Weighting for item non-response in attitude scales by using latent variable models with covariates Irini Moustaki and Martin Knott London School of Economics and Political Science, UK [Received December 1999. Revised June 2000] Summary. We discuss the use of latent variable models with observed covariates for computing response propensities for sample respondents. A response propensity score is often used to weight item and unit responders to account for item and unit non-response and to obtain adjusted means and proportions. In the context of attitude scaling, we discuss computing response propensity scores by using latent variable models for binary or nominal polytomous manifest items with covariates. Our models allow the response propensity scores to be found for several different items without re®tting. They allow any pattern of missing responses for the items. If one prefers, it is possible to estimate population proportions directly from the latent variable models, so avoiding the use of propensity scores. Arti®cial data sets and a real data set extracted from the 1996 British Social Attitudes Survey are used to compare the various methods proposed. Keywords: Latent trait models; Non-ignorable non-response; Weighting 1. Introduction LittleandRubin1987)discussedbothweightingandimputationmethodsforaccountingfor unit and item non-response respectively in survey data. Both these techniques try to adjust respondents in an ecient way to account for non-response. In this paper we concentrate on the weighting method for item non-response. In Little and Rubin's weighting scheme the non-respondentsareignoredandweightsareassignedtorespondentsthatattempttoaccount for the non-respondents. To weight for non-response the sample members are divided into classes.Withineachclasstherespondentsaregivenweightsthatareinverselyproportionalto their response probability, to make up for the non-respondents in that class. The sample is divided into groups by using classi®cation covariates or a cross-classi®cation based on a set of covariates such as demographic and socioeconomic variables. Those covariates should be observed for both respondents and non-respondents. The eectiveness of the weighting applied depends on how close the characteristics of the respondents are to the characteristics of the non-respondents within the de®ned classes. The smaller the size of the classes used keeping the sample size ®xed) the more homogeneous they will be and the more eective the weighting system will be. However, the use of many small classes might lead to variable weights and eventually to a large variance for the estimates. As mentioned in Little and Rubin 1987) no precise theory exists for forming classes. Two methods are proposed in Little 1986, 1988). The ®rst method is proposed for imputation purposesandiscalledtheconditionalmeanmethodandthesecondisproposedforweighting and is called the response propensity method. Address for correspondence: Irini Moustaki, Department of Statistics, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE, UK. E-mail: i.moustaki@lse.ac.uk & 2000 Royal Statistical Society 0964±1998/00/163445 J. R. Statist. Soc. A 2000) 163, Part 3, pp. 445±459