We consider latent variable models for an infinite sequence (or universe) of manifest (observable) variables that may be discrete, continuous or some combination of these. The main theorem is a general characterization by empirical conditions of when it is possible to construct latent variable models that satisfy unidimensionality, monotonicity, conditional independence, and tail-measurability. Tail-measurability means that the latent variable can be estimated consistently from the sequence of manifest variables even though an arbitrary finite subsequence has been removed. The characterizing, necessary and sufficient, conditions that the manifest variables must satisfy for these models are conditional association and vanishing conditional dependence (as one conditions upon successively more other manifest variables). Our main theorem considerably generalizes and sharpens earlier results of Ellis and van den Wollenberg (1993), Holland and Rosenbaum (1986), and Junker (1993). It is also related to the work of Stout (1990).

The main theorem is preceded by many results for latent variable models in general—not necessarily unidimensional and monotone. They pertain to the uniqueness of latent variables and are connected with the conditional independence theorem of Suppes and Zanotti (1981). We discuss new definitions of the concepts of “true-score” and “subpopulation,” which generalize these notions from the “stochastic subject,” “random sampling,” and “domain sampling” formulations of latent variable models (e.g., Holland, 1990; Lord & Novick, 1968). These definitions do not require the a priori specification of a latent variable model.

Previous studies have indicated that between 60 and 80% of a population of entomopathogenic nematodes do not infect their insect hosts at any one period in time. Two hypotheses explain this behaviour: the first that there is a subpopulation of non-infectious nematodes and the second that the non-infectious group is created by inhibitory cues derived from infected insects. Through an experimental approach with the Galleria mellonella–Steinernema feltiae system we show that both mechanisms operate together. When conditions for infection were optimized, the sum of individual infection behaviours was similar to the number infecting as a population, implying observed infection rates are driven by intrinsic mechanisms. In addition, there was evidence that an infected host released a chemical cue into the environment which inhibited subsequent levels of infection. This degree of inhibition was independent of the number of infecting nematodes. Both these mechanisms are dynamic, so the observed proportion of infectious nematodes depended heavily on the time of exposure. The implications of these findings for both the design of laboratory trials and the use of entomopathogenic nematodes in biological control are discussed.