hoyt1, fitted = TRUE): object 'Hoyt1' not found
# add one-way association of Status with factors
hoyt.mod1 <- loglm(~ Status * (Sex + Rank + Occupation) + (Sex*Rank*Occupation),
data=Hoyt1)
hoyt.mod1
#> Call:
#> loglm(formula = ~Status * (Sex + Rank + Occupation) + (Sex *
#> Rank * Occupation), data = Hoyt1)
#>
#> Statistics:
#> X^2 df P(> X^2)
#> Likelihood Ratio 50.10913 32 0.02175915
#> Pearson 49.33936 32 0.02578430
mosaic(hoyt.mod1,
gp=shading_Friendly,
main="Status * (Sex + Rank + Occ)")
#> Error in loglm(formula = ~Status * (Sex + Rank + Occupation) + (Sex * Rank * Occupation), data = Hoyt1, fitted = TRUE): object 'Hoyt1' not found
# can we drop any terms?
drop1(hoyt.mod1, test="Chisq")
#> Error in loglm(formula = ~Status + Sex + Rank + Occupation + Status:Rank + Status:Occupation + Sex:Rank + Sex:Occupation + Rank:Occupation + Sex:Rank:Occupation, data = Hoyt1, evaluate = FALSE): object 'Hoyt1' not found
# assess model fit
anova(hoyt.mod0, hoyt.mod1)
#> LR tests for hierarchical log-linear models
#>
#> Model 1:
#> ~Status + (Sex * Rank * Occupation)
#> Model 2:
#> ~Status * (Sex + Rank + Occupation) + (Sex * Rank * Occupation)
#>
#> Deviance df Delta(Dev) Delta(df) P(> Delta(Dev)
#> Model 1 2080.35910 41
#> Model 2 50.10913 32 2030.24997 9 0.00000
#> Saturated 0.00000 0 50.10913 32 0.02176
# what terms to add?
add1(hoyt.mod1, ~.^2, test="Chisq")
#> Error in loglm(formula = ~Status + Sex + Rank + Occupation + Status:Sex + Status:Rank + Status:Occupation + Sex:Rank + Sex:Occupation + Rank:Occupation + Sex:Rank:Occupation + Status:Sex:Rank, data = Hoyt1, evaluate = FALSE): object 'Hoyt1' not found
# add interaction of Sex:Occupation on Status
hoyt.mod2 <- update(hoyt.mod1, ~ . + Status:Sex:Occupation)
mosaic(hoyt.mod2,
gp=shading_Friendly,
main="Adding Status:Sex:Occupation")
#> Error in loglm(formula = ~Status + Sex + Rank + Occupation + Status:Sex + Status:Rank + Status:Occupation + Sex:Rank + Sex:Occupation + Rank:Occupation + Sex:Rank:Occupation + Status:Sex:Occupation, data = Hoyt1, fitted = TRUE): object 'Hoyt1' not found
# compare model fits
anova(hoyt.mod0, hoyt.mod1, hoyt.mod2)
#> LR tests for hierarchical log-linear models
#>
#> Model 1:
#> ~Status + (Sex * Rank * Occupation)
#> Model 2:
#> ~Status * (Sex + Rank + Occupation) + (Sex * Rank * Occupation)
#> Model 3:
#> ~Status + Sex + Rank + Occupation + Status:Sex + Status:Rank + Status:Occupation + Sex:Rank + Sex:Occupation + Rank:Occupation + Sex:Rank:Occupation + Status:Sex:Occupation
#>
#> Deviance df Delta(Dev) Delta(df) P(> Delta(Dev)
#> Model 1 2080.35910 41
#> Model 2 50.10913 32 2030.24997 9 0.00000
#> Model 3 21.01300 26 29.09613 6 0.00006
#> Saturated 0.00000 0 21.01300 26 0.74129
# Alternatively, try stepwise analysis, heading toward the saturated model
steps <- step(hoyt.mod0,
direction="forward",
scope=~Status*Sex*Rank*Occupation)
#> Start: AIC=2166.36
#> ~Status + (Sex * Rank * Occupation)
#>
#> Error in loglm(formula = ~Status + Sex + Rank + Occupation + Sex:Rank + Sex:Occupation + Rank:Occupation + Status:Sex + Sex:Rank:Occupation, data = Hoyt1, evaluate = FALSE): object 'Hoyt1' not found
# display anova
steps$anova
#> Error in eval(expr, envir, enclos): object 'steps' not found