All parametric statistical analyses have certain assumptions about the data that must be met reasonably to warrant the use of a given analysis. Distributional normality, for example, is a common assumption. There is a variety of ways that data in a distribution may detract from normality, but one common problem is the presence of outliers. Many…

Use of the method of reciprocal biweighted means (MBM) for dealing with the outlier problem in dual scaling compared favorably with other robust estimation procedures, such as the method of trimmed reciprocal averages. Four datasets from previous studies were used. Advantages of the MBM are discussed. (SLD)

This paper gives concise descriptions of a robust location statistic, the remedian of P. Rousseeuw and G. Bassett (1990) and a robust measure of dispersion, the "Sn" of P. Rousseeuw and C. Croux (1993). The use of Sn in least absolute errors regression (L1) is discussed, and BASIC programs for both statistics are provided. The remedian…

P. Rousseeuw and A. Leroy (1987) proposed a very robust alternative to classical estimates of mean vectors and covariance matrices, the Minimum Volume Ellipsoid (MVE). This paper describes the MVE technique and presents a BASIC program to implement it. The MVE is a "high breakdown" estimator, one that can cope with samples in which as…

This study developed a robust linear regression technique based on the idea of weighted least squares. In this technique, a subsample of the full data of interest is drawn, based on a measure of distance, and an initial set of regression coefficients is calculated. The rest of the data points are then taken into the subsample, one after another,…

In this study, the robustness of item parameter estimates with respect to the underlying distribution of abilities was explored. Using simulated datasets, item parameters were derived from a large sample representing the population versus samples representing a subset of ability and subsequently compared for possible mismatch. Comparisons were…

Examined the asymptotic distributions of three reliability coefficient estimates: (1) sample coefficient alpha; (2) reliability estimate of a composite score following factor analysis; and (3) maximal reliability of a linear combination of item scores after factor analysis. Findings show that normal theory based asymptotic distributions for these…

Assessed the robustness of an estimation method for multilevel and path analysis with hierarchical data proposed by B. Muthen (1989) with unequal groups and small sample sizes and in the presence of a low or high intraclass correlation. Simulation results show the effects of varying these conditions on the within-group and between-groups part of…

Studied the efficiency and robustness of alternative estimators of regression coefficients for three-level data. A simulation study shows that, as expected, the hierarchical model analyses produced more efficient point estimates than did analyses that ignored the covariance structure in the data, even when the normality assumption was violated.…

The robustness of the polytomous Item Response Theory (IRT) model to violations of the unidimensionality assumption was studied. A secondary purpose was to provide guidelines to practitioners to help in deciding whether to use an IRT model to analyze their data. In a simulation study, the unidimensionality assumption was deliberately violated by…

Studied the one-parameter Item Response Theory model with normal item-characteristic curves in a longitudinal context. Results of a simulation suggest that the proposed procedure is rather robust against departures from normality. However, the estimation of the correlations between regression parameters can be seriously biased. (SLD)

Studied the effects of test dimensionality, theta distribution shape, and estimation program (BILOG, MULTILOG, or XCALIBRE) on the accuracy of item and person parameter estimates through simulation. Derived guidelines for estimating parameters of multidimensional test items using unidimensional item response theory models. (SLD)

A high-breakdown estimator is a robust statistic that can withstand a large amount of contaminated data. In linear regression, high-breakdown estimators can detect outliers and distinguish between good and bad leverage points. This paper summarizes the case for high-breakdown regression and emphasizes the least quartile difference estimator (LQD)…

This paper reports an attempt to identify appropriate and robust location estimators for situations that tend to occur among various types of empirical data. Emphasizing robustness across broad unidentifiable ranges of contamination, an attempt was made to replicate, on a somewhat smaller scale, the definitive Princeton Robustness Study of 1972 to…

Two important parameters of the general utility function--the standard deviation of job performance and predictor performance--were examined in terms of their sensitivity to departures from underlying mathematical assumptions. Integral calculus was used to assess the effects of statistical violations of the assumptions underlying these parameters.…