multiLCA: Estimates and plots single- and multilevel latent class...

View source: R/MLCAfunctions.R

multiLCAR Documentation

Estimates and plots single- and multilevel latent class models

Description

The multiLCA function in the multilevLCA package estimates single- and multilevel measurement and structural latent class models. Moreover, the function performs two different strategies for model selection. Methodological details can be found in Bakk et al. (2022), Bakk and Kuha (2018), and Di Mari et al. (2023).

Different output visualization tools are available for all model specifications. See, e.g., plot.multiLCA.

Usage

multiLCA(
data,
Y,
iT,
id_high = NULL,
iM = NULL,
Z = NULL,
Zh = NULL,
extout = FALSE,
dataout = TRUE,
kmea = TRUE,
sequential = TRUE,
numFreeCores = 2,
maxIter = 1e3,
tol = 1e-8,
reord = TRUE,
fixedpars = 1,
NRmaxit = 100,
NRtol = 1e-6,
verbose = TRUE
)

Arguments

data

Input matrix or dataframe.

Y

Names of data columns with indicators.

iT

Number of lower-level latent classes.

id_high

Name of data column with higher-level id. Default: NULL.

iM

Number of higher-level latent classes. Default: NULL.

Z

Names of data columns with lower-level covariates (non-numeric covariates are treated as nominal). Default: NULL.

Zh

Names of data columns with higher-level covariates (non-numeric covariates are treated as nominal). Default NULL

extout

Whether to output extensive model and estimation information. Default: FALSE.

dataout

Whether to match class predictions to the observed data. Default: TRUE.

kmea

Whether to compute starting values for single-level model using K-means (TRUE), which is recommended for algorithmic stability, or K-modes (FALSE). Default: TRUE.

sequential

Whether to perform sequential model selection (TRUE) or parallelized model selection (FALSE). Default: TRUE.

numFreeCores

If performing parallelized model selection, the number of CPU cores to keep free. Default: 2.

maxIter

Maximum number of iterations for EM algorithm. Default: 1e3.

tol

Tolerance for EM algorithm. Default: 1e-8.

reord

Whether to (re)order classes in decreasing order according to probability of scoring yes on all items. Default: TRUE.

fixedpars

One-step estimator (0), two-step estimator (1) or two-stage estimator (2). Default: 1.

NRmaxit

Maximum number of iterations for Newton-Raphson algorithm. Default: 100.

NRtol

Tolerance for Newton-Raphson algorithm. Default: 1e-6.

verbose

Whether to print estimation progress. Default: TRUE.

Details

The indicator columns may be coded as as consecutive sequence of integers from 0, or as characters.

To directly estimate a latent class model, iT and (optionally) iM should be specified as a single positive integer. To perform model selection over range of consecutive positive integers as the number of latent classes, iT and/or iM may be specified in the form iT_min:iT_max and/or iM_min:iM_max. It is possible to specify iT = iT_min:iT_max with either iM = NULL or iM equal to a single positive integer, iM = iM_min:iM_max with iT equal to a single positive integer, or iT = iT_min:iT_max with iM = iM_min:iM_max. All model selection procedures return the output of the optimal model based on the BIC.

In the case where both iT and iM are defined as a range of consecutive positive integers, model selection can be performed using the sequential three-stage approach (Lukociene et al., 2010) or a simultaneous approach. The sequential approach involves (first step) estimating iT_min:iT_max single-level models and identifying the optimal alternative iT_opt1 based on the BIC, (second step) estimating iM_min:iM_max|iT = iT_opt1 multilevel models and identifying the optimal alternative iM_opt2 based on the higher-level BIC, and (third step) estimating iT_min:iT_max|iM = iM_opt2 multilevel models and identifying the optimal alternative iT_opt3 based on the lower-level BIC. The simultaneous approach involves devoting multiple CPU cores on the local machine to estimate all combinations in iT = iT_min:iT_max, iM = iM_min:iM_max and identifying the optimal alternative based on the lower-level BIC.

