An R Package for Multiple-Group Latent Class Analysis

Description

Fits latent class analysis (LCA) including group variable and covariates. The group variable can be handled either by multilevel LCA described in Vermunt (2003) <DOI:10.1111/j.0081-1750.2003.t01-1-00131.x> or standard LCA at each level of group variable. The covariates can be incorporated in the form of logistic regression (Bandeen-Roche et al. (1997) <DOI:10.1080/01621459.1997.10473658>).

Extracts glca Model Coefficients

Description

Extracts regression coefficients of glca model if the model includes covariates.

Usage

## S3 method for class 'glca'
coef(
  object,
  intercept = FALSE,
  digits = max(3, getOption("digits") - 3),
  show.signif.stars = getOption("show.signif.stars"),
  ...
)

Arguments

Value

Coefficient matrix from the glca model

If the model has calculated standard errors, coefficient matrix contains standard errors, t-statistic, and its p-value.

See Also

glca

Examples

## For examples see example(glca)

Fits Latent Class Models for Data Containing Group Variable and Covariates

Description

Function for fitting latent class models with multiple groups, which may or may not include latent class structure for group variable.

Usage

glca(
  formula,
  group = NULL,
  data = NULL,
  nclass = 3,
  ncluster = NULL,
  std.err = TRUE,
  measure.inv = TRUE,
  coeff.inv = TRUE,
  init.param = NULL,
  n.init = 10,
  decreasing = FALSE,
  testiter = 50,
  maxiter = 5000,
  eps = 1e-06,
  na.rm = FALSE,
  seed = NULL,
  verbose = TRUE
)

Arguments

Details

The glca is the function for implementing LCA consist of two-type latent categorical variables (i.e., level-1 and level-2 latent class). The level-1 (individual-level) latent class is identified by the association among the individuals' responses to multiple manifest items, but level-2 (group-level) latent class is categorized by the prevalence of level-1 latent class for group variable. The function glca can handle two types of covariates: level-1 and level-2 covariates. If covariates vary across individuals, they are considered as level-1 covariates. When group and ncluster (>1) are given, covariates which are varying across groups are considered as level-2 covariates. Both types of covariates have effect on level-1 class prevalence.

The formula should consist of an ~ operator between two sides. Manifest items should be indicated in LHS of formula using item function and covariates should be specified in RHS of formula. For example,
item(y1, y2, y3) ~ 1
item(y1, y2, y3) ~ x1 + x2
where the first fomula indicates LCA with three manifest variables (y1, y2, and y3) and no covariate, and the second formula includes two covariates (x1 and x2). Two types of covariates (i.e., level-1 and level-2 covariates) will be automatically detected by glca.

The estimated parameters in glca are rho, gamma, delta, and beta. The set of item response probabilities for each level-1 class is rho. The sets of prevalences for level-1 and level-2 class are gamma and delta, respectively. The prevalence for level-1 class (i.e., gamma) can be modeled as logistic regression using level-1 and/or level-2 covariates. The set of logistic regression coefficients is beta in glca output.

Value

glca returns an object of class "glca".

The function summary prints estimates for parameters and glca.gof function gives goodness of fit measures for the model.

An object of class "glca" is a list containing the following components:

References

Vermunt, J.K. (2003) Multilevel latent class models. Sociological Methodology, 33, 213–239. doi:10.1111/j.0081-1750.2003.t01-1-00131.x

Collins, L.M. and Lanza, S.T. (2009) Latent Class and Latent Transition Analysis: With Applications in the Social, Behavioral, and Health Sciences. John Wiley & Sons Inc.

See Also

gss08 nyts18

Examples

##
## Example 1. GSS dataset
##
data("gss08")
# LCA
lca = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
            data = gss08, nclass = 3, n.init = 1)
summary(lca)

# LCA with covariate(s)
lcr = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ AGE,
           data = gss08, nclass = 3, n.init = 1)
summary(lcr)
coef(lcr)


# Multiple-group LCA (MGLCA)
mglca = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
             group = DEGREE, data = gss08, nclass = 3, n.init = 1)
summary(mglca)

# Multiple-group LCA with covariate(s) (MGLCR)
mglcr = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ SEX,
             group = DEGREE, data = gss08, nclass = 3, n.init = 1)
summary(mglcr)
coef(mglcr)


##
## Example 2. NYTS dataset
##
data("nyts18")
# Multilevel LCA (MLCA)
mlca = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ 1,
            group = SCH_ID, data = nyts18, nclass = 3, ncluster = 2, n.init = 1)
summary(mlca)

# MLCA with covariate(s) (MLCR)
# (SEX: level-1 covariate, SCH_LEV: level-2 covariate)
mlcr = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ SEX + SCH_LEV,
            group = SCH_ID, data = nyts18, nclass = 3, ncluster = 2, n.init = 1)
coef(mlcr)

Goodness of Fit Tests for Fitted glca Model

Description

Provides AIC, BIC, entropy and deviance statitistic for goodness of fit test for the fitted model. Given object2, the function computes the log-likelihood ratio (LRT) statisic for comparing the goodness of fit for two models. The bootstrap p-value can be obtained from the empirical distribution of LRT statistic by choosing test = "boot".

