With the causal structuring in Figure 3, using y5 and y6 as multiple indicators of a latent would demand use of η3B at the latent level in Figure 2, whereas use of a single indicator, or a pair of single indicators, would permit the latent level of the model to contain η3A alone, or η3B alone, or η3C alone, or both η3B and η3C.
The existence of multiple similarly worded indicators is no longer a license to squelch theory by saturating the latent level of the model with factor correlations, or by failing to assert a latent's meaning with a fixed measurement error variance for the best of the multiple indicators.
We could use y5 as an indicator of η3C, and y6 as an indicator of η3B, and add precision to the latent level of the model by assessing whether the latent-level effects connected to η3 in Figure 2 enter into, or emerge from, specifically η3B, or η3C, or both.
For example, if y5 was a single indicator and its error variance was not rendered identified by the latent level of the model, the fit and modification indices would be unable to signal a problematic error variance specification, or warn of the biases in the latent effect estimates that might arise from this.
The remaining 40% of genes were simulated as constant meaning the latent level of expression remains unchanged across conditions.
Such potential inconsistencies render the model testable, but before we turn to testing, let us reconsider the latent level of the model.
Indeed, it may sometimes be possible to model two latents (one being the latent of interest, the other being a specific or "method-factor" latent) with only a single indicator if the two latents are clearly and substantially differentially embedded at the latent level of the model.
The example in Figure 6 was chosen because the latent level of the model is moderately complex – it has two touching reciprocal effects – that are cleanly estimated with single indicators assigned between 5 and 10% measurement error variance.
If Figure 3 provides the proper causal specification for y5 and y6, using both y5 and y6 as single indicators would not permit incorporating both η3A and η3B in the latent level of the model.
According to Figure 3, η3B is the appropriate version of η3 for matching the covariance between y5 and y6, but we have not yet confirmed that η3B is also the version of η3 required to engage in causal actions at the latent level of the Figure 2 model – where η3 receives effects from η1 and η2, and sends effects to η4 and beyond.
In this work, using non parametric IRT analyses, we found that WHO-DAS II items and options discriminate well among different latent levels of disablement and that it is a nonbiased instrument with respect to gender.
