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Mark Lyons-Amos

random effect are now captured by dummy variables which index each cluster (save for one omit-
ted cluster to identify the model).
This has some advantages over and can overcome some of the conceptual limitation of random
effects models. The model makes no distributional assumptions for cluster level variance and hence
is protected against misspecification. This also allows deviation from the overall population line to
exhibit the clumpy characteristics expected under circumstances where regime typologies exist (e.g.,
Elzinga and Liefbroer, 2007). Moreover, since the model will remove via differencing both observed
and unobserved j level variation, the fixed effects model is commonly applied under circumstances
where causal inferences are required.
That said, there are drawbacks to this approach. Firstly the dummy variables identifying clusters
refer only to the sample under analysis; hence, it is impossible to make inference beyond the ob-
served data. Secondly, where there are relatively few observations within cluster then the estimated
fixed effects will tend to be unreliable. Indeed, the random effects model in general will tend to be
more efficient, since the deviations from the population line are captured by one parameter, while the
fixed effects model requires the estimation of J − 1 dummy variables (for a model with J clusters).
Finally, the use of fixed effects models can preclude the use of country or cluster level covariates
since these are confounded with their own fixed effect. This is a distinct disadvantage when seeking
to understand the effect of country level information, such as national level policy.
2.2 Latent Class Analysis

To overcome the limitations highlighted, the use of Two-level Latent Class models is proposed,
which will be demonstrated go some way to overcoming the limitations of both random and fixed
effects models for longitudinal data analysis. Latent class models use country level information to
create classes, allocate countries to classes and produce woman level information within that class.
There are a number of advantages to this approach. Firstly, the fact that the cluster level effect is de-
scribed by classes means that specifying a Normal (or indeed any other distribution) is no longer
required, and hence ‘clumpiness’ can be accurately captured. Moreover, the fact that the country lev-
el of analysis is now generated from policy indicators means that the class can be ascribed qualita-
tive meaning for interpretation purposes, either by generating empirical groupings or validating
theoretically derived groupings as per Elzinga and Liefbroer (2007) or Esping-Andersen (1990 and
1999). The grouping variable is a categorical variable represented in Figure 1 by the class indicator
C. The model has the advantage over the fixed effects model that since C is a ‘random’ effect, it is
possible to make inferences beyond the data within the sample at cluster level. Forming classes
based on variables of interest explicitly includes contextual (country level) information in the model,
and interactions between cluster and individual level information can be included by allowing indi-
vidual level covariates to depend on class membership. The disadvantage of this lack of confounding
of the latent class approach is that residual confounding may exist due to variables omitted from
those used in class formation; hence, it is harder to make causal claims from latent class compared to
fixed effects models.
Figure 1 represents the structural form of the latent class model. Within the figure, we observe the
response variable at a series of timepoints =t 1, =t 2, , =t T observed at the level of the indi-
vidual. The level of the response variable at each time point is determined by an intercept () and
slope (). The shape of the slope trajectory can take a variety of forms (quadratic, cubic).The values
of the intercept and slope are allowed to vary according to membership of a higher level class, C,
which is determined at the cluster/country level. In this instance, class membership is determined by
a set of relevant cluster level variables here denoted by the vector x.

2.3 Number of Classes

A disadvantage of the latent class approach is that the researcher needs some means by which to

International Journal of Population Studies | 2016, Volume 2, Issue 2 47