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Fit a latent class measurement model (Step 1)

Source: R/tse_lca.R
tse_lca.Rd

Estimates the measurement model: the class sizes and the class-conditional item-response probabilities of the indicators on the left-hand side of formula. This is the first step of three-step estimation; covariates and distal outcomes are related to the classes afterwards, holding this model fixed.

Usage

tse_lca(
  formula,
  data,
  nclass,
  start = NULL,
  missing = c("listwise", "fiml"),
  control = tse_control()
)

Arguments

formula

A formula cbind(Y1, Y2, ...) ~ 1 naming the indicators. The measurement model has no covariates.

data

A data frame.

nclass

Number of latent classes, or a vector of numbers of classes to compare (e.g. 1:6).

start

Optional fixed starting point for the EM algorithm (single nclass only): an integer vector with one class per row of data, or a matrix of item-response probabilities P(Y = k | X = t) with one row per item category (in the order of the indicators) and one column per class, such as item_probs() of a fitted model (whose binary items have one row, P(Y = 1 | X = t)). Bypasses the default k-means initialization.

missing

Handling of missing indicator values: "listwise" (default) drops rows with any missing indicator; "fiml" keeps rows with at least one observed indicator (full-information maximum likelihood).

control

Estimation settings, see tse_control().

Value

For a single nclass, a tseLCA_measurement object (see class_sizes(), item_probs(), posterior(), predict(); it keeps data for tse_classify()); for several, a tseLCA_select object: the enumeration table with the fitted models, see best_model().

Details

With a vector nclass, a model is fitted for each number of classes and the result is a class-enumeration table of fit statistics (see Details).

The number of classes is chosen from the measurement model alone, before any structural variables are considered, typically by the BIC, the interpretability of the classes, and their separation; see Nylund, Asparouhov, and Muthén (2007) and Masyn (2013). The enumeration table reports, for each number of classes, the log-likelihood, number of free parameters, AIC, BIC, sample-size adjusted BIC (SABIC; Sclove 1987), entropy R\(^2\), and the smallest estimated class proportion. The one-class model is the independence model, fitted in closed form.

Indicators may be factors, logicals, character, or numeric codes; their categories are stored with the model and reused when the model is applied to new data (see predict.tseLCA_measurement()) or in later steps.

References

Masyn, K. E. (2013). Latent class analysis and finite mixture modeling. In T. D. Little (Ed.), The Oxford Handbook of Quantitative Methods, Vol. 2, 551–611. Oxford University Press.

Nylund, K. L., Asparouhov, T., & Muthén, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling, 14(4), 535–569. doi:10.1080/10705510701575396

Sclove, S. L. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52(3), 333–343. doi:10.1007/BF02294360

Examples

d <- generate_data(500, "high", "covariate", seed = 1)

# Class enumeration
sel <- tse_lca(cbind(Y1, Y2, Y3, Y4, Y5, Y6) ~ 1, data = d, nclass = 1:4)
sel
#> Latent class enumeration (measurement model)
#> 
#>  nclass logLik npar      AIC      BIC    SABIC entropy.R2 min.class
#>       1  -1966    6 3943.64  3968.93  3949.89          NA    1.0000
#>       2  -1616   13 3257.61  3312.40  3271.13      0.8252    0.4327
#>       3  -1456   20 2951.01* 3035.30* 2971.82*     0.8780    0.3122
#>       4  -1452   27 2958.31  3072.10  2986.40      0.7890    0.1569
#> 
#> * smallest value of each criterion. N = 500 
plot(sel)


# The selected model
m <- best_model(sel, criterion = "BIC")
m
#> Latent class measurement model
#>   Classes: 3   N: 500
#>   Log-lik: -1455.5052 (df = 20)   AIC: 2951.01   BIC: 3035.30
#>   Entropy R²: 0.8780
class_sizes(m)
#>       C1       C2       C3 
#> 0.356968 0.330817 0.312215 
item_probs(m)
#>                C1         C2         C3
#> P(Y1|C) 0.9236633 0.86214325 0.11873274
#> P(Y2|C) 0.9083137 0.92191148 0.11779413
#> P(Y3|C) 0.9147941 0.95708298 0.07311785
#> P(Y4|C) 0.8843251 0.14814076 0.08749354
#> P(Y5|C) 0.8817229 0.13404819 0.11180684
#> P(Y6|C) 0.9174174 0.08892803 0.12521007
head(predict(m, newdata = d[1:5, ]))
#>             C1           C2           C3
#> 1 1.824468e-03 0.9968413220 0.0013342102
#> 2 1.506890e-06 0.0006435223 0.9993549708
#> 3 1.946520e-03 0.8924386567 0.1056148230
#> 4 9.986386e-01 0.0010902070 0.0002712095
#> 5 1.506890e-06 0.0006435223 0.9993549708