More frequently, studies involving latent variables have been published in the recent medical literature (see Streiner & Norman, 1995 for a review). Typical application evaluates how a collection of variables (questionnaire) is related to a single common construct of interest (a continuous latent variable). For example, the latent variable under investigation might be pain, fatigue, depression, cognitive functioning, self-esteem or quality of life. Many questionnaire forms are now available, but the most popular method is the self-administered instrument which lists several multiple-items subscales. The subscales are designed with the purpose of ensuring that the items within a subscale all measure a single common construct. To cast this objective, Factor Analysis or Item Response Theory (Latent Trait Models) are used with continuous observed variables or with observed binary or polytomous data, respectively. They verify that items within a subscale are statistically independent after conditioning on a latent variable represents the construct under investigation. However, the process of computing of the Item Response Theory approach is still not generally available, except in specific softwares, indeed limited to one or two latent variables (BILOG, MULTILOG, FACONE, POLYFAC, and many others). Additional latent variables affect the computational efficacy of the various proposed algorithms (WLS method, ML using EM method, empirical Bayes method). For this reason, Factor Analysis is frequently processed on dichotomous or polytomous (ordinal) data especially in exploratory work on constructing scales for unobservable constructs. An eigenvalue-eingenvector exploratory method suitable for qualitative data is Multiple Correspondence Analysis (MCA), a special case of Principal Component Analysis. MCA is a popular techniques for processing, compressing and visualising categorical data using an Euclidean model and geometrical representations. MCA is also an "optimal" scaling method, an alternative name of MCA is Homogeneity Analysis or Dual Scaling. Bartholomew & Knott (1999) suggest how the MCA dimensions of a set of observed categorical data may be determined through approximate maximum-likelihood estimation of parameters in a latent variable model closely related to Item Response Theory. Alternatively Takane & de Leeuw (1987) discusse a probabilistic generalisation of MCA related to Factor Analysis of unordered categorical data. We consider a direct reformulation of the MCA model using classical Measurement Theory to derive the Bartholomew's result. The objective of this research is to provide a more systematic comparison on the theoretical and empirical relationships of the latent variables techniques of binary or polytomous (ordinal or nominal) data using different data sets. First, a cross-over trial evaluating quality of life scales changes in pacemaker implanted patients; two different options of the pacemaker device are investigated (Mayou, 1990). Second, a two-panel data (1993 and 1999 waves) from the European Community Respiratory Health Survey (ECRHS), an observational multicenter survey, aimed to assess the prevalence of asthma in different EEC countries (Burney et al, 1994). A screening questionnaire, measuring the presence of asthma-like symptoms, is under investigation.
Some Aspects of Principal Components Analysis as Measurement Error Model
Biino G
1999
Abstract
More frequently, studies involving latent variables have been published in the recent medical literature (see Streiner & Norman, 1995 for a review). Typical application evaluates how a collection of variables (questionnaire) is related to a single common construct of interest (a continuous latent variable). For example, the latent variable under investigation might be pain, fatigue, depression, cognitive functioning, self-esteem or quality of life. Many questionnaire forms are now available, but the most popular method is the self-administered instrument which lists several multiple-items subscales. The subscales are designed with the purpose of ensuring that the items within a subscale all measure a single common construct. To cast this objective, Factor Analysis or Item Response Theory (Latent Trait Models) are used with continuous observed variables or with observed binary or polytomous data, respectively. They verify that items within a subscale are statistically independent after conditioning on a latent variable represents the construct under investigation. However, the process of computing of the Item Response Theory approach is still not generally available, except in specific softwares, indeed limited to one or two latent variables (BILOG, MULTILOG, FACONE, POLYFAC, and many others). Additional latent variables affect the computational efficacy of the various proposed algorithms (WLS method, ML using EM method, empirical Bayes method). For this reason, Factor Analysis is frequently processed on dichotomous or polytomous (ordinal) data especially in exploratory work on constructing scales for unobservable constructs. An eigenvalue-eingenvector exploratory method suitable for qualitative data is Multiple Correspondence Analysis (MCA), a special case of Principal Component Analysis. MCA is a popular techniques for processing, compressing and visualising categorical data using an Euclidean model and geometrical representations. MCA is also an "optimal" scaling method, an alternative name of MCA is Homogeneity Analysis or Dual Scaling. Bartholomew & Knott (1999) suggest how the MCA dimensions of a set of observed categorical data may be determined through approximate maximum-likelihood estimation of parameters in a latent variable model closely related to Item Response Theory. Alternatively Takane & de Leeuw (1987) discusse a probabilistic generalisation of MCA related to Factor Analysis of unordered categorical data. We consider a direct reformulation of the MCA model using classical Measurement Theory to derive the Bartholomew's result. The objective of this research is to provide a more systematic comparison on the theoretical and empirical relationships of the latent variables techniques of binary or polytomous (ordinal or nominal) data using different data sets. First, a cross-over trial evaluating quality of life scales changes in pacemaker implanted patients; two different options of the pacemaker device are investigated (Mayou, 1990). Second, a two-panel data (1993 and 1999 waves) from the European Community Respiratory Health Survey (ECRHS), an observational multicenter survey, aimed to assess the prevalence of asthma in different EEC countries (Burney et al, 1994). A screening questionnaire, measuring the presence of asthma-like symptoms, is under investigation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
