Questions? Call 800-624-6242

| Items in cart [0]

PAPERBACK
price:\$37.25

## Food Insecurity and Hunger in the United States: An Assessment of the Measure (2006) Committee on National Statistics (CNSTAT)

### Citation Manager

. "5 Item Response Theory and Food Insecurity." Food Insecurity and Hunger in the United States: An Assessment of the Measure. Washington, DC: The National Academies Press, 2006.

Please select a format:

 Page 81

The following HTML text is provided to enhance online readability. Many aspects of typography translate only awkwardly to HTML. Please use the page image as the authoritative form to ensure accuracy.

Food Insecurity and Hunger in the United States: An Assessment of the Measure

Gaussian distribution for the case of food insecurity because the full set of food insecurity questions is asked only for those households that are likely to have large values of .

The latent distribution, f(), along with the item response functions, P{Xi = xi | }, may be combined using equation (5) to specify the joint distribution of the manifest variables, i.e.,

(9)

for continuous latent variables; a sum replaces the integral in equation (9) for discrete latent variables.

The parameters of the joint distribution of the X’s in equation (9) include both the item parameters from the item response functions and possibly other parameters from the latent distribution. It is this joint distribution for the manifest variables that allows these parameters to be estimated and for the latent variable model to be tested against data.

##### Multiple Groups of Respondents

It often happens that important subgroups of respondents need to be studied separately. For example, households with children are asked questions that are not appropriate for households without children. It is possible for the latent distribution to vary with the subgroup. When there are large differences in these latent distributions, it may be important to include them in the model for the manifest variables.

To denote this situation, let G be a variable that distinguishes between different subgroups of respondents. For example G = 0 could indicate a household without children, while G = 1 indicates a household with children. In this setting, equation (9) can be expanded to

(10)

where G = g denotes one of the subgroups of interest. In many IRT applications, the latent distributions, f(| G = g), are assumed to be Gaussian with means and variances that vary with g.

##### Differential Item Functioning

In order for equation (10) to be a correct formula, has to “explain” (in the sense of conditional independence mentioned earlier) any dependence between subgroup membership and responses to the questions. In

 Page 81
 Front Matter (R1-R12) Executive Summary (1-12) 1 Introduction (13-22) 2 History of the Development of Food Insecurity and Hunger Measures (23-40) 3 Concepts and Definitions (41-54) 4 Survey Measurement of Food Insecurity and Hunger (55-70) 5 Item Response Theory and Food Insecurity (71-98) 6 Survey Vehicles to Measure Food Insecurity and Hunger (99-107) 7 Applicability of Food Insecurity Outcomes for Assessment of Program Performance (108-112) 8 Closing Remarks (113-114) References (115-124) Acronyms and Abbreviations (125-126) Appendix A Current Population Survey Food Security Supplement Questionnaire, December 2003 (127-133) Appendix B Biographical Sketches of Panel Members and Staff (134-138) Index (139-144)