lca_entropy
Stata command for entropy fit statistics for latent class analysis
lca_entropy is a Stata command that calculates an entropy fit statistic for a latent class analysis (LCA) model. The LCA model should be fit using gsem in Stata with the lclass() option. Entropy summarizes how cleanly the model separates the observations into classes: it runs from 0 to 1, and values closer to 1 indicate that each observation is assigned to one class with high posterior probability.
Entropy is discussed in my graduate course slides on latent class analysis (pages 742–744): Latent Class Analysis slides. All of the materials for the course are on the Latent Variable Modeling page.
Installation
net install lca_entropy, from("https://tdmize.github.io/data") replaceTo read the help file in Stata, type help lca_entropy; it is also on this site.
Citation
Please cite the use of lca_entropy as:
Mize, Trenton D. 2024. “lca_entropy: Stata command for entropy fit statistics for latent class analysis.” https://www.trentonmize.com/software/lca_entropy
Example
The example recreates the three-class model of cultural participation in Alderson, Junisbai, and Heacock (2007) from seven GSS items on attending the opera, dance, drama, and art museums, popular music concerts, reading fiction, and going to the movies. Load the 1998 and 2002 GSS respondents who answered every item:
use "https://tdmize.github.io/data/data/cda_gss", clear(cda_gss.dta | GSS 1972-2021 CDA - Categorical Data Analysis | date created 2023)keep if year == 1998 | year == 2002(63,249 observations deleted)drop if missing(opera, dance, drama, visitart, popmusic, readfict, seemovie)(2,813 observations deleted)Fit the LCA with gsem. The constraint on the intercept of opera in class 1 handles a boundary estimate – a class in which essentially no one attends the opera – so that the model converges:
gsem (-> opera dance drama visitart popmusic readfict seemovie, logit) ///
(1: opera <- _cons@-15) ///
, lclass(Class 3)Fitting class model:
Iteration 0: (class) log likelihood = -3058.5366
Iteration 1: (class) log likelihood = -3058.5366
Fitting outcome model:
Iteration 0: (outcome) log likelihood = -8109.6013
Iteration 1: (outcome) log likelihood = -7932.4997
Iteration 2: (outcome) log likelihood = -7917.6417
Iteration 3: (outcome) log likelihood = -7916.7526
Iteration 4: (outcome) log likelihood = -7916.7418
Iteration 5: (outcome) log likelihood = -7916.7418
Refining starting values:
Iteration 0: (EM) log likelihood = -11406.301
Iteration 1: (EM) log likelihood = -11442.997
Iteration 2: (EM) log likelihood = -11427.125
Iteration 3: (EM) log likelihood = -11408.48
Iteration 4: (EM) log likelihood = -11394.017
Iteration 5: (EM) log likelihood = -11383.627
Iteration 6: (EM) log likelihood = -11376.274
Iteration 7: (EM) log likelihood = -11371.043
Iteration 8: (EM) log likelihood = -11367.264
Iteration 9: (EM) log likelihood = -11364.478
Iteration 10: (EM) log likelihood = -11362.371
Iteration 11: (EM) log likelihood = -11360.735
Iteration 12: (EM) log likelihood = -11359.428
Iteration 13: (EM) log likelihood = -11358.358
Iteration 14: (EM) log likelihood = -11357.459
Iteration 15: (EM) log likelihood = -11356.688
Iteration 16: (EM) log likelihood = -11356.014
Iteration 17: (EM) log likelihood = -11355.418
Iteration 18: (EM) log likelihood = -11354.883
Iteration 19: (EM) log likelihood = -11354.399
Iteration 20: (EM) log likelihood = -11353.958
note: EM algorithm reached maximum iterations.