Value

Single-level model estimation returns (if extout = TRUE, a subset):

vPi

Class proportions

mPhi

Response probabilities given the latent classes

mU

Matrix of posterior class assignment (proportional assignment)

mU_modal

Matrix of posterior class assignment (modal assignment)

vU_modal

Vector of posterior class assignment (modal assignment)

mClassErr

Expected number of classification errors

mClassErrProb

Expected proportion of classification errors

AvgClassErrProb

Average of mClassErrProb

R2entr

Entropy-based R^2

BIC

Bayesian Information Criterion (BIC)

AIC

Akaike Information Criterion (AIC)

vGamma

Intercepts in logistic parametrization for class proportions

mBeta

Intercepts in logistic parametrization for response probabilities

parvec

Vector of logistic parameters

SEs

Standard errors

Varmat

Variance-covariance matrix

iter

Number of iterations for EM algorithm

eps

Difference between last two elements of log-likelihood sequence for EM algorithm

LLKSeries

Full log-likelihood series for EM algorithm

mScore

Contributions to log-likelihood score

spec

Model specification

Single-level model estimation with covariates returns (if extout = TRUE, a subset):

mPi

Class proportions given the covariates

vPi_avg

Sample average of mPi

mPhi

Response probabilities given the latent classes

mU

Matrix of posterior class assignment (proportional assignment)

mClassErr

Expected number of classification errors

mClassErrProb

Expected proportion of classification errors

AvgClassErrProb

Average of mClassErrProb

R2entr

Entropy-based R^2

BIC

Bayesian Information Criterion (BIC)

AIC

Akaike Information Criterion (AIC)

cGamma

Intercept and slope parameters in logistic models for conditional class membership

mBeta

Intercepts in logistic parametrization for response probabilities

parvec

Vector of logistic parameters

SEs_unc

Uncorrected standard errors

SEs_cor

Corrected standard errors

SEs_cor_gamma

Corrected standard errors only for the gammas

mQ

Cross-derivatives for asymptotic standard error correction in two-step estimation (see Bakk & Kuha, 2018; Di Mari et al., 2023)

Varmat_unc

Uncorrected variance-covariance matrix

Varmat_cor

Corrected variance-covariance matrix

mV2

Inverse of information matrix for structural model

iter

Number of iterations for EM algorithm

eps

Difference between last two elements of log-likelihood sequence for EM algorithm

LLKSeries

Full log-likelihood series for EM algorithm

spec

Model specification

Multilevel model estimation returns (if extout = TRUE, a subset):

vOmega

Higher-level class proportions

mPi

Lower-level class proportions given the higher-level latent classes

mPhi

Response probabilities given the lower-level latent classes

cPMX

Posterior joint class assignment (proportional assignment)

cLogPMX

Log of cPMX

cPX

Posterior lower-level class assignment given high-level class membership (proportional assignment)

cLogPX

Log of cPX

mSumPX

Posterior higher-level class assignment for lower-level units after marginalization over the lower-level classes (proportional assignment)

mPW

Posterior higher-level class assignment for higher-level units (proportional assignment)

mlogPW

Log of mPW

mPW_N

Posterior higher-level class assignment for lower-level units (proportional assignment)

mPMsumX

Posterior lower-level class assignment for lower-level units after marginalization over the higher-level classes (proportional assignment)

R2entr_low

Lower-level entropy-based R^2

R2entr_high

Higher-level entropy-based R^2

BIClow

Lower-level Bayesian Information Criterion (BIC)

BIChigh

Higher-level Bayesian Information Criterion (BIC)

