the responses to the food insecurity questions are indicators of the underlying latent variable of food insecurity.
In order to complete the model for the joint distribution of responses to a set of food security questions, it is necessary to assume a latent distribution for . The simplest assumption is that has a Gaussian distribution with mean 0 and variance 1. However, due to the level of prior screening of households who are asked the FSS questions, Johnson (2004) suggested using a truncated Gaussian distribution, rather than the standard Gaussian distribution.
When there are several items being modeled, it is assumed that the measurement errors, Vi, are independent across the items, as in the dichotomous case. The independence of the measurement errors implies the conditional independence of the responses to questions given the latent variable , so that equation (5) holds.
As a final point, the panel observes that the type of IRT model just described allows frequency information that is currently collected to be more systematically examined than it is now. However, it does not address the measurement of the duration of spells of food insecurity. In order to address duration, more detailed data would need to be collected and more complicated time-dependent IRT models would need to be used to analyze them.
Many issues have been raised in this chapter about the use of IRT models in the measurement of food insecurity and, in particular, the specific use of the Rasch model. These and related issues are summarized below and recommendations for improvement are presented.
Regarding food insecurity as an unobserved latent variable with the observed USDA survey questions regarded as a collection of manifest indicators of that latent variable is appropriate.
IRT models are appropriate for modeling survey responses that collect information on food insecurity of households.
Some empirical evidence suggests that the assumption of the Rasch model of equal item discrimination may not hold particularly well for the bank of survey items currently being used by USDA in its measurement of food insecurity.
The current practice in which responses to the food insecurity questions are dichotomized when, in fact, most of the questions have ordered polytomous response options may lead to a significant amount of information loss regarding that household’s level of food