Type:	Package
Title:	Structural Modeling for Multiple Latent Class Variables
Version:	1.3.0
Maintainer:	Youngsun Kim <yskstat@gmail.com>
Description:	Provides comprehensive tools for the implementation of Structural Latent Class Models (SLCM), including Latent Transition Analysis (LTA; Linda M. Collins and Stephanie T. Lanza, 2009) <doi:10.1002/9780470567333>, Latent Class Profile Analysis (LCPA; Hwan Chung et al., 2010) <doi:10.1111/j.1467-985x.2010.00674.x>, and Joint Latent Class Analysis (JLCA; Saebom Jeon et al., 2017) <doi:10.1080/10705511.2017.1340844>, and any other extended models involving multiple latent class variables.
License:	GPL (≥ 3)
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.3.1
LinkingTo:	Rcpp
Imports:	DiagrammeR, magrittr, MASS, Rcpp, stats
Depends:	R (≥ 2.10)
URL:	https://kim0sun.github.io/slca/
BugReports:	https://github.com/kim0sun/slca/issues
Suggests:	testthat (≥ 3.0.0)
Config/testthat/edition:	3
NeedsCompilation:	yes
Packaged:	2024-12-12 18:18:21 UTC; kim0sun
Author:	Youngsun Kim [aut, cre], Hwan Chung [aut]
Repository:	CRAN
Date/Publication:	2024-12-13 03:20:02 UTC

slca: An R Package for Structural Modeling for Multiple Latent Class Variables

Description

The slca package provides a comprehensive toolkit for the implementation of Structural Latent Class Models (SLCM). This includes tools for conducting Latent Transition Analysis (LTA), Latent Class Profile Analysis (LCPA), and Joint Latent Class Analysis (JLCA), facilitating the analysis of complex latent structures in statistical data.

Author(s)

Maintainer: Youngsun Kim yskstat@gmail.com (ORCID)

Authors:

• Hwan Chung hwanch@korea.ac.kr (ORCID)

See Also

Useful links:

• https://kim0sun.github.io/slca/

• Report bugs at https://github.com/kim0sun/slca/issues

Adolescent Depression Data from the Add Health Study

Description

This dataset contains responses from the National Longitudinal Study of Adolescent Health (Add Health), focusing on adolescents' experiences with depression. The subjects, who were in Grades 10 and 11 during the 1994–1995 academic year, provided data on at least one measure of adolescent delinquency in Wave I.
These data can be used to replicate the latent class analysis conducted by Collins and Lanza (2009).
The dataset includes five covariates, notably grade level and sex of respondents, along with variables capturing depressive emotions: sadness (S1-S4), feeling disliked (D1-D2), and feelings of failure (F1-F2).
Responses for these variables were initially categorized as "Never," "Sometimes," "Often," or "Most or All of the Time." In this dataset, responses have been recoded as "No" for "Never" and "Yes" for all other responses, providing a longitudinal perspective on adolescent depression across Waves I and II. Variables with the suffix "w1" are from Wave I, while those with the suffix "w2" are from Wave II.

Usage

addhealth

Format

A data frame with 2061 rows and 18 variables:

GRADE

Respondent's grade level at Wave I.

SEX

Respondent's sex
levels: (1)Male, (2)Female.

S1w1, S1w2

I felt that I could not shake off the blues even with help from my family and friends.

S2w1, S2w2

I felt depressed.

S3w1, S3w2

I felt lonely.

S4w1, S4w2

I felt sad.

D1w1, D1w2

People were unfriendly to me.

D2w1, D2w2

I felt that people disliked me

F1w1, F1w2

I thought my life had been a failure.

F2w1, F2w2

I felt life was not worth living

Source

https://addhealth.cpc.unc.edu/data/#public-use

References

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

J.R. Udry. The National Longitudinal Study of Adolescent Health (Add Health), Waves I & II, 1994-1996. Carolina Population Center, University of North Carolina at Chapel Hill, Chapel Hill, NC, 2003.

