HT 24: Selected statistical methods with applications

Vt 24: Multivariate analysis

• Linear models (mixed linear models, multilevel models)
• Multivariate statistics (multivariate linear models)
• Matrix algebra and its applications to Statistics
• Statistical diagnostics in mixed linear models
• Small area estimation

A selection from Stockholm University publication database

• Teacher-student relationships and students' self-efficacy beliefs. Rationale, validation and further potential of two instruments

  2023. Ulf Jederlund, Tatjana von Rosen. Education Inquiry 14 (4), 529-553

  Article

  High quality of teacher–student relationships is widely recognized as fundamental part of good education. Moreover, students’ self-efficacy beliefs, or their confidence to succeed within different domains at school, are important impact factors to achievement. Although there is support for an association between student-perceived teacher–student relationship quality and students’ self-efficacy judgements, which mediates achievement, no tool explores this association. This article suggests that two instruments, respectively measuring students’ perceptions of teacher–student relationship quality (TSR) and student’s self-efficacy (SSE), can be used in parallel for a multifaceted exploration of individual students’ perception of TSR quality, in relationship to their self-efficacy. Two well-established instruments were adopted, validated and their factor structures re-confirmed in a Swedish sample, using data from students in five schools (n=382). Factor analysis showed that models with three underlying dimensions of TSR and four underlying dimensions of SSE were the most appropriate. All sub-scales showed good-to-excellent reliability (Cronbach’s α = 0.75–0.94). Findings indicated a lack of multigroup invariance across gender and school level for the TSR-model. Substantial associations were found between student-perceived teacher support, and students’ self-efficacy for self-regulated learning and global academic success. We discuss utility and limitations, need of model improvement, and future potential.   

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• Changes in Students’ School Trust as a Reflection of Teachers’ Collective Learning Processes: Findings from a Longitudinal Study

  2022. Ulf Jederlund, Tatjana von Rosen. Scandinavian Journal of Educational Research 66 (7), 1161-1182

  Article

  This 2-year longitudinal study compares students’ trajectories for perceived teacher–student relationship quality and students’ selfefficacy (together discussed as students’ school trust) to previously documented teacher-perceived experiences in teacher teams’ collective learning processes. The article’s main contribution is the reflection in students’ perceptions, of their teachers’ perceived quality and attainment in collective learning processes. Comparisons between schools show that trajectories for students belonging to the only teacher team that experienced a more mature and successful learning process in an earlier study, differed significantly from the trajectories for students in compared teams. Differences demonstrated large positive effect sizes (d=0.81–1.14). Individual analysis provides deeper insights about how these students’ perceptions changed. Additionally, the full sample data confirms earlier findings of substantial cross-associations between student-perceived teacher–student relationship quality and student self-efficacy. For example, sustainable associations between supportive teacher–student relationships and students’ global academic self-efficacy and self-efficacy for self-regulative learning were found (r = 0.43–0.51).

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• Hypothesis testing in multivariate normal models with block circular covariance structures

  2022. Yuli Liang, Carlos A. Coelho, Tatjana von Rosen. Biometrical Journal 64 (3), 557-576

  Article

  In this article, we address the problem of simultaneous testing hypothesis about mean and covariance matrix for repeated measures data when both the mean vector and covariance matrix are patterned. In particular, tests about the mean vector under block circular and doubly exchangeable covariance structures have been considered. The null distributions are established for the corresponding likelihood ratio test statistics, and expressions for the exact or near-exact probability density and cumulative distribution functions are obtained. The application of the results is illustrated by both a simulation study and a real-life data example.

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• On properties of Toeplitz-type covariance matrices in models with nested random effects

  2021. Yuli Liang, Dietrich von Rosen, Tatjana von Rosen. Statistical papers 62, 2509-2528

  Article

  Models that capture symmetries present in the data have been widely used in different applications, with early examples from psychometric and medical research. The aim of this article is to study a random effects model focusing on the covariance structure that is block circular symmetric. Useful results are obtained for the spectra of these structured matrices.

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• A new method for obtaining explicit estimators in unbalanced mixed linear models

  2020. Tatjana von Rosen, Dietrich von Rosen, Julia Volaufova. Statistical papers 61 (1), 371-383

  Article

  The general unbalanced mixed linear model with two variance components is considered. Through resampling it is demonstrated how the fixed effects can be estimated explicitly. It is shown that the obtained nonlinear estimator is unbiased and its variance is also derived. A condition is given when the proposed estimator is recommended instead of the ordinary least squares estimator.

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• Bilinear regression with random effects and reduced rank restrictions

  2020. Tatjana von Rosen, Dietrich von Rosen. Japanese journal of statistics and data science 3 (1), 63-72

  Article

  Bilinear models with three types of effects are considered: fixed effects, random effects and latent variable effects. In the literature, bilinear models with random effects and bilinear models with latent variables have been discussed but there are no results available when combining random effects and latent variables. It is shown, via appropriate vector space decompositions, how to remove the random effects so that a well-known model comprising only fixed effects and latent variables is obtained. The spaces are chosen so that the likelihood function can be factored in a convenient and interpretable way. To obtain explicit estimators, an important standardization constraint on the random effects is assumed to hold. A theorem is presented where a complete solution to the estimation problem is given.

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• Small area estimation using reduced rank regression models

  2020. Tatjana von Rosen, Dietrich von Rosen. Communications in Statistics - Theory and Methods 49 (13), 3286-3297

  Article

  Small area estimation techniques have got a lot of attention during the last decades due to their important applications in survey studies. Mixed linear models and reduced rank regression analysis are jointly used when considering small area estimation. Estimates of parameters are presented as well as prediction of random effects and unobserved area measurements.

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Show all publications by Tatjana von Rosen at Stockholm University