While use of hierarchical linear modeling (HLM) to predict an outcome is reasonable and desirable, employing the model for prediction without first establishing the model’s predictive validity is ill-advised. Estimating the predictive validity of a regression model by cross-validation has been thoroughly researched, but there is a dearth of research investigating the cross-validation of hierarchical linear models. One of the major obstacles in cross-validating HLM is the lack of a measure of explained variance similar to the squared multiple correlation coefficient in regression analysis. The purpose of this Monte Carlo simulation study is to explore the impact of sample size, centering, and predictor-criterion correlation magnitudes on potential cross-validation measurements for hierarchical linear modeling. This study considered the impact of 64 simulated conditions across three explained variance approaches: Raudenbush and Bryk’s (2002) proportional reduction in error variance, Snijders and Bosker’s (1994) modeled variance, and a measure of explained variance proposed by Gagné and Furlow (2009). For each of the explained variance approaches, a cross-validation measurement, shrinkage, was obtained. The results indicate that sample size, predictor-criterion correlations, and centering impact the cross-validation measurement. The degree and direction of the impact differs with the explained variance approach employed. Under some explained variance approaches, shrinkage decreased with larger level-2 sample sizes and increased in others. Likewise, in comparing group- and grand-mean centering, with some approaches grand-mean centering resulted in higher shrinkage estimates but smaller estimates in others. Larger total sample sizes yielded smaller shrinkage estimates, as did the predictor-criterion correlation combination in which the group-level predictor had a stronger correlation. The approaches to explained variance differed substantially in their usability for cross-validation. The Snijders and Bosker approach provided relatively large shrinkage estimates, and, depending on the predictor-criterion correlation, shrinkage under both Raudenbush and Bryk approaches could be sizable to the degree that the estimate begins to lack meaning. Researchers seeking to cross-validate HLM need to be mindful of the interplay between the explained variance approach employed and the impact of sample size, centering, and predictor-criterion correlations on shrinkage estimates when making research design decisions.

This study investigates the effects of student sex, student’s interest in learning science and school characteristics – school type and school size- on 15-year-old scientific literacy in Canada through HLM. Using PISA data in 2006, the results showed 19% of the total variability in scientific literacy could be attributed to schools in Canada. There is a significant sex difference in scientific literacy in Canada at the student level. In addition, students’ interest in learning science is related to their scientific literacy significantly. Students who have a higher interest in learning the subjects of physics, chemistry, human biology, astronomy, and geology are predicted to achieve higher science scores than those students who have less interest in learning these subjects. In terms of the school characteristics variables, students who attend public schools have better scientific literacy scores. Also, students who go to bigger schools significantly outperform in scientific literacy.

The relative income is often cited as a reason why happiness of nations does not grow in time with growing GDP. The study replicates the methodology of several different researchers from basic scatterplots, standard OLS and ordered probit models to hierarchical linear multilevel models (HLM). The results provide evidence that the happiness is actually rising with the growing GDP, although slowly and with the GDP measured in logarithm. On the contrary, the relevance of relative income to happiness is ambiguous through all the proposed models. Furthermore, the individual characteristics like marital status or employment status are proved to explain the differences in happiness much better than income. Finally it is shown that income has similar effects on different measurements of subjective well-being (health, happiness and emotional well-being).

Self-efficacy is a person's own perception about performing a task with a certain level of proficiency (Bandura, 1986). An important affective aspect of learning chemistry is chemistry self-efficacy (CSE). Several researchers have found chemistry self-efficacy to be a fair predictor of achievement in chemistry. This study was done in a college preparatory chemistry class for science majors exploring chemistry self-efficacy and its change as it relates to achievement. A subscale of CAEQ, Chemistry Attitudes and Experiences Questionnaire (developed by Dalgety et al, 2003) as well as student interviews were used to determine student chemistry self-efficacy as it changed during the course. The questionnaire was given to the students five times during the semester: in the first class and the class before each the four tests taken through the semester. Twenty-six students, both men and women, of the four major races/ethnicities were interviewed three times during the semester and events that triggered changes in CSE were followed through the interviews. HLM (hierarchical linear modeling) was used to model the results of the CSE surveys. Among the findings, women who started at significantly lower CSE than men accomplished a significant gain by the end of the semester. Blacks' CSE trends through the semester were found to be significantly different from the rest of the ethnicities.

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