The package poLCAExtra offers convenient functions to improve the
workflow of poLCA(Linzer & Lewis,
2011)
# Current development version
remotes::install_github(repo = "quantmeth/poLCAExtra")Either by using many latent class models like
# poLCAExtra has two data sets examples
jd <- ex1.poLCA
# Formula
f1 <- as.formula(cbind(V1, V2, V3, V4, V5, V6) ~ 1)
# Four latent classes analysis of increasing classes
LCA1 <- poLCA(f1, data = jd, nclass = 1, verbose = FALSE)
LCA2 <- poLCA(f1, data = jd, nclass = 2, verbose = FALSE)
LCA3 <- poLCA(f1, data = jd, nclass = 3, verbose = FALSE)
LCA4 <- poLCA(f1, data = jd, nclass = 4, maxiter = 1000, nrep = 10, verbose = FALSE)which can then be compared with
anova(LCA1, LCA2, LCA3, LCA4)## nclass df llike AIC BIC Rel.Entropy LMR p Classes.size
## 1 57 -2687.896 5387.793 5415.900 800
## 2 50 -2463.806 4953.612 5014.512 0.897 426.893 < .001 98|702
## 3 43 -2195.821 4431.642 4525.334 0.840 510.513 < .001 101|345|354
## 4 36 -2190.270 4434.540 4561.025 0.871 10.574 0.158 49|73|324|354
The function readily gathers some relevant statitics to choose the number of classes.
This new version of poLCA can also handle many number of classes and
yield the same output.
LCAE <- poLCA(f1, data = jd, nclass = 1:4)
LCAEBoth previous tables can be easily exported.
The original plot() (from poLCA) function has been updated to
account for the multiple LCA.
plot(LCAE, nclass = 3)
There is also a new plot that works with a single LCA output.
poLCA.plot(LCA3)
Or all the LCA output, which may help to compare diffent number of classes.
poLCA.plot(LCAE)
# If only a subset is required
# poLCA.plot(LCAE, nclass = 2:3)
# poLCA.plot(LCA2, LCA3)The SABIC, CAIC, and AIC3 statistics have been added to poLCA.
LCA3$sabic## [1] 4461.823
LCA3$caic## [1] 4525.359
LCA3$aic3## [1] 4451.642
The relative entropy, which is more often requested than the entropy, has been added.
poLCA.relentropy(LCA3)## [1] 0.8396916
The Lo-Mendell-Rubin adjusted likelihood ratio test and the Vuong-Lo-Mendell-Rubin likelihood ratio test have been added.
poLCA.lrt(LCA3)## $vlmr
## [1] 338.9282
##
## $lmr
## [1] 322.83
##
## $df
## [1] 7
##
## $lmr.p
## [1] 8.005233e-66
##
## $vlmr.p
## [1] 2.885461e-69
The bootstrapped Vuong-Lo-Mendell-Rubin likelihood ratio test which is more generally recommended is also added. Note that the bootstrapped tests are quite time-consuming.
poLCA.blrt(LCAE)## Vuong-Lo-Mendell-Rubin Likelihood Ratio Test
##
## test H0_llik X2loglik_diff npar mean s.e. p
## 2 vs 1 -2687.896 645.222 7 8.503 4.249 < .001
## 3 vs 2 -2365.285 338.928 7 9.423 4.188 < .001
## 4 vs 3 -2195.821 11.102 7 12.085 36.009 0.260
##
## At 95% condidence, blrt recommends 3 classes.
# poLCA.blrt(LCA3)Predicted probabilities and classes
head(round(predict(LCA3), 3))## Pr(Class==1) Pr(Class==2) Pr(Class==3) Pred
## 1 0.004 0.039 0.957 3
## 2 0.003 0.020 0.977 3
## 3 0.005 0.000 0.994 3
## 4 0.003 0.020 0.977 3
## 5 0.001 0.455 0.543 3
## 6 0.001 0.638 0.362 2
# head(round(predict(LCAE, nclass = 3),3))Analysis of residual (also known as Tech10 in Mplus) to investigate local independence.
