Individual differences in the perception of similarity and difference.

Thematically related concepts like coffee and milk are judged to be more similar than thematically unrelated concepts like coffee and lemonade. We investigated whether thematic relations exert a small effect that occurs consistently across participants (i.e., a generalized model), or a large effect that occurs inconsistently across participants (i.e., an individualized model). We also examined whether difference judgments mirrored similarity or whether these judgments were, in fact, non-inverse. Five studies demonstrated the necessity of an individualized model for both perceived similarity and difference, and additionally provided evidence that thematic relations affect similarity more than difference. Results suggest that models of similarity and difference must be attuned to large and consistent individual variability in the weighting of thematic relations

Online Updating of Statistical Inference in the Big Data Setting

We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop iterative estimating algorithms and statistical inferences for linear models and estimating equations that update as new data arrive. These algorithms are computationally efficient, minimally storage-intensive, and allow for possible rank deficiencies in the subset design matrices due to rare-event covariates. Within the linear model setting, the proposed online-updating framework leads to predictive residual tests that can be used to assess the goodness-of-fit of the hypothesized model. We also propose a new online-updating estimator under the estimating equation setting. Theoretical properties of the goodness-of-fit tests and proposed estimators are examined in detail. In simulation studies and real data applications, our estimator compares favorably with competing approaches under the estimating equation setting.Comment: Submitted to Technometric

Individual differences in the perception of similarity and difference

Thematically related concepts like coffee and milk are judged to be more similar than thematically unrelated concepts like coffee and lemonade. We investigated whether thematic relations exert a small effect that occurs consistently across participants (i.e., a generalized model), or a large effect that occurs inconsistently across participants (i.e., an individualized model). We also examined whether difference judgments mirrored similarity or whether these judgments were, in fact, non-inverse. Five studies demonstrated the necessity of an individualized model for both perceived similarity and difference, and additionally provided evidence that thematic relations affect similarity more than difference. Results suggest that models of similarity and difference must be attuned to large and consistent individual variability in the weighting of thematic relations

Aligned Rank Statistics for Repeated Measurement Models with Orthonormal Design, Employing a Chernoff-Savage Approach

AMS classifications: 62G10, 62G20; 62J05.aligned rank statistics;orthonormal design matrix;repeated measurements;Chernoff-Savage approach

An Invariance Property of Common Statistical Tests

Let A be a symmetric matrix and B be a nonnegative definite (nnd) matrix. We obtain a characterization of the class of nnd solutions Σ for the matrix equation AΣA = B. We then use the characterization to obtain all possible covariance structures under which the distributions of many common test statistics remain invariant, that is, the distributions remain the same except for a scale factor. Applications include a complete characterization of covariance structures such that the chisquaredness and independence of quadratic forms in ANOVA problems is preserved. The basic matrix theoretic theorem itself is useful in other characterizing problems in linear algebra. © 1997 Elsevier Science Inc