Estimating IRT models with gllamm

Within the framework of economic evaluation, health econometricians are interested in constructing a meaningful health index that is consistent with individual or societal preferences. One way to derive such an index is based on the EQ-5D description and valuation of health-related quality of life (HRQOL). The purpose of this study was to analyze how well the EQ-5D reflects one latent construct of HRQOL and how large the potential impact of measurement variance is with respect to six different countries. Data came from the European Study of the Epidemiology of Mental Disorders (ESEMeD), a cross-sectional survey of a representative random sample (N = 21,425) in Belgium, France, Germany, Italy, The Netherlands, and Spain. At least in psychology, much attention is paid to different forms of item response theory (IRT) models and particularly the Rasch model, since it is the only model featuring specific objectivity, which enables what is called a “fair comparison” with respect to the latent dimension to be measured. Therefore the dimensionality of the construct is evaluated by means of one-parameter and two-parameter IRT. Differential item functioning is tested with respect to the six countries and both the difficulty and discrimination parameters. Results show that a unidimensional one-parameter IRT model holds for all countries only if the item “anxiety/depression” is omitted. If both the physical and the mental components of HRQOL should be represented, the questionnaire should be extended to a two-dimensional construct. Consequently, more items to portray the mental component are needed. This presentation will focus on the possibilities and restrictions in estimating these models with gllamm. It will be shown how these models can be established and tested. Problems regarding the structure of the data and the assignment of incidental parameters to individual observations will be discussed.