Usage

gofglca(
  object,
  ...,
  test = NULL,
  nboot = 50,
  criteria = c("AIC", "BIC", "entropy"),
  maxiter = 500,
  eps = 1e-04,
  seed = NULL,
  verbose = FALSE
)

Arguments

Value

gtable, which is always included in output of this function, includes goodness-of-fit criteria which are indicated criteria arguments for the object(s). dtable are contained when the objects are competing models. (when used items of the models are identical) dtable prints deviance and p-value. (bootstrap or chi-square) Lastly, when the boostrap sample is used, the G^2-statistics for each bootstrap samples will be included in return object..

References

Akaike, H. (1974) A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723. doi:10.1109/tac.1974.1100705

Schwarz, G. (1978) Estimating the dimensions of a model. The Annals of Statistics, 6, 461–464. doi:10.1214/aos/1176344136

Langeheine, R., Pannekoek, J., and van de Pol, F. (1996) Bootstrapping goodness-of-fit measures in categorical data analysis. Sociological Methods and Research. 24. 492-516. doi:10.1177/0049124196024004004

Ramaswamy, V., Desarbo, W., Reibstein, D., & Robinson, W. (1993). An Empirical Pooling Approach for Estimating Marketing Mix Elasticities with PIMS Data. Marketing Science, 12(1), 103-124. doi:10.1287/mksc.12.1.103

See Also

glca gss08 nyts18

Examples

## Example 1.
## Model selection between two LCA models with different number of latent classes.
data(gss08)
class2 = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
              data = gss08, nclass = 2,  n.init = 1)
class3 = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
              data = gss08, nclass = 3,  n.init = 1)
class4 = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
              data = gss08, nclass = 4,  n.init = 1)

gofglca(class2, class3, class4)
## Not run: gofglca(class2, class3, class4, test = "boot")

## Example 2.
## Model selection between two MLCA models with different number of latent clusters.
cluster2 = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ 1,
                group = SCH_ID, data = nyts18, nclass = 2, ncluster = 2, n.init = 1)
cluster3 = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ 1,
                group = SCH_ID, data = nyts18, nclass = 2, ncluster = 3, n.init = 1)

gofglca(cluster2, cluster3)
## Not run: gofglca(cluster2, cluster3, test = "boot")

## Example 3.
## MGLCA model selection under the measurement (invariance) assumption across groups.
measInv = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
               group = DEGREE, data = gss08, nclass = 3, n.init = 1)
measVar = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
               group = DEGREE, data = gss08, nclass = 3, n.init = 1, measure.inv = FALSE)

gofglca(measInv, measVar)

General Social Study (GSS) 2008

Description

This dataset includes 6 manifest items about abortion and several covariates from 355 respondents to the 2008 General Social Survey. Respondents answer the questions whether or not think it should be possible for a pregnant woman to obtain a legal abortion. The covariates include age, sex, race, region, and degree of respondents.

Format

A data frame with 355 observations on 11 variables.

DEFECT

If there is a strong chance of serious defect in the baby?

HLTH

If the womans own health is seriously endangered by the pregnancy?

RAPE

If she became pregnant as a result of rape?

POOR

If the family has a very low income and cannot afford any more children?

SINGLE

If she is not married and does not want to marry the man?

NOMORE

If she is married and does not want any more children?

AGE

Respondent's age

SEX

Respondent's race

RACE

Respondent's sex

REGION

Region of interview

DEGREE

Respondent's degree

Source

https://gss.norc.org/

References

Smith, Tom W, Peter Marsden, Michael Hout, and Jibum Kim. General Social Surveys, 2008/Principal Investigator, Tom W. Smith; Co-Principal Investigator, Peter V. Marsden; Co-Principal Investigator, Michael Hout; Sponsored by National Science Foundation. -NORC ed.- Chicago: NORC at the University of Chicago

Examples

data("gss08")
# Model 1: LCA
lca = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
           data = gss08, nclass = 3)
summary(lca)

# Model 2: LCA with a covariate
lcr = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ SEX,
           data = gss08, nclass = 3)
summary(lcr)
coef(lcr)

# Model 3: MGLCA
mglca = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
             group = REGION, data = gss08, nclass = 3)

# Model 4: MGLCA with covariates
summary(mglca)
mglcr = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ AGE,
             group = SEX, data = gss08, nclass = 3)
summary(mglcr)
coef(mglcr)

Specifies Manifest Items for glca

Description

Specifying manifest items in formula of glca function.