ICL_BIClow

Lower-level BIC-type approximation the integrated complete likelihood

ICL_BIChigh

Higher-level BIC-type approximation the integrated complete likelihood

AIC

Akaike Information Criterion (AIC)

vAlpha

Intercepts in logistic parametrization for higher-level class proportions

mGamma

Intercepts in logistic parametrization for conditional lower-level class proportions

mBeta

Intercepts in logistic parametrization for response probabilities

parvec

Vector of logistic parameters

SEs

Standard errors

Varmat

Variance-covariance matrix

Infomat

Expected information matrix

iter

Number of iterations for EM algorithm

eps

Difference between last two elements of log-likelihood sequence for EM algorithm

LLKSeries

Full log-likelihood series for EM algorithm

vLLK

Current log-likelihood for higher-level units

mScore

Contributions to log-likelihood score

spec

Model specification

Multilevel model estimation with lower-level covariates returns (if extout = TRUE, a subset):

vOmega

Higher-level class proportions

mPi

Lower-level class proportions given the higher-level latent classes and the covariates

mPi_avg

Sample average of mPi

mPhi

Response probabilities given the lower-level latent classes

cPMX

Posterior joint class assignment (proportional assignment)

cLogPMX

Log of cPMX

cPX

Posterior lower-level class assignment given high-level class membership (proportional assignment)

cLogPX

Log of cPX

mSumPX

Posterior higher-level class assignment for lower-level units after marginalization over the lower-level classes (proportional assignment)

mPW

Posterior higher-level class assignment for higher-level units (proportional assignment)

mlogPW

Log of mPW

mPW_N

Posterior higher-level class assignment for lower-level units (proportional assignment)

mPMsumX

Posterior lower-level class assignment for lower-level units after marginalization over the higher-level classes (proportional assignment)

R2entr_low

Lower-level entropy-based R^2

R2entr_high

Higher-level entropy-based R^2

BIClow

Lower-level Bayesian Information Criterion (BIC)

BIChigh

Higher-level Bayesian Information Criterion (BIC)

ICL_BIClow

Lower-level BIC-type approximation the integrated complete likelihood

ICL_BIChigh

Higher-level BIC-type approximation the integrated complete likelihood

AIC

Akaike Information Criterion (AIC)

vAlpha

Intercepts in logistic parametrization for higher-level class proportions

cGamma

Intercept and slope parameters in logistic models for conditional lower-level class membership

mBeta

Intercepts in logistic parametrization for response probabilities

parvec

Vector of logistic parameters

SEs_unc

Uncorrected standard errors

SEs_cor

Corrected standard errors

SEs_cor_gamma

Corrected standard errors only for the gammas

mQ

Cross-derivatives for asymptotic standard error correction in two-step estimation (see Bakk & Kuha, 2018; Di Mari et al., 2023)

Varmat_unc

Uncorrected variance-covariance matrix

Varmat_cor

Corrected variance-covariance matrix

Infomat

Expected information matrix

cGamma_Info

Expected information matrix only for the gammas

mV2

Inverse of information matrix for structural model

iter

Number of iterations for EM algorithm

eps

Difference between last two elements of log-likelihood sequence for EM algorithm

LLKSeries

Full log-likelihood series for EM algorithm

vLLK

Current log-likelihood for higher-level units

mScore

Contributions to log-likelihood score

mGamma_Score

Contributions to log-likelihood score only for the gammas

spec

Model specification

Multilevel model estimation with lower- and higher-level covariates returns (if extout = TRUE, a subset):

mOmega

Higher-level class proportions given the covariates

vOmega_avg

Higher-level class proportions averaged over higher-level units

mPi

Lower-level class proportions given the higher-level latent classes and the covariates

mPi_avg

Sample average of mPi

mPhi

Response probabilities given the lower-level latent classes

cPMX

Posterior joint class assignment (proportional assignment)

cLogPMX

Log of cPMX

cPX

Posterior lower-level class assignment given high-level class membership (proportional assignment)

cLogPX

Log of cPX

mSumPX

Posterior higher-level class assignment for lower-level units after marginalization over the lower-level classes (proportional assignment)

mPW

Posterior higher-level class assignment for higher-level units (proportional assignment)

mlogPW

Log of mPW

mPW_N

Posterior higher-level class assignment for lower-level units (proportional assignment)

mPMsumX

Posterior lower-level class assignment for lower-level units after marginalization over the higher-level classes (proportional assignment)

R2entr_low

Lower-level entropy-based R^2

R2entr_high

Higher-level entropy-based R^2

BIClow

Lower-level Bayesian Information Criterion (BIC)

