Hierarchical linear models (HLM) solve the problems associated with the unit of analysis problem such as misestimated standard errors, heterogeneity of regression and aggregation bias by modeling all levels of interest simultaneously. Hierarchical linear modeling resolves the problem of misestimated standard errors by incorporating a unique random…

Three ridge regression solutions are compared with ordinary least squares regression and with principal components regression using all components. Ridge regression, particularly the Lawless-Wang solution, out-performed ordinary least squares regression and the principal components solution on the criteria of stability of coefficient and closeness…

This article presents findings from the first independent, third-party appraisal on the impact of the Teacher Advancement Program (TAP) on student test score gains in mathematics. TAP is a comprehensive school reform model designed to attract highly-effective teachers, improve instructional effectiveness, and elevate student achievement. We use a…

The iterative expanding reweighted least squares (IERLS), a weighted-least-squares robust regression procedure, is developed and compared with Huber's M estimator (P. Huber, 1973), the Least Absolute Deviations, the Least Median of Squares, and the Ordinary Least Squares. Data with various outliers contamination were simulated and analyzed. The…

Tests of mean equality proposed by Alexander and Govern (1994) and Tsakok (1978) were compared to the well-known procedures of Brown and Forsythe (1974), James (1951), and Welch (1951) for their ability to limit the number of Type I errors in one-way designs where the underlying distributions were nonnormal, variances were nonhomogeneous, and…

The purpose of this paper is to illustrate the use of tobit analysis and tobit decomposition in educational research. Tobit estimates of growth rate in the presence of a ceiling effect were compared with ordinary least squares (OLS) and weighted least squares (WLS) estimates. The tobit estimates had the smallest standard error, the smallest bias,…

The use of two-stage least squares (2SLS) for the estimation of feedback linkages is inappropriate for nonorthogonal data sets because 2SLS is extremely sensitive to multicollinearity. It is argued that what is needed is use of a different estimating criterion than the least squares criterion. Theoretically the variance normalization criterion has…

A Monte Carlo study was performed to test under what conditions and to what degree various alternatives would be superior to multiple linear regression (MLR). The criteria used was the mean squared error of prediction of individual scores and the mean squared error of estimation of the regression weights. Populations were simulated containing…

This study examined the structural organizational characteristics of 51 higher education institutions in a single state (23 four-year and 28 two-year campuses) in relation to student performance and growth. In all, 7,658 students completed the assessment instrument at the end of their second year. The study found that organizational measures of…

A Monte Carlo study was conducted to assess the robustness of the limited information two-stage least squares (2SLS) estimation procedure on a confirmatory factor analysis model with nonnormal distributions. Full information maximum likelihood methods were used for comparison. One hundred model replications were used to generate data. (TJH)

This study compared the model of J. E. Grizzle, C. F. Starmer, and G. G. Koch (GSK, 1969) and log-linear model-based approaches for testing hypotheses in r x c contingency tables. Tables were simulated under various conditions of table, sample, row-effect size, and column-effect size. Test statistics for column (main) and interaction effects were…

Latent Variables Path (LVP) models have been found to be a helpful device for the formulation and validation of complex theories in educational sciences. The estimation of parameters for LVP models can use the Maximum Likelihood (ML) or the Partial Least Squares (PLS) method. This paper focusses on the PLS method introduced by H. Wold, and…

The intent of the study was to determine the extent to which test statistics computed by the unweighted means analysis are F-distributed. Applicability criteria were sought in terms of the number of factor levels and the degree to which cell frequencies differ. The unweighted means analysis, a frequently used approximate analysis, was contrasted…

A modified regression procedure for finding a common metric for item response theory (IRT) parameter estimates and for total test scores is proposed and compared to the chi-square method of equating. The chi-square method was chosen after literature review for the currently used scaling procedures. The modification used with the regression…

Several regression methods were examined within the framework of weighted structural regression (WSR), comparing their regression weight stability and score estimation accuracy in the presence of outlier contamination. The methods compared are: (1) ordinary least squares; (2) WSR ridge regression; (3) minimum risk regression; (4) minimum risk 2;…