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PEDAR: Research Methodology  The Road Lsss Traveled? Students Who Enroll in Multiple Institutions
Introduction
Beginning Postsecondary Students Longitudinal Study
The 2001 Baccalaureate and Beyond Longitudinal Study
Accuracy of Estimates
Item Response Rates
Data Analaysis System
Statistical Procedures
Differences Between Means
Linear Trends
Multivariate Commonality Analysis
Missing Data and Adjusting for Complex Sampling Design
Interpreting the Results
Executive Summary
References
Full Report (PDF)
Executive Summary (PDF)
 Statistical Procedures: Multivariate Commonality Analysis

Many of the independent variables included in the analyses in this report are related, and to some extent the pattern of differences displayed in the descriptive tables reflect a common variation. For example, when examining the degree attainment by multiple institution attendance patterns, some of the observed relationship may be due to differences in other factors related to attending multiple institutions, such as attendance intensity and persistence risk factors. However, if nested tables were used to present the influence of all related factors, cell sizes would become too small to find the significant differences in patterns. When the sample size becomes too small to include another level of variation, other methods must be used to take such variation into account.

The method in this report uses multiple linear regression to adjust for the common variation among a list of independent variables.10 This approach is sometimes referred to as commonality analysis11 because it identifies lingering relationships after adjustment for common variation. This method is used simply to confirm statistically significant associations observed in the bivariate analysis while taking into account the interrelationship of the independent variables. The analysis is not based on a theoretical model or used to establish causal inferences and the regression model is not reduced. In other words, subsequent models were not run that removed nonsignificant independent variables. Significant coefficients reported in the regression tables indicate that when the variable is deleted from the model, it results in a non-zero change in R-squared, which is the basis of the commonality analysis. In other words, a significant coefficient means that the independent variable has a relationship that is unique, or distinct from the independent variables’ common relationship with other independent variables in the model.

As discussed in the section “Data Analysis System” above, all analyses included in PEDAR reports must be based on the DAS, which is available to the public on-line. Exclusively using the DAS in this way provides readers direct access to the findings and methods used in the report so that they may replicate or expand on the estimates presented. However, the DAS does not allow users access to the raw data, which limits the range of covariation procedures that can be used. Specifically, the DAS produces correlation matrices, which can be used as input in standard statistical packages to produce least squares regression models. This means that logit or probit procedures, which are more appropriate for dichotomous dependent variables, cannot be used.12 However, empirical studies have shown that when the mean value of a dichotomous dependent variable falls between 0.25 and 0.75 (as it does in this analysis), regression and log-linear models are likely to produce similar results.13

The independent variables analyzed in this study and subsequently included in the multivariate model were chosen based on the descriptive analysis rather than on a theoretical model. Before conducting the study, a detailed analysis plan was reviewed by a Technical Review Panel (TRP) of experts in the field of higher education research and additional independent variables requested by the TRP were considered for inclusion. The analysis plan listed all the independent variables to be included in the study. The TRP also reviewed the preliminary results as well as the first draft of this report. The analysis plan and subsequent report were modified based on TRP comments and criticism.


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National Center for Education Statistics - http://nces.ed.gov
U.S. Department of Education