Examples

library(magrittr)
data <- addhealth[1:300,]
lta5 <- slca(
   DEP1(5) ~ S1w1 + S2w1 + S3w1 + S4w1 + D1w1 + D2w1 + F1w1 + F2w1,
   DEP2(5) ~ S1w2 + S2w2 + S3w2 + S4w2 + D1w2 + D2w2 + F1w2 + F2w2,
   DEP1 ~ DEP2
) %>% estimate(data, control = list(em.tol = 1e-6))
lta5inv <- slca(
   DEP1(5) ~ S1w1 + S2w1 + S3w1 + S4w1 + D1w1 + D2w1 + F1w1 + F2w1,
   DEP2(5) ~ S1w2 + S2w2 + S3w2 + S4w2 + D1w2 + D2w2 + F1w2 + F2w2,
   DEP1 ~ DEP2,
   constraints = c("DEP1", "DEP2")
) %>% estimate(data, control = list(em.tol = 1e-6))

compare(lta5inv, lta5, test = "chisq")
lta5inv %>% param()

Compare Two Fitted slca Models

Description

Conducts a relative model fit test between two fitted SLCM models using the deviance statistic.

Usage

compare(
  model1,
  model2,
  test = c("none", "chisq", "boot"),
  nboot = 50,
  method = c("hybrid", "em", "nlm"),
  plot = FALSE,
  maxiter = 1000,
  tol = 1e-08,
  verbose = FALSE
)

Arguments

Value

A data.frame containing the number of parameters (Df), loglikelihood, AIC, BIC, G-squared statistics, and the residual degree of freedom for each object. If a statistical test is conducted (via test), the resulting p-value for the comparison is also included.

See Also

gof

Examples

library(magrittr)
data <- gss7677[gss7677$COHORT == "YOUNG", ]
stat2 <- slca(status(2) ~ PAPRES + PADEG + MADEG) %>%
   estimate(data = data, control = list(verbose = FALSE))
stat3 <- slca(status(3) ~ PAPRES + PADEG + MADEG) %>%
   estimate(data = data, control = list(verbose = FALSE))
stat4 <- slca(status(4) ~ PAPRES + PADEG + MADEG) %>%
   estimate(data = data, control = list(verbose = FALSE))

gof(stat2, stat3, stat4)
gof(stat2, stat3, stat4, test = "chisq")

gof(stat2, stat3, stat4, test = "boot")


compare(stat3, stat4)
compare(stat3, stat4, test = "chisq")

compare(stat3, stat4, test = "boot")

Confidence Intervals for Model Parameters

Description

Computes confidence intervals for one or more parameters of a fitted model.

Usage

## S3 method for class 'slcafit'
confint(object, parm, level = 0.95, type = c("param", "logit"), ...)

Arguments

Value

A matrix with two columns representing the confidence intervals for the selected parameters. The column names correspond to the specified confidence level:

• ⁠100 * (level / 2)%⁠: The lower bound of the confidence interval.

• ⁠100 * (1 - level / 2)%⁠: The upper bound of the confidence interval.

The level argument determines the confidence level, with common values being 0.95 for a 95% confidence interval and 0.99 for a 99% confidence interval.

Examples

param(nlsy_jlcpa, index = TRUE)
confint(nlsy_jlcpa)
confint(nlsy_jlcpa, 1:4)

Estimate Parameters of an slca Object

Description

Estimates the parameters of a model created using the slca function.

Usage

estimate(x, ...)

## S3 method for class 'slca'
estimate(x,
   data,
   method = c("em", "hybrid", "nlm"),
   fix2zero = NULL,
   control = slcaControl(), ...)

Arguments

Details

The fix2zero argument allows you to constrain specific parameters to zero. Each parameter is associated with a unique index, which can be identified using the param function with the argument index = TRUE. To apply constraints, provide the relevant parameter indices in the fix2zero arguments with vector.

Value

An object of class slcafit containing the following components:

The returned object can be further processed using the param function to extract the estimated parameters or their standard errors. The regress function allows for logistic regression analysis using a three-step approach to evaluate the effects of external variables on latent class variables. Additionally, several other methods are available, including predict.slcafit, reorder.slcafit, gof, and others.