BIChigh

Higher-level Bayesian Information Criterion (BIC)

ICL_BIClow

Lower-level BIC-type approximation the integrated complete likelihood

ICL_BIChigh

Higher-level BIC-type approximation the integrated complete likelihood

AIC

Akaike Information Criterion (AIC)

mAlpha

Intercept and slope parameters in logistic models for conditional higher-level class membership

cGamma

Intercept and slope parameters in logistic models for conditional lower-level class membership

mBeta

Intercepts in logistic parametrization for response probabilities

parvec

Vector of logistic parameters

SEs_unc

Uncorrected standard errors

SEs_cor

Corrected standard errors

SEs_cor_alpha

Corrected standard errors only for the alphas

SEs_cor_gamma

Corrected standard errors only for the gammas

mQ

Cross-derivatives for asymptotic standard error correction in two-step estimation (see Bakk & Kuha, 2018; Di Mari et al., 2023)

Varmat_unc

Uncorrected variance-covariance matrix

Varmat_cor

Corrected variance-covariance matrix

Infomat

Expected information matrix

cAlpha_Info

Expected information matrix only for the alphas

cGamma_Info

Expected information matrix only for the gammas

mV2

Inverse of information matrix for structural model

iter

Number of iterations for EM algorithm

eps

Difference between last two elements of log-likelihood sequence for EM algorithm

LLKSeries

Full log-likelihood series for EM algorithm

vLLK

Current log-likelihood for higher-level units

mScore

Contributions to log-likelihood score

mAlpha_Score

Contributions to log-likelihood score only for the alphas

mGamma_Score

Contributions to log-likelihood score only for the gammas

spec

Model specification

References

Bakk, Z., & Kuha, J. (2018). Two-step estimation of models between latent classes and external variables. Psychometrika, 83, 871-892.

Bakk, Z., Di Mari, R., Oser, J., & Kuha, J. (2022). Two-stage multilevel latent class analysis with covariates in the presence of direct effects. Structural Equation Modeling: A Multidisciplinary Journal, 29(2), 267-277.

Di Mari, Bakk, Z., R., Oser, J., & Kuha, J. (2023). A two-step estimator for multilevel latent class analysis with covariates. Psychometrika.

Lukociene, O., Varriale, R., & Vermunt, J. K. (2010). The simultaneous decision(s) about the number of lower-and higher-level classes in multilevel latent class analysis. Sociological Methodology, 40(1), 247-283.

Examples


# Use the artificial data set
data = dataTOY

# Define vector with names of columns with items
Y = colnames(data)[1+1:10]

# Define name of column with higher-level id
id_high = "id_high"

# Define vector with names of columns with lower-level covariates
Z = c("Z_low")

# Define vector with names of columns with higher-level covariates
Zh = c("Z_high")

# Single-level 3-class LC model with covariates
out = multiLCA(data, Y, 3, Z = Z, verbose = FALSE)
out

# Multilevel LC model
out = multiLCA(data, Y, 3, id_high, 2, verbose = FALSE)
out

# Multilevel LC model lower-level covariates
out = multiLCA(data, Y, 3, id_high, 2, Z, verbose = FALSE)
out

# Multilevel LC model lower- and higher-level covariates
out = multiLCA(data, Y, 3, id_high, 2, Z, Zh, verbose = FALSE)
out

# Model selection over single-level models with 1-3 classes
out = multiLCA(data, Y, 1:3, verbose = FALSE)
out

# Model selection over multilevel models with 1-3 lower-level classes and
# 2 higher-level classes
out = multiLCA(data, Y, 1:3, id_high, 2, verbose = FALSE)
out

# Model selection over multilevel models with 3 lower-level classes and 
# 1-2 higher-level classes
out = multiLCA(data, Y, 3, id_high, 1:2, verbose = FALSE)
out

# Model selection over multilevel models with 1-3 lower-level classes and 
# 1-2 higher-level classes using the default sequential approach
out = multiLCA(data, Y, 1:3, id_high, 1:2, verbose = FALSE)
out


multilevLCA documentation built on June 22, 2024, 7:38 p.m.