poLCA.residual.pattern(LCAE, nclass = 3)## The 20 most frequent patterns
##
## pattern observed expected z chi llik.contribution p check
## 111111 200 201.26 -0.09 0.01 -2.50 0.46
## 122121 166 165.34 0.05 0.00 1.32 0.48
## 112121 48 47.67 0.05 0.00 0.66 0.48
## 121121 42 46.13 -0.61 0.37 -7.88 0.27
## 122111 39 37.76 0.20 0.04 2.52 0.42
## 111121 38 32.91 0.89 0.79 10.93 0.19
## 111211 32 30.69 0.24 0.06 2.67 0.41
## 222222 29 28.14 0.16 0.03 1.75 0.44
## 111112 25 27.20 -0.42 0.18 -4.22 0.34
## 112111 23 28.33 -1.00 1.00 -9.58 0.16
## 121111 22 18.61 0.79 0.62 7.37 0.22
## 122222 11 12.68 -0.47 0.22 -3.13 0.32
## 122122 10 10.90 -0.27 0.07 -1.72 0.39
## 211111 10 7.97 0.72 0.51 4.53 0.24
## 222122 9 8.92 0.03 0.00 0.16 0.49
## 122221 8 5.43 1.10 1.22 6.20 0.13
## 112112 7 2.99 2.32 5.38 11.91 0.01 *
## 221222 7 6.79 0.08 0.01 0.43 0.47
## 111212 6 4.25 0.85 0.72 4.14 0.20
## 112222 6 2.55 2.16 4.65 10.25 0.02 *
##
## Number of observed patterns: 50
## Number of empty cells: 14
## Total number of possible patterns: 64
# poLCA.tech10(LCA3)Another one to inspect the covariance matrice.
poLCA.cov(LCAE, nclass = 3)## Relevant statistics :
## Chisq : 1.807
## df : 4
## p : 0.771
##
## Top 15 covariances :
##
## pair Observed Expected chisq p
## V5 ~~ V1 0.026 0.030 0.558 0.455
## V2 ~~ V1 0.032 0.029 0.449 0.503
## V6 ~~ V4 0.064 0.062 0.230 0.631
## V6 ~~ V2 0.021 0.023 0.160 0.690
## V6 ~~ V3 0.022 0.020 0.101 0.751
## V5 ~~ V3 0.130 0.128 0.097 0.755
## V4 ~~ V2 0.013 0.015 0.088 0.767
## V4 ~~ V3 0.013 0.012 0.032 0.857
## V5 ~~ V4 0.015 0.017 0.032 0.858
## V3 ~~ V1 0.026 0.025 0.017 0.895
## V4 ~~ V1 0.054 0.055 0.016 0.898
## V3 ~~ V2 0.131 0.130 0.013 0.908
## V6 ~~ V1 0.058 0.058 0.010 0.921
## V5 ~~ V2 0.137 0.137 0.003 0.957
## V6 ~~ V5 0.025 0.025 0.000 0.988
# poLCA.cov(LCA3)The 3-step approaches will be improved.
Here are two examples that can be readily be implemented.
d3 <- d3step("categorical", LCAE, nclass = 3)
# d3step("categorical", LCA3)
d3## The statistics
## LR AIC df p
## 16.380 -12.380 2.000 0.001
##
##
## The median and its confidence intervals.
## , , Pr(categorical==0)
##
## 2.5% 50% 97.5%
## Pr(Class==1) 0.292 0.307 0.322
## Pr(Class==2) 0.431 0.447 0.464
## Pr(Class==3) 0.290 0.318 0.349
##
## , , Pr(categorical==1)
##
## 2.5% 50% 97.5%
## Pr(Class==1) 0.678 0.693 0.708
## Pr(Class==2) 0.536 0.553 0.569
## Pr(Class==3) 0.651 0.682 0.710
r3 <- r3step("continuous", LCAE, nclass = 3)
# r3step("continuous", LCA3)
r3## The statistics
## LR AIC df R2 p
## 11.458 -18.917 2.000 0.028 0.000
##
##
## The median and its confidence intervals.
## 2.5% 50% 97.5%
## Pr(Class==1) 21.483 21.723 21.942
## Pr(Class==2) 23.758 24.012 24.266
## Pr(Class==3) 20.798 21.205 21.639
d3step plot
plot(d3, ci = c(.05,.95))
r3step plot
plot(r3, ci = c(.05, .95))
Caron, P.-O. (2024). poLCAExtra : New and Convenient Functions for the Package ‘poLCA’. https://github.com/quantmeth/poLCAExtra
Linzer, D. A., & Lewis, J. B. (2011). poLCA: An R package for polytomous variable latent class analysis. Journal of Statistical Software, 42(10), 1–29. https://www.jstatsoft.org/v42/i10/