This dataset contains responses from the General Social Survey (GSS) for the years 1976 and 1977, focusing on social status and tolerance towards minorities
The latent class models can be fitted using this dataset replicate the analysis carried on McCutcheon (1985) and Bakk et al. (2014).
The data contains some covariates including year of the interview, age, sex, race, degree, and income of respondents.
The variables associating social status include father's occupation and education level, and mother's education level, while the variables associating tolerance towards minorities are created by agreeing three related questions: (1) allowing public speaking, (2) allowing teaching, and (3) allowing literatures.
Format
A data frame with 2942 rows and 14 variables:
YEARInterview year (1976, 1977)
COHORTRespondent's age
levels: (1)YOUNG, (2)YOUNG-MIDDLE, (4)MIDDLE, (5)OLDSEXRespondent's sex
levels: (1)MALE, (2)FEMALERACERespondent's race
levels: (1)WHITE(2)BLACK, (3)OTHERDEGREERespondent's degree
levels: (1)LT HS, (2)HIGH-SCH, (3)HIGHERREALRINCIncome of respondents
PAPRESFather's prestige (occupation)
levels: (1)LOW, (2)MIDIUM, (2)HIGHPADEGFather's degree
levels: (1)LT HS, (2)HIGH-SCH, (3)COLLEGE, (4)BACHELOR, (5)GRADUATEMADEGMother's degree
levels: (1)LT HS, (2)HIGH-SCH, (3)COLLEGE, (4)BACHELOR, (5)GRADUATETOLRACTolerance towards racists
TOLCOMTolerance towards communists
TOLHOMOTolerance towards homosexuals
TOLATHTolerance towards atheists
TOLMILTolerance towards militarists
References
Bakk Z, Kuha J. (2021) Relating latent class membership to external variables: An overview. Br J Math Stat Psychol. 74(2):340-362.
McCutcheon, A. L. (1985). A latent class analysis of tolerance for nonconformity in the American public. Public Opinion Quarterly, 49, 474–488.
Examples
library(magrittr)
data <- gss7677[gss7677$RACE == "BLACK",]
model_stat <- slca(status(3) ~ PAPRES + PADEG + MADEG) %>%
estimate(data = data, control = list(verbose = FALSE))
summary(model_stat)
#> Structural Latent Class Model
#>
#> Summary of analysis
#>
#> Number of observations 287
#> Number of manifest variables 3
#> Number of latent class variables 1
#>
#>
#> Summary of model structure
#>
#> Latent variables (Root*):
#> Label: status*
#> nclass: 3
#>
#> Measurement model:
#> status -> { PAPRES, PADEG, MADEG } a
#>
#>
#> Summary of manifest variables
#>
#> Categories for each variable:
#> response
#> 1 2 3 4 5
#> PAPRES LOW MIDIUM HIGH
#> PADEG LT-HS HIGH-SCH COLLEGE BACHELOR GRADUATE
#> MADEG LT-HS HIGH-SCH COLLEGE BACHELOR GRADUATE
#>
#> Frequencies for each categories:
#> response
#> 1 2 3 4 5 <NA>
#> PAPRES 80 114 8 85
#> PADEG 155 27 1 2 102
#> MADEG 183 44 4 4 1 51
#>
#>
#> Summary of model fit
#>
#> Number of free parameters 32
#> Log-likelihood -387.769
#> Information criteria
#> Akaike (AIC) 839.537
#> Bayesian (BIC) 956.641
#> Chi-squared Tests
#> Residual degree of freedom (df) 42