See Also

slca() param() slcaControl()

Examples

m <- slca(lc[3] ~ y1 + y2 + y3 + y4)
pi <- rep(1 / 3, 3)
rho <- c(.9, .1, .9, .1, .9, .1, .9, .1, # class 1
         .9, .1, .9, .1, .1, .9, .1, .9, # class 2
         .1, .9, .1, .9, .1, .9, .1, .9) # class 3
dt <- simulate(m, 200, parm = c(pi, rho))
estimate(m, dt$response)

# Several estimation methods
estimate(m, dt$response, method = "em",
         control = slcaControl(verbose = TRUE)) # default
estimate(m, dt$response, method = "nlm",
         control = slcaControl(verbose = TRUE))
estimate(m, dt$response, method = "hybrid",
         control = slcaControl(verbose = TRUE))

# Parameter restriction
mf <- estimate(m, dt$response)
param(mf, index = TRUE)
mf0 <- estimate(mf, fix2zero = c(4, 6, 8, 10))
param(mf0)

# Estimation control
estimate(m, dt$response, control = slcaControl(nrep = 3, verbose = TRUE))
estimate(m, dt$response, control = slcaControl(init.param = c(pi, rho)))

Goodness-of-Fit Test for Fitted slca Model

Description

Computes the AIC, BIC, and deviance statistic (G-squared) for assessing the goodness-of-fit of a fitted slca model. If the test argument is specified, absolute model fit can be evaluated using deviance statistics.

Usage

gof(object, ...)

## S3 method for class 'slcafit'
gof(
   object, ..., test = c("none", "chisq", "boot"),
   nboot = 100, plot = FALSE,
   maxiter = 100, tol = 1e-6, verbose = FALSE
)

## S3 method for class 'slcafit'
gof(
  object,
  ...,
  test = c("none", "chisq", "boot"),
  nboot = 100,
  plot = FALSE,
  maxiter = 100,
  tol = 1e-06,
  verbose = FALSE
)

Arguments

Value

A data.frame containing the number of parameters (Df), loglikelihood, AIC, BIC, G-squared statistics, and the residual degree of freedom for each object. If a statistical test is performed (using test), the result includes the corresponding p-value.

See Also

compare

Examples

library(magrittr)
data <- gss7677[gss7677$COHORT == "YOUNG", ]
stat2 <- slca(status(2) ~ PAPRES + PADEG + MADEG) %>%
   estimate(data = data, control = list(verbose = FALSE))
stat3 <- slca(status(3) ~ PAPRES + PADEG + MADEG) %>%
   estimate(data = data, control = list(verbose = FALSE))
stat4 <- slca(status(4) ~ PAPRES + PADEG + MADEG) %>%
   estimate(data = data, control = list(verbose = FALSE))

gof(stat2, stat3, stat4)
gof(stat2, stat3, stat4, test = "chisq")

gof(stat2, stat3, stat4, test = "boot")


compare(stat3, stat4)
compare(stat3, stat4, test = "chisq")

compare(stat3, stat4, test = "boot")

GSS 1976-1977 Data on Social Status and Tolerance towards Minorities

Description

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 dataset can be used to replicate the analyses conducted in McCutcheon (1985) and Bakk et al. (2014).
It includes covariates such as interview year, age, sex, race, education level, and income. Social status-related variables include father's occupation and education level, as well as mother's education level. Tolerance towards minorities is measured by agreement with three questions: (1) allowing public speaking, (2) allowing teaching, and (3) allowing literature publication.

Usage

gss7677

Format

A data frame with 2942 rows and 14 variables:

YEAR

Interview year (1976, 1977).

COHORT

Respondent's age cohort.
Levels: (1) YOUNG, (2) YOUNG-MIDDLE, (4) MIDDLE, (5) OLD.

SEX

Respondent's sex.
Levels: (1) MALE, (2) FEMALE.

RACE

Respondent's race.
Levels: (1) WHITE, (2) BLACK, (3) OTHER.

DEGREE

Respondent's education level.
Levels: (1) LT HS, (2) HIGH-SCH, (3) HIGHER.

REALRINC

Respondent's income.

PAPRES

Father's occupational prestige.
Levels: (1) LOW, (2) MEDIUM, (3) HIGH.

PADEG

Father's education level.
Levels: (1) LT HS, (2) HIGH-SCH, (3) COLLEGE, (4) BACHELOR, (5) GRADUATE.

MADEG

Mother's education level.
Levels: (1) LT HS, (2) HIGH-SCH, (3) COLLEGE, (4) BACHELOR, (5) GRADUATE.

