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We propose structural equation models with latent variables (1) to quantify the latent risk of infection and to identify, among the many potential mediators of infection, the few ones that influence it significantly and (2) to estimate direct and indirect levels of tolerance of animals infected naturally with pathogens.

Latent variable models allow for the analysis of multidimensional response variables that reveal the indicator's underlying relationship that are caused by the latent variables.

Fig. 2 Measurements of the latent variables.

Such results validate the latent variables for the model composition.

The double-headed arrows are correlations between the latent variables.

It defines the relationship among the latent variables.

The CR refers to the reliability of the latent variables, while AVE refers to the validity of the latent variables.

In addition, the AVE of each latent variable is larger than SMC between each pair of the latent variables.

We use searching factorial analysis to examine the latent variables and obtained seven latent variables (see Table 4).

The measurement model part in the SEM model includes the latent variables and several observable variables used to test the latent variables (shown variables).

Paths connecting latent variables (circles) to each other represent the correlations between the constructs and the numbers from the latent variables to the manifest variables (squares) represent the loadings of each task onto the latent variable.

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