 # Exploring Explanatory Models: An Event History Application

## Article excerpt

Factor analysis and econometric techniques have the reputation for being like oil and water - invaluable for cooking but not easy to combine. The classic methods of factor analysis (e.g. PCA, MCA) are of course powerful tools for dimension reduction (synthesizing heterogeneity into a small number of factors), but they preclude any pre-established explanatory schema and are unsuitable for exploring cause and effect, and this for two main reasons. They present two characteristics that are not easily compatible with explanatory modelling: first, a variable relating approach confined to pairwise relations between the variables; second, a high degree of symmetry between variables. These bivariate relations cannot be used to measure the partial effect of one variable on another, i.e. after the influence of other determinants has been netted out. Another particularity of these factor analytic methods is that they do not order the observations sequentially and are thus unsuitable for studying dynamic processes. When observations are dated, studying a dynamic process usually requires that future outcomes be modelled as a function of conditions in the past(1), which necessarily involves sequentially ordering the observations(2).

For their part, econometric techniques, which are based on conditional models, study partial relations and are thus entirely suitable for explanatory analysis. But they must use parsimonious models if they are to avoid the multicollinearity problem caused by excessive redundancy in the explanatory variables, and produce stable estimates(3). Very often, therefore, a preliminary stage of dimension reduction is needed.

Thus it can be seen how these techniques are complementary and why in practice their sequencing is strict. Factor analysis is employed first, purely for exploratory purposes, in order to extract a limited number of strong dimensions (or factors) from the data. In a second stage, these dimensions are introduced into an econometric model that is underpinned by an explanatory schema(4).

Unfortunately, this sequence cannot always be operationalized. First, as the variables selected in the dimension-reduction phase are calculated without reference to any explanatory schema, there is no certainty that they are the most relevant for the subsequent modelling. second, factor analysis is seriously handicapped by censored observations, whereas modelling often permits a rigorous handling of this problem. For these two reasons an explanatory model needs to be included from the start of analysis.

The response to this situation has been the development of a new method of factor analysis, thematic components analysis (TCA) (Bry, 2003), which puts the explanatory model at the source of the dimension reduction. This method is a generalization of the partial least squares (PLS) regression developed by Wold (Wold, 1985). By construction it is adapted to classic linear modelling of continuous variables when working with nontemporal data. In this article we present a way of "plugging" it into generalized linear models, and in particular with Cox's semi-parametric model. We begin by setting out this methodological approach, and then apply it to original data derived from a recent African survey, in an analysis of the divorce behaviour of men in Dakar.

I. Modelling based on latent variables

Econometric modelling is always founded on a conceptual schema. This schema is the synthesis of a substantive theoretical reflection that can alone provide the underpinning for its explanatory character. The conceptual model is often presented in the form of an oriented graph where the vertices represent various concepts or themes, which serve to characterize the observations, while the edges stand for the relations of cause-andeffect or more generally of influence between these concepts. We refer to this schema as a thematic model.

For example, to model the risk of divorce for men, we propose the thematic model shown in Figure 1. …

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