TOLRAC

Tolerance towards racists.

TOLCOM

Tolerance towards communists.

TOLHOMO

Tolerance towards homosexuals.

TOLATH

Tolerance towards atheists.

TOLMIL

Tolerance towards militarists.

Source

General Social Survey (GSS) 1976, 1977

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)
gss500 <- gss7677[1:500,] %>% na.omit
model_stat <- slca(status(3) ~ PAPRES + PADEG + MADEG) %>%
   estimate(data = gss500, control = list(em.tol = 1e-6))
summary(model_stat)
param(model_stat)

model_tol <- slca(tol(4) ~ TOLRAC + TOLCOM + TOLHOMO + TOLATH + TOLMIL) %>%
   estimate(data = gss500, control = list(em.tol = 1e-6))
summary(model_tol)
param(model_tol)

model_lta <- slca(
   status(3) ~ PAPRES + PADEG + MADEG,
   tol(4) ~ TOLRAC + TOLCOM + TOLHOMO + TOLATH + TOLMIL,
   status ~ tol
) %>% estimate(data = gss500, control = list(em.tol = 1e-6))
summary(model_lta)
param(model_lta)


regress(model_lta, status ~ SEX, gss500)
regress(model_lta, status ~ SEX, gss500, method = "BCH")
regress(model_lta, status ~ SEX, gss500, method = "ML")

NLSY97 Substance Use Data

Description

This dataset contains substance use behavior data from the National Longitudinal Survey of Youth 1997 (NLSY97) for three years: 1998, 2003, and 2008. The dataset focuses on youth born in 1984 and tracks three types of substance use behaviors: tobacco/cigarette smoking, alcohol drinking, and marijuana use.

Usage

nlsy97

Format

A data frame with 1004 rows and 38 columns:

SEX

Respondent's sex

RACE

Respondent's race

ESMK_98, ESMK_03, ESMK_08

(Ever smoked) Ever smoked in 1998, 2003, and 2008 (0: No, 1: Yes)

FSMK_98, FSMK_03, FSMK_08

(Frequent smoke) Monthly smoking in 1998, 2003, and 2008 (0: No, 1: Yes)

DSMK_98, DSMK_03, DSMK_08

(Daily smoke) Daily smoking in 1998, 2003, and 2008 (0: No, 1: Yes)

HSMK_98, HSMK_03, HSMK_08

(Heavy smoke) 10+ cigarettes per day in 1998, 2003, and 2008 (0: No, 1: Yes)

EDRK_98, EDRK_03, EDRK_08

(Ever drunk) Ever drunk in 1998, 2003, and 2008? (0: No, 1: Yes)

CDRK_98, CDRK_03, CDRK_08

(Current drinker) Monthly drinking in 1998, 2003, and 2008 (0: No, 1: Yes)

WDRK_98, WDRK_03, WDRK_08

(Weakly drinker) 5+ days drinking in a month in 1998, 2003, and 2008 (0: No, 1: Yes)

BDRK_98, BDRK_03, BDRK_08

(Binge drinker) 5+ drinks on the same day at least one time in the last 30 day (0: No, 1: Yes)

EMRJ_98, EMRJ_03, EMRJ_08

(Ever marijuana used) Have you ever used marijuana in 1998, 2003, and 2008? (0: No, 1: Yes)

CMRJ_98, CMRJ_03, CMRJ_08

(Current marijuana user) Monthly marijuana use in 1998, 2003, and 2008 (0: No, 1: Yes)

OMRJ_98, OMRJ_03, OMRJ_08

(Occasional marijuana user) 10+ days marijuana use in a month in 1998, 2003, and 2008 (0: No, 1: Yes)

SMRJ_98, SMRJ_03, SMRJ_08

(School/work marijuana user) Marijuana use before/during school or work in 1998, 2003, and 2008 (0: No, 1: Yes)

Source

National Longitudinal Survey of Youth 1997 (NLSY97)

References

Bureau of Labor Statistics, U.S. Department of Labor. National Longitudinal Survey of Youth 1997 cohort, 1997-2017 (rounds 1-18). Produced and distributed by the Center for Human Resource Research (CHRR), The Ohio State University. Columbus, OH: 2019.

