The interplay of g and mathematical abilities in large-scale assessments across grades

Saß, Steffani; Kampa, Nele; Köller, Olaf

doi:10.1016/j.intell.2017.05.001

Cited by 70 publications

(21 citation statements)

References 68 publications

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“…Also Gustafsson and Balke [2] selected one indicator (letter grouping) to define the g factor of aptitudes. Other examples of applying bifactor( S -1) models are Brunner’s [17] and Saß et al’s [21] studies, in which a g factor of cognitive abilities was defined by fluid ability. Likewise, Benson et al [15] defined their g factor of cognitive abilities by the test story completion.…”

Section: Alternatives To Extended Bifactor Modelsmentioning

confidence: 99%

“…There is another prominent approach to separate general from specific abilities: the bifactor model [13]. Although its introduction dates way back, the bifactor model is recently and increasingly applied in studies predicting criterion variables by general and specific factors, not only in the area of cognitive abilities and school performance measures (e.g., [14,15,16,17,18,19,20,21,22,23,24]), but also in different other areas of psychological research such as motivation and engagement (e.g., [25,26,27]), clinical psychology (e.g., [28,29,30]), organizational psychology (e.g., [31]), personality psychology (e.g., [32,33]), and media psychology (e.g., [34]). The multitude of recently published studies using the bifactor model shows that it has become a standard model for predicting criterion variables by general and specific components.…”

Section: Introductionmentioning

confidence: 99%

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Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions

et al. 2018

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The bifactor model is a widely applied model to analyze general and specific abilities. Extensions of bifactor models additionally include criterion variables. In such extended bifactor models, the general and specific factors can be correlated with criterion variables. Moreover, the influence of general and specific factors on criterion variables can be scrutinized in latent multiple regression models that are built on bifactor measurement models. This study employs an extended bifactor model to predict mathematics and English grades by three facets of intelligence (number series, verbal analogies, and unfolding). We show that, if the observed variables do not differ in their loadings, extended bifactor models are not identified and not applicable. Moreover, we reveal that standard errors of regression weights in extended bifactor models can be very large and, thus, lead to invalid conclusions. A formal proof of the nonidentification is presented. Subsequently, we suggest alternative approaches for predicting criterion variables by general and specific factors. In particular, we illustrate how (1) composite ability factors can be defined in extended first-order factor models and (2) how bifactor(S-1) models can be applied. The differences between first-order factor models and bifactor(S-1) models for predicting criterion variables are discussed in detail and illustrated with the empirical example.

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Section: Alternatives To Extended Bifactor Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions

et al. 2018

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“…One could ask whether these correlations between test scores for one ability and component skills for the other ability call the validity of the intended construct interpretation into question. We argue that this is not the case, because competencies and general cognitive skills are assumed to be related, for instance because schooling may affect reasoning, and there is ongoing discussion about the extent to which those skills can be separated (Brunner, 2005; Nagy, 2006; Rindermann, 2006; Prenzel et al, 2007; Baumert et al, 2009; Rindermann and Baumeister, 2015; Saß et al, 2017). Hence, it is not surprising that component skills for reading correlate with tests scores for reasoning tasks and vice versa, and this does not call the validity of the test score interpretation into question.…”

Section: Discussionmentioning

confidence: 98%

“…The wide range of situations to which general cognitive skills can be applied bring them into play as an alternative interpretation of competence scores. Whether competence tests used in large-scale assessments are also based on general cognitive skills and to what extent they represent the outcomes of learning processes have been investigated in numerous studies based on item scores (Brunner, 2005; Nagy, 2006; Rindermann, 2006; Prenzel et al, 2007; Baumert et al, 2009; Rindermann and Baumeister, 2015; Saß et al, 2017). The construct interpretation should be challenged through alternative interpretations that see general cognitive skills as also involved in literacy items.…”

Section: Research Questionsmentioning

confidence: 99%

Validating Test Score Interpretations Using Time Information

Engelhardt

Goldhammer

2019

Front. Psychol.

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A validity approach is proposed that uses processing times to collect validity evidence for the construct interpretation of test scores. The rationale of the approach is based on current research of processing times and on classical validity approaches, providing validity evidence based on relationships with other variables. Within the new approach, convergent validity evidence is obtained if a component skill, that is expected to underlie the task solution process in the target construct, positively moderates the relationship between effective speed and effective ability in the corresponding target construct. Discriminant validity evidence is provided if a component skill, that is not expected to underlie the task solution process in the target construct, does indeed not moderate the speed-ability relation in this target construct. Using data from a study that follows up the German PIAAC sample, this approach was applied to reading competence, assessed with PIAAC literacy items, and to quantitative reasoning, assessed with Number Series. As expected from theory, the effect of speed on ability in the target construct was only moderated by the respective underlying component skill, that is, word meaning activation skill as an underlying component skill of reading competence, and perceptual speed as an underlying component skill of reasoning. Accordingly, no positive interactions were found for the component skill that should not underlie the task solution process, that is, word meaning activation for reasoning and perceptual speed for reading. Furthermore, the study shows the suitability of the proposed validation approach. The use of time information in association with task results brings construct validation closer to the actual response process than widely used correlations of test scores.

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“…Further studies based on international large-scale assessments provided further evidence that test data are best modelled by general and specific factors (e.g. Saß, Kampa, and Köller 2017;Brunner 2005;Nagy 2006;Gustafsson and Balke 1993).…”

Section: Research On the Dimensionality Of Achievement In International Assessmentsmentioning

confidence: 98%

Disentangling general achievement levels and subject-specific strengths and weaknesses in mathematics, reading, and science

2020

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The paper uses data from the combined TIMSS (Trends in International Mathematics and Science Study) and PIRLS (Progress in International Reading Literacy Study) assessment in 2011 to explore the subject-specific strengths and weaknesses among fourth grade students worldwide. Previous research came to the conclusion that students only differed in overall achievement levels and did not exhibit subject-specific strengths and weaknesses. This research did, however, not control for differences in overall performance levels when searching for profile differences. Therefore, the present study uses factor mixture analysis to study qualitatively different performance profiles in mathematics, reading, and science while controlling for differences in performance levels. Our findings suggest that the majority of students do not show pronounced strengths and weaknesses and differ mainly in performance levels across mathematics, reading, and science. At the same time, a smaller share of students does indeed show pronounced subject-specific strengths and weaknesses. This result does not represent an artefact, but we find clear and theory-conforming associations between the identified profiles and covariates. We find evidence for cross-country differences in the frequency of subject-specific strengths and weaknesses and gender differences, as well as differences between students who do not or only sometimes speak the language of test at home.

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The interplay of g and mathematical abilities in large-scale assessments across grades

Cited by 70 publications

References 68 publications

Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions

Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions

Validating Test Score Interpretations Using Time Information

Disentangling general achievement levels and subject-specific strengths and weaknesses in mathematics, reading, and science

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