#> Pearson Chi-squared (X-squared) 4531545579066822527179116041846117901058120351744.000
#> P(>Chi) 0.000
#> Likelihood Ratio (G-squared) 31.612
#> P(>Chi) 0.879
param(model_stat)
#> PI :
#> (status)
#> class
#> 1 2 3
#> 0.1220 0.7684 0.1095
#>
#> RHO :
#> (a)
#> class
#> response 1 2 3
#> 1(V1) 0.0000 0.4526 0.4220
#> 2 0.7896 0.5474 0.4422
#> 3 0.2104 0.0000 0.1358
#> 1(V2) 0.5849 1.0000 0.0000
#> 2 0.4151 0.0000 0.8546
#> 3 0.0000 0.0000 0.0485
#> 4 0.0000 0.0000 0.0000
#> 5 0.0000 0.0000 0.0969
#> 1(V3) 0.9152 0.8642 0.0000
#> 2 0.0000 0.1358 0.7504
#> 3 0.0000 0.0000 0.1539
#> 4 0.0848 0.0000 0.0572
#> 5 0.0000 0.0000 0.0385
#>
#> V1 V2 V3
#> status PAPRES PADEG MADEG
model_tol <- slca(tol(4) ~ TOLRAC + TOLCOM + TOLHOMO + TOLATH + TOLMIL) %>%
estimate(data = data, control = list(verbose = FALSE))
summary(model_tol)
#> Structural Latent Class Model
#>
#> Summary of analysis
#>
#> Number of observations 287
#> Number of manifest variables 5
#> Number of latent class variables 1
#>
#>
#> Summary of model structure
#>
#> Latent variables (Root*):
#> Label: tol*
#> nclass: 4
#>
#> Measurement model:
#> tol -> { TOLRAC, TOLCOM, TOLHOMO, TOLATH, TOLMIL } a
#>
#>
#> Summary of manifest variables
#>
#> Categories for each variable:
#> response
#> 1 2
#> TOLRAC TOLERANT INTOLERANT
#> TOLCOM TOLERANT INTOLERANT
#> TOLHOMO TOLERANT INTOLERANT
#> TOLATH TOLERANT INTOLERANT
#> TOLMIL TOLERANT INTOLERANT
#>
#> Frequencies for each categories:
#> response
#> 1 2 <NA>
#> TOLRAC 64 216 7
#> TOLCOM 83 184 20
#> TOLHOMO 103 164 20
#> TOLATH 67 212 8
#> TOLMIL 74 203 10
#>
#>
#> Summary of model fit
#>
#> Number of free parameters 23
#> Log-likelihood -644.804
#> Information criteria
#> Akaike (AIC) 1335.609
#> Bayesian (BIC) 1419.777
#> Chi-squared Tests
#> Residual degree of freedom (df) 8
#> Pearson Chi-squared (X-squared) 6.773
#> P(>Chi) 0.561
#> Likelihood Ratio (G-squared) 7.099
#> P(>Chi) 0.526
param(model_tol)
#> PI :
#> (tol)
#> class
#> 1 2 3 4
#> 0.1248 0.5747 0.2272 0.0733
#>
#> RHO :
#> (a)
#> class
#> response 1 2 3 4
#> 1(V1) 1.0000 0.0000 0.4018 0.1747
#> 2 0.0000 1.0000 0.5982 0.8253
#> 1(V2) 0.9714 0.0654 0.3509 1.0000
#> 2 0.0286 0.9346 0.6491 0.0000
#> 1(V3) 0.9003 0.1342 0.5254 0.9531
#> 2 0.0997 0.8658 0.4746 0.0469
#> 1(V4) 1.0000 0.0084 0.4540 0.1852
#> 2 0.0000 0.9916 0.5460 0.8148
#> 1(V5) 0.8657 0.1057 0.2190 0.6944
#> 2 0.1343 0.8943 0.7810 0.3056
#>
#> V1 V2 V3 V4 V5
#> tol TOLRAC TOLCOM TOLHOMO TOLATH TOLMIL
model_lta <- slca(
status(3) ~ PAPRES + PADEG + MADEG,
tol(4) ~ TOLRAC + TOLCOM + TOLHOMO + TOLATH + TOLMIL,
status ~ tol
) %>% estimate(data = data, control = list(verbose = FALSE))
summary(model_lta)
#> Structural Latent Class Model
#>
#> Summary of analysis
#>
#> Number of observations 287
#> Number of manifest variables 8
#> Number of latent class variables 2
#>
#>
#> Summary of model structure
#>
#> Latent variables (Root*):
#> Label: status* tol
#> nclass: 3 4
#>