Examples

library(magrittr)
nlsy_smoke <- slca(SMK_98(3) ~ ESMK_98 + FSMK_98 + DSMK_98 + HSMK_98) %>%
   estimate(data = nlsy97, control = list(verbose = FALSE))
summary(nlsy_smoke)


# JLCA
model_jlca <- slca(
   SMK_98(3) ~ ESMK_98 + FSMK_98 + DSMK_98 + HSMK_98,
   DRK_98(3) ~ EDRK_98 + CDRK_98 + WDRK_98 + BDRK_98,
   MRJ_98(3) ~ EMRJ_98 + CMRJ_98 + OMRJ_98 + SMRJ_98,
   SUB_98(4) ~ SMK_98 + DRK_98 + MRJ_98
) %>% estimate(data = nlsy97, control = list(verbose = FALSE))
summary(model_jlca)
param(model_jlca)

# JLCPA
nlsy_jlcpa <- slca(
   SMK_98(3) ~ ESMK_98 + FSMK_98 + DSMK_98 + HSMK_98,
   DRK_98(3) ~ EDRK_98 + CDRK_98 + WDRK_98 + BDRK_98,
   MRJ_98(3) ~ EMRJ_98 + CMRJ_98 + OMRJ_98 + SMRJ_98,
   SUB_98(5) ~ SMK_98 + DRK_98 + MRJ_98,
   SMK_03(3) ~ ESMK_03 + FSMK_03 + DSMK_03 + HSMK_03,
   DRK_03(3) ~ EDRK_03 + CDRK_03 + WDRK_03 + BDRK_03,
   MRJ_03(3) ~ EMRJ_03 + CMRJ_03 + OMRJ_03 + SMRJ_03,
   SUB_03(5) ~ SMK_03 + DRK_03 + MRJ_03,
   SMK_08(3) ~ ESMK_08 + FSMK_08 + DSMK_08 + HSMK_08,
   DRK_08(3) ~ EDRK_08 + CDRK_08 + WDRK_08 + BDRK_08,
   MRJ_08(3) ~ EMRJ_08 + CMRJ_08 + OMRJ_08 + SMRJ_08,
   SUB_08(5) ~ SMK_08 + DRK_08 + MRJ_08,
   PROF(4) ~ SUB_98 + SUB_03 + SUB_08,
   constraints = list(
      c("SMK_98", "SMK_03", "SMK_08"),
      c("DRK_98", "DRK_03", "DRK_08"),
      c("MRJ_98", "MRJ_03", "MRJ_08"),
      c("SUB_98 ~ SMK_98", "SUB_03 ~ SMK_03", "SUB_08 ~ SMK_08"),
      c("SUB_98 ~ DRK_98", "SUB_03 ~ DRK_03", "SUB_08 ~ DRK_08"),
      c("SUB_98 ~ MRJ_98", "SUB_03 ~ MRJ_03", "SUB_08 ~ MRJ_08")
   )
) %>% estimate(nlsy97, control = list(verbose = FALSE))

JLCPA Model Estimated with NLSY97 Data

Description

An slca model estimated using the NLSY97 dataset.

Usage

nlsy_jlcpa

Format

An slcafit object estimated for JLCPA model using nlsy97 dataset.

References

Bureau of Labor Statistics, U.S. Department of Labor. National Longitudinal Survey of Youth 1997 cohort, 1997-2017 (rounds 1-18). Produced and distributed by the Center for Human Resource Research (CHRR), The Ohio State University. Columbus, OH: 2019.

Jeon, S., Seo, T. S., Anthony, J. C., & Chung, H. (2022). Latent Class Analysis for Repeatedly Measured Multiple Latent Class Variables. Multivariate Behavioral Research, 57(2–3), 341–355.

See Also

reorder.slcafit

Print Estimated Parameters of an slcafit Object

Description

Prints the estimated parameters of an slca model using an slcafit object.

Usage

param(object, ...)

## S3 method for class 'slcafit'
param(
   object, type = c("probs", "logit"),
   se = FALSE, index = FALSE, ...
)

Arguments

Value

A list containing the requested estimated parameters or their standard errors (if se = TRUE). The components of the list include:

Model Predictions for Estimated slca Object

Description

Provides predicted class memberships or posterior probabilities for new data based on a fitted slca model.