Fitting full model:
Iteration 0: Log likelihood = -10148.704
Iteration 1: Log likelihood = -10148.525
Iteration 2: Log likelihood = -10148.523
Iteration 3: Log likelihood = -10148.523
Generalized structural equation model Number of obs = 2,784
Log likelihood = -10148.523
( 1) [opera]1bn.Class = -15
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
1.Class | (base outcome)
-------------+----------------------------------------------------------------
2.Class |
_cons | 0.344 0.139 2.472 0.013 0.071 0.617
-------------+----------------------------------------------------------------
3.Class |
_cons | -0.121 0.133 -0.909 0.364 -0.382 0.140
------------------------------------------------------------------------------
Class: 1
Response: opera
Family: Bernoulli
Link: Logit
Response: dance
Family: Bernoulli
Link: Logit
Response: drama
Family: Bernoulli
Link: Logit
Response: visitart
Family: Bernoulli
Link: Logit
Response: popmusic
Family: Bernoulli
Link: Logit
Response: readfict
Family: Bernoulli
Link: Logit
Response: seemovie
Family: Bernoulli
Link: Logit
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
opera |
_cons | -15.000 (constrained)
-------------+----------------------------------------------------------------
dance |
_cons | -5.023 0.833 -6.030 0.000 -6.655 -3.390
-------------+----------------------------------------------------------------
drama |
_cons | -3.596 0.338 -10.629 0.000 -4.258 -2.933
-------------+----------------------------------------------------------------
visitart |
_cons | -2.277 0.180 -12.658 0.000 -2.630 -1.925
-------------+----------------------------------------------------------------
popmusic |
_cons | -2.897 0.377 -7.683 0.000 -3.635 -2.158
-------------+----------------------------------------------------------------
readfict |
_cons | -0.295 0.110 -2.686 0.007 -0.510 -0.080
-------------+----------------------------------------------------------------
seemovie |
_cons | -0.808 0.177 -4.574 0.000 -1.154 -0.462
------------------------------------------------------------------------------
Class: 2
Response: opera
Family: Bernoulli
Link: Logit
Response: dance
Family: Bernoulli
Link: Logit
Response: drama
Family: Bernoulli
Link: Logit
Response: visitart
Family: Bernoulli
Link: Logit
Response: popmusic
Family: Bernoulli
Link: Logit
Response: readfict
Family: Bernoulli
Link: Logit
Response: seemovie
Family: Bernoulli
Link: Logit
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
opera |
_cons | -2.692 0.240 -11.201 0.000 -3.163 -2.221
-------------+----------------------------------------------------------------
dance |
_cons | -2.150 0.202 -10.657 0.000 -2.546 -1.755
-------------+----------------------------------------------------------------
drama |
_cons | -1.776 0.169 -10.495 0.000 -2.107 -1.444
-------------+----------------------------------------------------------------
visitart |
_cons | -0.740 0.122 -6.080 0.000 -0.979 -0.502
-------------+----------------------------------------------------------------
popmusic |
_cons | -0.008 0.117 -0.064 0.949 -0.237 0.222
-------------+----------------------------------------------------------------
readfict |
_cons | 1.197 0.111 10.777 0.000 0.979 1.414
-------------+----------------------------------------------------------------
seemovie |
_cons | 1.681 0.164 10.240 0.000 1.359 2.002
------------------------------------------------------------------------------
Class: 3
Response: opera
Family: Bernoulli
Link: Logit
Response: dance
Family: Bernoulli
Link: Logit
Response: drama
Family: Bernoulli
Link: Logit
Response: visitart
Family: Bernoulli
Link: Logit
Response: popmusic
Family: Bernoulli
Link: Logit
Response: readfict
Family: Bernoulli
Link: Logit
Response: seemovie
Family: Bernoulli
Link: Logit
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
opera |
_cons | 0.092 0.108 0.858 0.391 -0.119 0.304
-------------+----------------------------------------------------------------
dance |
_cons | 0.468 0.113 4.147 0.000 0.247 0.690
-------------+----------------------------------------------------------------
drama |
_cons | 0.873 0.135 6.447 0.000 0.608 1.139
-------------+----------------------------------------------------------------
visitart |
_cons | 1.630 0.171 9.510 0.000 1.294 1.966
-------------+----------------------------------------------------------------
popmusic |
_cons | 0.643 0.093 6.917 0.000 0.461 0.825
-------------+----------------------------------------------------------------
readfict |
_cons | 2.203 0.154 14.329 0.000 1.901 2.504
-------------+----------------------------------------------------------------
seemovie |
_cons | 2.227 0.168 13.242 0.000 1.897 2.556
------------------------------------------------------------------------------Estimate entropy with lca_entropy; the statistic is also returned in r(entropy):
lca_entropyEntropy = 0.607Reference
Alderson, Arthur S., Azamat Junisbai, and Isaac Heacock. 2007. “Social Status and Cultural Consumption in the United States.” Poetics 35(2–3): 191–212. https://www.sciencedirect.com/science/article/abs/pii/S0304422X07000186