International studies like PISA use context student or school questionnaires to collect data on student family background, attitudes and learning context. Questionnaire constructs are typically measured using dichotomous or Likert-type items. Scaling of questionnaire items in order to obtain measures of family background, student attitudes or perceptions of learning context requires a thorough cross-country validation of the underlying constructs. Two methodological approaches to construct validation are applied within the context of the OECD PISA study: (1) Confirmatory Factor Analysis (CFA) based on mean and covariance structures can be used to test the measurement equivalence and help to detect possible socio-cultural differences on the constructs; and (2) Item Response Theory (IRT) has been used for scaling items using a logistic function and obtaining measures of the latent construct. This paper describes ways of implementing tests of parameter invariance in CFA and IRT, examines results using these two different approaches to validate questionnaire constructs based on data from the OECD PISA study and discusses their implications for cross-national or cross-cultural research. Appended are: (1) Multiple-group model results; and (2) Country effects on item parameters. (Contains 18 tables and 8 footnotes.)