Usage

## S3 method for class 'slcafit'
predict(object, newdata, type = c("class", "posterior"), ...)

Arguments

Value

A data.frame or list depending on the type:

• For type = "class", a data.frame is returned where rows represent observations and columns correspond to latent class variables.

• For type = "posterior", a list is returned containing data.frames with posterior probabilities for each latent class variable.

Regress Exogenous Variables on Latent Variables

Description

Performs regression analysis to examine the influence of exogenous (external) variables on latent class variables in an estimated slca model. The function uses logistic regression with a three-step approach to account for measurement error.

Usage

regress(object, ...)

## S3 method for class 'slcafit'
regress(
   object, formula, data = parent.frame(),
   imputation = c("modal", "prob"),
   method = c("naive", "BCH", "ML"), ...
)

## S3 method for class 'slcafit'
regress(
  object,
  formula,
  data = parent.frame(),
  imputation = c("modal", "prob"),
  method = c("naive", "BCH", "ML"),
  ...
)

Arguments

Value

A list of class reg.slca with the following components:

The summary function can be used to display the regression coefficients, standard errors, Wald statistics, and p-values.

References

Vermunt, J. K. (2010). Latent Class Modeling with Covariates: Two Improved Three-Step Approaches. Political Analysis, 18(4), 450–469. http://www.jstor.org/stable/25792024

Examples

library(magrittr)
names(nlsy97)
nlsy_jlcpa %>% regress(SMK_98 ~ SEX, nlsy97)

nlsy_jlcpa %>% regress(PROF ~ SEX, nlsy97)

Reorder Latent Class Membership of Latent Class Variables

Description

Reorders the latent class membership for specified latent class variables in an slcafit object.

Usage

## S3 method for class 'slcafit'
reorder(x, ...)

Arguments

Value

A modified slcafit object with the latent classes reordered according to the specified order.

Examples

library(magrittr)
nlsy_jlcpa %>% param

# Reorder the RHO parameters as ascending order
reordered1 <- nlsy_jlcpa %>%
   reorder(SMK_98 = c(1, 3, 2),
           DRK_98 = c(3, 2, 1),
           MRJ_98 = c(3, 1, 2))
reordered1 %>% param
# Label class1: nonuse
#       class2: lifetime use
#       class3: current use

# Reorder the TAU parameters for joint classes as ascending order
reordered2 <- reordered1 %>%
   reorder(SUB_98 = c(3, 4, 5, 1, 2))
reordered2 %>% param
# Label class1: nonuse
#       class2: heavy drinking only
#       class3: not heavy use
#       class4: heavy drinking & smoking
#       class5: heavy use

# Reorder the TAU paramters for profiles as ascending order
reordered3 <- reordered2 %>%
   reorder(PROF = c(4, 1, 3, 2))
reordered3 %>% param
# Label class1: nonuse stayer
#       class2: heavy drinking advancer
#       class3: heavy drk & smk advancer
#       class4: heavy use advancer

Simulate Data from an slca Model

Description

Simulates data based on a specified slca model. If the model parameters are not already estimated, they can either be provided by the user or generated randomly.

Usage

## S3 method for class 'slca'
simulate(object, nsim = 500, seed = NULL, parm, nlevel, ...)

Arguments

Value

A list with the following components:

Examples

m1 <- slca(lc1[3] ~ x1 + x2 + x3 + x4 + x5,
              lc2[4] ~ y1 + y2 + y3 + y4 + y5)
sim <- simulate(m1, 1000)
sapply(sim$class, table)

# simulate data with defined number of levels of manifest items
m2 <- slca(lc1[3] ~ x1 + x2 + x3 + x4)
sim <- simulate(m2, nlevel = c(3, 3, 3, 3))
d <- sim$response
sapply(d, table)

sim <- simulate(m2, nlevel = c(x1 = 2, x3 = 3, x4 = 4, x5 = 5))
d <- sim$response
sapply(d, table)

# simulate data with user-defined parameters
pi <- rep(1 / 3, 3)
rho <- c(.9, .1, .9, .1, .9, .1, .9, .1,
         .9, .1, .9, .1, .1, .9, .1, .9,
         .1, .9, .1, .9, .1, .9, .1, .9)
par <- c(pi, rho)
m3 <- slca(lc[3] ~ y1 + y2 + y3 + y4)
sim <- simulate(m3, parm = par)
mf <- estimate(m3, sim$response)
param(mf)

Construct Structural Latent Class Model

Description

Constructs a latent structure with multiple latent class variables.