#> Measurement model:
#> status -> { PAPRES, PADEG, MADEG } a
#> tol -> { TOLRAC, TOLCOM, TOLHOMO, TOLATH, TOLMIL } b
#>
#> Structural model:
#> status -> { tol }
#>
#> Dependency constraints:
#> A
#> status -> tol
#>
#> Tree of structural model:
#> status -> tol
#>
#>
#> Summary of manifest variables
#>
#> Categories for each variable:
#> response
#> 1 2 3 4 5
#> PAPRES LOW MIDIUM HIGH
#> PADEG LT-HS HIGH-SCH COLLEGE BACHELOR GRADUATE
#> MADEG LT-HS HIGH-SCH COLLEGE BACHELOR GRADUATE
#> TOLRAC TOLERANT INTOLERANT
#> TOLCOM TOLERANT INTOLERANT
#> TOLHOMO TOLERANT INTOLERANT
#> TOLATH TOLERANT INTOLERANT
#> TOLMIL TOLERANT INTOLERANT
#>
#> Frequencies for each categories:
#> response
#> 1 2 3 4 5 <NA>
#> PAPRES 80 114 8 85
#> PADEG 155 27 1 2 102
#> MADEG 183 44 4 4 1 51
#> TOLRAC 64 216 7
#> TOLCOM 83 184 20
#> TOLHOMO 103 164 20
#> TOLATH 67 212 8
#> TOLMIL 74 203 10
#>
#>
#> Summary of model fit
#>
#> Number of free parameters 61
#> Log-likelihood -1023.309
#> Information criteria
#> Akaike (AIC) 2168.617
#> Bayesian (BIC) 2391.845
#> Chi-squared Tests
#> Residual degree of freedom (df) 2338
#> Pearson Chi-squared (X-squared) 73439981827502899854237373222465416178615306877158727700413671110533637342545223540916196699758629013844421674480676704619484676096.000
#> P(>Chi) 0.000
#> Likelihood Ratio (G-squared) 217.236
#> P(>Chi) 1.000
param(model_lta)
#> PI :
#> (status)
#> class
#> 1 2 3
#> 0.3302 0.1641 0.5057
#>
#> TAU :
#> (A)
#> parent
#> child 1 2 3
#> 1 0.0000 0.3554 0.4029
#> 2 0.2370 0.2294 0.0046
#> 3 0.2182 0.0000 0.5187
#> 4 0.5448 0.4152 0.0738
#>
#> parent status
#> child tol
#>
#> RHO :
#> (a)
#> class
#> response 1 2 3
#> 1(V1) 0.6363 0.2849 0.2726
#> 2 0.3637 0.5246 0.7077
#> 3 0.0000 0.1905 0.0196
#> 1(V2) 1.0000 0.0000 1.0000
#> 2 0.0000 0.9000 0.0000
#> 3 0.0000 0.0333 0.0000
#> 4 0.0000 0.0000 0.0000
#> 5 0.0000 0.0667 0.0000
#> 1(V3) 0.7069 0.3148 0.9719
#> 2 0.2931 0.4839 0.0192
#> 3 0.0000 0.1015 0.0000
#> 4 0.0000 0.0745 0.0089
#> 5 0.0000 0.0254 0.0000
#>
#> V1 V2 V3
#> status PAPRES PADEG MADEG
#> (b)
#> class
#> response 1 2 3 4
#> 1(V1) 0.0001 0.9708 0.0203 0.3774
#> 2 0.9999 0.0292 0.9797 0.6226
#> 1(V2) 0.0603 0.9863 0.0380 0.5803
#> 2 0.9397 0.0137 0.9620 0.4197
#> 1(V3) 0.3006 0.9002 0.0000 0.6755
#> 2 0.6994 0.0998 1.0000 0.3245
#> 1(V4) 0.0454 1.0000 0.0146 0.3932
#> 2 0.9546 0.0000 0.9854 0.6068
#> 1(V5) 0.0000 0.8963 0.1824 0.3582
#> 2 1.0000 0.1037 0.8176 0.6418
#>
#> V1 V2 V3 V4 V5
#> tol TOLRAC TOLCOM TOLHOMO TOLATH TOLMIL
regress(model_lta, status ~ SEX, data)
#> Coefficients:
#> class (Intercept) SEXFEMALE
#> 1/3 -0.430 -0.192
#> 2/3 -1.147 -0.573
# \donttest{
regress(model_lta, status ~ SEX, data, method = "BCH")
#> Coefficients:
#> class (Intercept) SEXFEMALE
#> 1/3 -0.431 -0.299
#> 2/3 -1.154 -0.767
regress(model_lta, status ~ SEX, data, method = "ML")
#> Coefficients:
#> class (Intercept) SEXFEMALE
#> 1/3 -0.651 -0.316
#> 2/3 -1.626 -0.834
# }