The present study investigated (a) how a latent profile analysis based on representative data of N ϭ 74,868 4th graders from 17 European countries would cluster the students on the basis of their reading, mathematics, and science achievement test scores; (b) whether there would be gender differences at various competency levels, especially among the top performers; (c) and whether societal gender equity might account for possible cross-national variation in the gender ratios among the top performers. The latent profile analysis revealed an international model with 7 profiles. Across these profiles, the test scores of all achievement domains progressively and consistently increased. Thus, consistent with our expectations, (a) the profiles differed only in their individuals' overall performance level across all academic competencies and not in their individuals' performance profile shape. From the national samples, the vast majority of the students could be reliably assigned to 1 of the profiles of the international model. Inspection of the gender ratios revealed (b) that boys were overrepresented at both ends of the competency spectrum. However, there was (c) some cross-national variation in the gender ratios among the top performers, which could be partly explained by women's access to education and labor market participation. The interrelatedness of academic competencies and its practical implications, the role of gender equity as a possible cause of gender differences among the top performers, and directions for future research are discussed.

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Background:In 2011 the Progress in International Reading Literacy Study (PIRLS) and the Trends in International Mathematics and Science Study (TIMSS) were conducted at fourth grade in a number of participating countries with a shared representative sample. In this article we investigate whether there are multidimensional proficiency patterns across the competency domains or not. Methods:In order to derive proficiency patterns across the reading (PIRLS), mathematics and science (TIMSS) competence domains, latent profile analyses (LPA) of students' plausible values were conducted. For this, the grade four student sample from 17 countries were combined and analyzed. The international reference model that resulted from this analysis was then applied with constraints to all 17 countries separately so that substantial comparisons between countries became possible. To describe and compare the differences between national profiles a classification system was developed and applied to all countries' profile patterns.Results: As a result of these international LPA seven groups of learners were identified. The profiles were approximately equidistant and parallel. For all countries we find that achievement across domains can be explained by a general level of achievement rather than subject-specific strengths or weaknesses of learners. However, subjectspecific strengths and weaknesses can be identified but are-with the exception of Malta and Northern Ireland-for most of the countries rather small. For only about half of the countries, a rather uniform pattern of subject-specific strengths and weaknesses can be found on all competence levels. The subject itself varies between countries. In the other countries high, intermediate and low achievers differ in their relative subjectspecific strength and weaknesses. Conclusions:The results suggest that differences in average achievement in TIMSS and PIRLS should also on country level be interpreted with caution. International comparative studies should further investigate potential reasons for the differences between countries.

A personal trait, for example a person’s cognitive ability, represents a theoretical concept postulated to explain behavior. Interesting constructs are latent, that is, they cannot be observed. Latent variable modeling constitutes a methodology to deal with hypothetical constructs. Constructs are modeled as random variables and become components of a statistical model. As random variables, they possess a probability distribution in the population of reference. In applications, this distribution is typically assumed to be the normal distribution. The normality assumption may be reasonable in many cases, but there are situations where it cannot be justified. For example, this is true for criterion-referenced tests or for background characteristics of students in large scale assessment studies. Nevertheless, the normal procedures in combination with the classical factor analytic methods are frequently pursued, despite the effects of violating this “implicit” assumption are not clear in general. In a simulation study, we investigate whether classical factor analytic approaches can be instrumental in estimating the factorial structure and properties of the population distribution of a latent personal trait from educational test data, when violations of classical assumptions as the aforementioned are present. The results indicate that having a latent non-normal distribution clearly affects the estimation of the distribution of the factor scores and properties thereof. Thus, when the population distribution of a personal trait is assumed to be non-symmetric, we recommend avoiding those factor analytic approaches for estimation of a person’s factor score, even though the number of extracted factors and the estimated loading matrix may not be strongly affected. An application to the Progress in International Reading Literacy Study (PIRLS) is given. Comments on possible implications for the Programme for International Student Assessment (PISA) complete the presentation.

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