Usage

slca(formula = NULL, ..., constraints = NULL)

Arguments

Details

The formula can be categorized into three types, each serving a distinct purpose:

1. Defining Latent Class Variables with Manifest Indicators: Specify the relationship between a latent class variable and its manifest indicators. The latent class variable is on the left-hand side (lhs), denoted with square brackets [] or parentheses () to indicate the number of classes, and manifest indicators are listed on the right-hand side (rhs). For example:

   LC1[k] ~ x1 + x2 + x3
   LC2[k] ~ y1 + y2 + y3
   LC3(k) ~ z1 + z2 + z3
      

   Here, k denotes the number of latent classes for the variable.

2. Relating Latent Class Variables to Each Other: Define relationships where one latent class variable influences another. For example:

   LC2 ~ LC1
      

   This formula implies that LC2 is conditionally dependent on LC1.

3. Defining Higher-Level Latent Class Variables: Specify relationships where a latent class variable is measured by other latent class variables instead of manifest indicators. For example:

   P[k] ~ LC1 + LC2 + LC3
      

   This indicates that the latent variable P is measured by the latent class variables LC1, LC2, and LC3.

In all formulas, variables on the lhs influence those on the rhs.

The constraints argument enforces specific conditions to ensure precise inference, such as measurement invariance. This is particularly useful for longitudinal analysis (eg. LTA or LCPA), where consistent meanings of latent classes across time are essential.

1. Measurement Invariance for the Measurement Model: Ensures probabilities associated with latent class variables remain consistent. For example:

   c("LC1", "LC2", "LC3")
      

   This ensures that LC1, LC2, and LC3 have semantically consistent measurement probabilities.

' 2. Measurement Invariance for the Structural Model: Applies constraints to ensure consistent interpretations of transition probabilities between latent class variables. For example:

c("P ~ LC1", "P -> LC2")
   

This ensures that the transitions from P to LC1 and P to LC2 are consistent.

Value

An object of class slca with the following components:

The printed model description is divided into four parts:

1. Latent variables: Lists the latent class variables and the number of classes for each variable. The root variable is marked with an asterisk (*).

2. Measurement model: Displays manifest indicators for each latent class variable and any applied measurement constraints (lowercase letters indicate consistency).

3. Structural model: Describes the conditional relationships between latent class variables.

4. Dependency constraints: Outlines constraints applied to conditional dependencies, where uppercase letters represent consistent dependency structures.

Examples

# Standard LCA
slca(lc[3] ~ y1 + y2 + y3 + y4)
# Latent transition analysis (LTA)
slca(lx[3] ~ x1 + x2 + x3 + x4,
     ly[2] ~ y1 + y2 + y3 + y4,
     lx ~ ly)
# LTA with measurement invariance
slca(l1[3] ~ y11 + y21 + y31 + y41,
     l2[3] ~ y12 + y22 + y32 + y42,
     l1 ~ l2, constraints = c("l1", "l2"))
# Joint latent class analysis
slca(lx[2] ~ x1 + x2 + x3 + x4,
     ly[3] ~ y1 + y2 + y3 + y4,
     lz[2] ~ z1 + z2 + z3 + z4,
     jc[3] ~ lx + ly + lz)
# Latent class profile analysis (with measurement invariance)
slca(l1[3] ~ x1 + x2 + x3 + x4,
     l2[3] ~ y1 + y2 + y3 + y4,
     l3[3] ~ z1 + z2 + z3 + z4,
     pf[4] ~ l1 + l2 + l3,
     constraints = c("l1", "l2", "l3"))

Control Parameters for slca Estimation

Description

Specifies control parameters for estimating slca model.

Usage

slcaControl(
  em.iterlim = 5000,
  em.tol = 1e-08,
  nlm.iterlim = 1000,
  nlm.tol = 1e-10,
  init.param = NULL,
  nrep = 1,
  test.iter = 500,
  na.rm = FALSE,
  verbose = FALSE
)

Arguments

See Also

slca