Taking into consideration the structure of the outcomes of interest, the analysis relies on two distinct models to estimate the effect of displacement. On the one hand, a multinomial logit model is employed; it considers the outcomes of school attendance and food security, as each is a categorical variable with various response possibilities. This can be formally expressed as:
where y represents category j for either school attendance or food security of household, i, xi indicates the vector of household-level covariates influencing school attendance or food security, and fij represents the vector of choice-specific coefficients.
On the other hand, because the outcome dietary diversity is of both a discrete and a continuous nature because of the fact that nearly half of households in the sample reported unable to eat meat during the previous week, a zero-censored tobit model is used and expressed by the following equation:
Y = max (0, Y) , and u ~ N(0, a1).
Here IDP, is a dummy variable taking the value of one if the household is internally displaced, X again represents household-level covariates, and U is the error term. In principle, the zero-censored tobit model takes into account the linearity of the latent variable for those observations not equal to zero, while also assuming normality and homoscedasticity of the residuals.