How do I fit a latent class model?
| Title |
|
Fitting latent class models in gllamm |
| Author |
Sophia Rabe-Hesketh, University of California, Berkeley |
| Date |
July 2012 |
Exploratory latent class model for binary variables
In an exploratory latent class model for I binary variables yij
for units j, each unit is assumed to belong to one of C latent classes c
with probability πc. Each latent class
has a different probability pi|c
that the ith variable takes the value 1. Given latent class membership, the variables
yij are conditionally independent.
The marginal probabilities are then
P(yij=1) = ∑c πcpi|c
(The sum over the latent classes of the probability that the subject belongs
to that latent class times the latent-class-specific probability that the variable is 1.)
Brief explanation of estimation in gllamm
Data preparation
As always, the data must be in long form, with all yij in one
variable y and with variables i
and j keeping track of the variable and unit identifiers,
i and j, respectively.
Parameterization in gllamm and syntax
In gllamm, we treat eic=logit[pi|c]
as the C discrete values that I latent variables can take. There is one
latent variable ηij for each response variable yij. The vector
ηj of latent variables for subject j takes the
values ec (with elements eic)
if subject j is in latent class c.
Such a discrete latent variable distribution, with associated probabilities
πc, is specified in gllamm using the
ip(fn) option. The number of latent classes (or masses)
is specified using the nip(#) option.
To ensure that the ith latent variable
represents the log-odds for the ith response variable, it must
be multiplied by a dummy variable di for i.
We can define the dummy variables d1, d2, d3, etc., using
tabulate i, generate(d)
Multiplying each latent variable by one of these dummies is accomplished by specifying
one equation for each latent variable, giving the required dummy variable after the
colon on the right-hand-side (the equation names before the colons are arbitrary but
are passed to gllamm in the eqs() option):
eq i1: d1
eq i2: d2
eq i3: d3
etc.
Then the gllamm command is (assuming I=5 and C=2):
gllamm y, i(j) nrf(5) eqs(i1 i2 i3 i4 i5) ip(fn) nip(2) link(logit) family(binom) nocons
Examples and documentation
- Standard exploratory latent class models (and beyond)
- Latent class models for nominal data and rankings
- Section 9.4 on A latent class model for rankings in
Rabe-Hesketh, S., Skrondal, A. and Pickles, A. (2004).
GLLAMM Manual.
U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 160.
-
Skrondal and Rabe-Hesketh (2004).
Generalized Latent Variable Modeling: Multilevel, Longitudinal and Structural Equation Models.
Chapman & Hall/CRC.
- Latent class models for continuous responses
- Section 5.1 on A simple finite mixture model
in Rabe-Hesketh, S., Skrondal, A. and Pickles, A. (2004).
GLLAMM Manual.
U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 160.
- Section 5.2 on Linear mixed model with discrete random effects
in Rabe-Hesketh, S., Skrondal, A. and Pickles, A. (2004).
GLLAMM Manual.
U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 160.
- Discrete latent covariates (or nonparametric covariate distribution)
- Latent complier status in complier average causal effects
- Skrondal and Rabe-Hesketh (2004).
Generalized Latent Variable Modeling: Multilevel, Longitudinal and Structural Equation Models.
Chapman & Hall/CRC.
References
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