Alvin C. Rencher

Inflation of R2 in Best Subset Regression

When subset selection is used in regression the expected value of R 2 is substantially inflated above its value without selection, especially when the number of observations is less than the number of predictor variables. The extent of this increase was investigated by a Monte Carlo simulation. Tables are given with average values and percentage points of R 2 for the null case of independence between the response variable and the predictor variables. Approximation formulas are provided to supplement the coverage in the tables.

Interpretation of Canonical Discriminant Functions, Canonical Variates, and Principal Components

Abstract Canonical discriminant functions are defined here as linear combinations that separate groups of observations, and canonical variates are defined as linear combinations associated with canonical correlations between two sets of variables. In standardized form, the coefficients in either type of canonical function provide information about the joint contribution of the variables to the canonical function. The standardized coefficients can be converted to correlations between the variables and the canonical function. These correlations generally alter the interpretation of the canonical functions. For canonical discriminant functions, the standardized coefficients are compared with the correlations, with partial t and F tests, and with rotated coefficients. For canonical variates, the discussion includes standardized coefficients, correlations between variables and the function, rotation, and redundancy analysis. Various approaches to interpretation of principal components are compared: the choice ...

Fifty‐four voices from two: the effects of simultaneous manipulations of rate, mean fundamental frequency, and variance of fundamental frequency on ratings of personality from speech

Utterances of two adults males were analyzed and synthesized by a fast Fourier Transforms method. Each of the two voices was synthesized in each of the twenty‐seven combinations of three levels each of rate, mean FO, and variance of FO (a total of fifty‐four “voices” generated from two). The effects of the rate, mean FO, and variance of FO manipulations, the interactive effects of rate and variance of FO, and the effects due to speaker were all statistically significant predictors of personality ratings given the voices. They accounted for 86%, 4%, 3%, 2%, and I% of the variance, respectively, in competence ratings and 48%, 1%, 6%, 1%, and 8% of the variance, respectively, in benevolence ratings. Increased speaking rate was found to decrease the benevolence ratings, and decreased rate was found to decrease competence ratings. Decreased variance of FO was found to decrease the ratings on both competence and benevolence. Increased mean FO in these male voices was also found to decrease competence and benevo...

Perceptions of personality from speech: effects of manipulations of acoustical parameters.

A speech analysis‐synthesis system was used to manipulate variance of fundamental frequency and a mechanical rate changer was used to manipulate speech rate. The synthesized and altered voices were tested for realism. Synthesized voices were mistaken for normal 50% to 58% of the time and rate‐changed voices were mistaken for normal 78% of the time. Additional studies were conducted to test the effects of these acoustical manipulations on the adjective ratings judges made of speakers. Variance of intonation was increased and decreased by 50% for eight speakers. There was a significant trend for increased intonation to cause voices to be rated more “benevolent” by judges and decreased intonation to cause them to be rated less “benevolent.” In two additional studies, rate was decreased and increased by varying amounts. Slowing the voices caused them to be rated less “competent.” Speeding the voices caused them to be rated less “benevolent.” Results were more consistent over speakers for rate manipulations th...

Bias in Wilks' A in Stepwise Discriminant Analysis

When stepwise dkriminant analysis or MANOVA is performed, the mean and percentage points of Wii A are shifted downward. This bias was examined by Monte Carlo methods for the case of no differences between groups. The downward bias is especially pronounced when the number of variables exceeds the degrees of freedom for error.

BIAS in apparent classification rates in stepwise discriminant analysis

When p variables in a discriminant analysis are chosen by stepwise selection, the mean and percentage points of the apparent correct classification rates are positively biased as compared to the setting where p variables are not selected from a larger set. This bias due to subset selection is examined by Monte Carlo methods and compared to the bias due solely to resubstitution of the original sample. Both types of bias are intensified when the number of variables exceeds the degrees of freedom for error.

A retrospective epidemiological study of morbidity at a large western copper smelter

Smelter workers were compared with employees at the mine, concentrator and refinery in an attempt to discover if the smelter environment has an effect on morbidity. The data for the study consisted of weekly indemnity insurance claim forms. It was found that the refinery, rather than the smelter, had the highest percent of employees submitting claims. Other major comparisons of morbidity among the four plants also showed the refinery to be highest, with the smelter closer to the mine and concentrator. This pattern was found to hold for respiratory disease classifications as well as overall morbidity levels.

Acoustic Parameters of Personality

Twenty‐four adult males of diverse socioeconomic background were recorded as they recited a standard passage. They also recited the same passage while pretending to be excited and pretending to be depressed. The normal passages were analyzed and then synthesized by means of a terminal analog synthesizer, and then again synthesized in the following altered forms: (1) raised or lowered pitch, (2) increased and decreased variance of intonation, and (3) faster or slower rate of speaking. Judges listened to normal, excited, depressed, and the various machine‐manipulated forms of all voices and made personality judgments on semantic differential adjectives. In every case slowing the voice mechanically made the person sound less competent and speeding it made him sound less benevolent. Mechanically increased intonation makes a speaker sound more competent. Profound changes in the ratings assigned a voice were also induced by the “excited” and “depressed” instructions. The effects of such conscious changes by the speaker were not predictable, whereas those for mechanically produced changes were. Implications of the findings for objective acoustic personality analysis and psychiatric diagnosis are being explored.

Methods of Multivariate Analysis.

Introduction. Matrix Algebra. Characterizing and Displaying Multivariate Data. The Multivariate Normal Distribution. Tests on One or Two Mean Vectors. Multivariate Analysis of Variance. Tests on Covariance Matrices. Discriminant Analysis: Description of Group Separation. Classification Analysis: Allocation of Observations to Groups. Multivariate Regression. Canonical Correlation. Principal Component Analysis. Factor Analysis. Cluster Analysis. Graphical Procedures. Tables. Answers and Hints to Problems. Data Sets and SAS Files. References. Index.