Dennis L. Jackson

Revisiting Sample Size and Number of Parameter Estimates: Some Support for the N:q Hypothesis.

A number of authors have proposed that determining an adequate sample size in structural equation modeling can be aided by considering the number of parameters to be estimated. While this advice seems plausible, little empirical support appears to exist. A previous study by Jackson (2001), failed to find support for this hypothesis, however, there were certain limitations to the study that likely led to the lack of findings. This study revisits the issue with a design modified to be more sensitive to practically significant effects of sample size to parameter estimate ratio. Consequently, some support was found for this hypothesis, notably among overall fit measures and tests. Results indicate that higher values of the observations per parameter ratio had a positive effect for some measures of fit. However, the overall effect was small relative to absolute sample size.

Sample Size and Number of Parameter Estimates in Maximum Likelihood Confirmatory Factor Analysis: A Monte Carlo Investigation

A number of authors have proposed that determining an adequate sample size in structural equation modeling can be aided by considering the number of parameters to be estimated. This study directly investigates this assumption in the context of maximum likelihood confirmatory factor analysis. The findings support previous research on the effect of sample size, measured-variable reliability, and the number of measured variables per factor. However, no practically significant effect was found for the number of observations per estimated parameter.

The Dimensions of Students' Perceptions of Teaching Effectiveness.

The use of student ratings of instructional quality is enhanced by an understanding of the nature of the underlying dimensions. In the current investigation, confirmatory factor analysis procedures were used to assess the fit of the original solution for the Student’s Perceptions of Teaching Effectiveness questionnaire to a more recent sample of more than 7,000 university classes. Furthermore, a new exploratory factor analysis was used to examine the factor pattern after excluding certain items. The latter solution was crossvalidated on an additional sample. The analyses provided a clear interpretation of six first-order and two second-order dimensions of instructional quality that are useful across a broad range of university courses. The dimensions of teaching quality obtained by researchers are examined and compared to the results of the current study. Implications for the evaluation of perceived teaching quality are discussed.

Reporting results of latent growth modeling and multilevel modeling analyses: some recommendations for rehabilitation psychology.

OBJECTIVE There has been a general increase in interest and use of modeling techniques that treat data as nested, whether it is people nested within larger units, such as families or treatment centers, or observations nested under people. The popularity can be witnessed by noting the number of new textbooks and articles related to latent growth curve modeling and multilevel modeling. This paper discusses both of these techniques in the context of longitudinal research designs, with the main purposes of highlighting some benefits and issues related to the use of these models and outlining guidelines for reporting results from studies using multilevel modeling or latent growth modeling. IMPLICATIONS These longitudinal analytic techniques can be greatly beneficial to researchers conducting rehabilitation studies, but there are several issues related to their use and reporting that need to be taken into consideration.

A Note on Sample Size and Solution Propriety for Confirmatory Factor Analytic Models

Determining an appropriate sample size for use in latent variable modeling techniques has presented ongoing challenges to researchers. In particular, small sample sizes are known to present concerns over sampling error for the variances and covariances on which model estimation is based, as well as for fit indexes and convergence failures. The literature on the topic has focused on conducting power analyses as well as identifying rules of thumb for deciding an appropriate sample size. Often the advice involves an assumption that sample size requirement is moderated by aspects of the model in question. In this study, an effort was undertaken to extend the findings of Gagné and Hancock (2006) on measurement model quality and solution propriety to a broader set of confirmatory factor analysis models. As well, we examined whether Herzog, Boomsma, and Reineckes (2007) findings for the Swain correction to the χ2 statistic for large models would generalize to models in our study. Our findings suggest that Gagné and Hancocks approach extends to large models with surprisingly little increase in sample size requirements and that the Swain correction to χ2 performs fairly well. We argue that likely rejection or model fit should be taken into account when determining sample size requirements and therefore, provide an updated table of minimum sample size that incorporates Gagné and Hancocks method and model fit.

Review of The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century, by David Salsburg

Today’s researcher would find it difficult to imagine a time when standard approaches to experimental design were not understood and documented. However, this was the case when Ronald Aylmer Fisher first arrived at the Rothamsted Agricultural Experimental Station in the early 1900s: A common approach to experimental design did not exist. In fact, for some 90 years prior to his arrival, researchers at Rothamsted had experimented with different fertilizer mixtures by applying a mixture to the entire field and dutifully recording rainfall, temperatures, and crop yield for the growing season. Then, during the next season they would repeat the experiment with a different fertilizer. Consequently, debates about which fertilizer mixtures were optimum had not been resolved. Fisher was hired to sort through the data. He promptly introduced experimental methods into the research, and soon evidence regarding the fertilizer mixtures that were effective emerged. In The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century, this story and numerous others have been compiled by David Salsburg. Beyond providing an overview of the history of the development of statistics in the 20th century, the book is notable for other reasons. First, Salsburg provides many interesting details about the characteristics and backgrounds of the people who most influenced the field of statistics; he also shares personal anecdotes as he has had the opportunity to meet many of the contributors to the field. The book is nearly worth reading for this reason alone. Second, Salsburg, a retired biostatistician, displays a real talent for elucidating the relevance of many statistical discoveries. He clearly describes the contributions of many statistical discoveries that are not as immediately obvious as, for example, Fisher’s work on experimental design. An example of this is the discussion of L. H. C. Tippett’s three asymptotes of the extreme—a discovery that allowed Tippett to connect the distribution of extreme values to the distribution from a sample of data. Salsburg adeptly explains the relevance of this discovery by pointing out that it has allowed the U.S. Army Corp of Engineers to estimate the probable height of a river during the worst flood conditions, without having measurements of the worst flood STRUCTURAL EQUATION MODELING, 10(4), 651–655 Copyright

A Structural Model of Appropriate Adult Functioning for Boys with Disruptive Behavior Disorders

Saint Francis Academy is a residential treatment center for boys with disruptive behavior disorders. Previously collected posttreatment data was factor analyzed yielding nine factors, six of which contributed to a second-order factor called Appropriate Adult Functioning. A structural model using these six factors produced from data collected from ex-residents at 2 years postrelease was analyzed using EQS (a structural modeling program). The model was then validated using data from subsequent follow-ups. Results required the removal of one path, but otherwise the a priori model fit the data for all three follow-ups. The adjustments in path values required for subsequent follow-ups allowed for dynamic interpretations. Of particular interest were the findings regarding the growing impact of Responsibility on Emotional-Well Being and Financial Independence and the relationship of Financial Independence to Legal Involvement. Implications for treatment design and evaluation strategies are given.