Usage

item(..., starts.with = NULL, ends.with = NULL)

Arguments

Value

a matrix of specified variables, which contains names and levels of manifest items.

See Also

glca

Examples

## For examples see example(glca)

National Youth Tobacco Survey (NYTS) 2018

Description

This dataset includes 5 manifest items about abortion and several covariates. From the original 2018 National Youth Tobacco Survey data, the Non Hispanic, white students are selected and schools with 30-50 students were selected. Thus, the dataset has 1743 respondents. The covariates include the sex of the respondents and the school ID to which the respondnets belong, and the level of the corresponding school.

Format

A data frame with 1734 observations on the following 8 variables.

ECIGT

Whether to have tried cigarette smoking, even one or two puffs

ECIGAR

Whether to have ever tried cigar smoking, even one or two puffs

ESLT

Whether to have used chewing tobacco, snuff, or dip

EELCIGT

Whether to have used electronic cigarettes or e-cigarettes

EHOOKAH

Whether to have tried smoking tobacco from a hookah or a waterpipe

SEX

Respondent's Sex

SCH_ID

School ID to which the respondent belongs

SCH_LEV

Level of the corresponding school

Source

https://www.cdc.gov/tobacco/

Examples

data("nyts18")

# Model 1: LCA
lca = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ 1,
           data = nyts18, nclass = 3)
summary(lca)

# Model 2: LCR
lca = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ SEX,
           data = nyts18, nclass = 3)
summary(lca)
coef(lca)

# Model 3: MGLCA
mglca = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ 1,
             group = SEX, data = nyts18, nclass = 3)
summary(mglca)

# Model 4: MLCA
mlca = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ 1,
   group = SCH_ID, data = nyts18, nclass = 3, ncluster = 2)
summary(mlca)

# Model 5: MLCA with level-1 covariate(s) only
mlcr = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ SEX,
            group = SCH_ID, data = nyts18, nclass = 3, ncluster = 2)
summary(mlcr)
coef(mlcr)

# Model 6: MLCA with level-1 and level-2 covariate(s)
# (SEX: level-1 covariate, PARTY: level-2 covariate)
mlcr2 = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ SEX + SCH_LEV,
             group = SCH_ID, data = nyts18, nclass = 3, ncluster = 2)
summary(mlcr2)
coef(mlcr2)

Plots the Estimated Parameters of Fitted glca Model

Description

plot method for class "glca".

Usage

## S3 method for class 'glca'
plot(x, ask = TRUE, ...)

Arguments

Value

This function plots estimated parameters of model.

See Also

glca gss08 nyts18

Examples

## Not run: 
# LCA
lca = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
            data = gss08, nclass = 3, na.rm = TRUE)
plot(lca)

# Multitple Group LCA (MGLCA)
mglca1 = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
             group = DEGREE, data = gss08, nclass = 3)
plot(mglca1)

# Multitple Group LCA (MGLCA) (measure.inv = FALSE)
mglca2 = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
             group = DEGREE, data = gss08, nclass = 3, measure.inv = FALSE)
plot(mglca2)
plot(mglca2, "all")

# Multilvel LCA (MLCA)
mlca = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ 1,
            group = SCH_ID, data = nyts18, nclass = 3, ncluster = 3)
plot(mlca)

## End(Not run)

Reorders the estimated parameters of glca model

Description

Function for reordering the estimated parameters for glca model.

Usage

## S3 method for class 'glca'
reorder(x, class.order = NULL, cluster.order = NULL, decreasing = TRUE, ...)

Arguments

Details

Since the latent classes or clusters can be switched according to the initial value of EM algorithm, the order of estimated parameters can be arbitrary.

Examples

lca = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
            data = gss08, nclass = 3, na.rm = TRUE)
plot(lca)

# Given ordering number
lca321 = reorder(lca, 3:1)
plot(lca321)

# Descending order
dec_lca = reorder(lca, decreasing = TRUE)
plot(dec_lca)

# Ascending order
inc_lca = reorder(lca, decreasing = FALSE)
plot(inc_lca)

Summarizes the Estimated Parameters of Fitted glca Model

Description

summary method for class "glca".

Usage

## S3 method for class 'glca'
summary(object, digits = max(3, getOption("digits") - 3), ...)

Arguments

Value

This function prints decriptions of model and its more detailed estimated parameters but returns NULL.

See Also

glca

Examples

## For examples see example(glca)