A likelihood ratio test for mixture effects

Under certain circumstances, it is theoretically important to decide whether a difference between two conditions in mean reaction time (RT) results from a relatively uniform slowing of all the responses in the slower condition or from a mixture of some slowed trials with some unslowed ones. This article describes a likelihood ratio test that can be used to differentiate between these two possibilities and reports computer simulations examining the power and Type I error rate of the test under conditions similar to those encountered in RT research. A freely available computer program, called MIXTEST, can be used both to carry out the likelihood ratio test and to conduct simulations evaluating the performance of the test within various settings.     

Theorems for a finite sequence from a two-state,first-order markov chain with stationary transition probabilities

Various theorems are obtained forN-trial sample sequences from the general two-state, first-order Markov chain with stationary transition probabilities. Four lemmas which facilitate the derivations are given. A brief discussion of applications to binary data, estimation, and evaluation is given, including a maximum-likelihood procedure for estimating transition probabilities which are restricted by inequalities.     

An asymptotic partial correlation test for the Goodman‐Kruskal λ

Goodman and Kruskal introduced a measure of predictive association when predicting the category of a variable A from a category of a variable B. This measure, denoted λ, is the asymmetric proportional reduction in error measure in predicting an individual's A category that can be eliminated by using knowledge of the B classification. It takes values on the unit interval, with a zero value meaning no predictive gain, while a value of unity indicates a perfect predictive association between A and B. A test of H₀: λ = 0 versus H₁: λ > 0 is analogous to a test for the significance of the correlation coefficient. A test of the partial λ coefficient, which is analogous to a test of the partial correlation coefficient, answers the question of whether knowledge of an additional third (or higher) classification or categorical variable results in a significant increase in predicting the variable A. Suich and Turek developed an exact test for the partial λ coefficient, but only for the situation where the predicted categorical variable A is dichotomous. The present paper completes the previous work by developing an asymptotic test where the predicted category A is any polytomous variable.     

Two-group classification in latent trait theory: Scores with monotone likelihood ratio

This paper deals with two-group classification when a unidimensional latent trait,, is appropriate for explaining the data,X. It is shown that ifX has monotone likelihood ratio then optimal allocation rules can be based on its magnitude when allocation must be made to one of two groups related to. These groups may relate to probabilistically via a non-decreasing functionp(), or may be defined by all subjects above or below a selected value on.In the case where the data arise from dichotomous items, then only the assumption that the items have nondecreasing item characteristic functions is enough to ensure that the unweighted sum of responses (the number-right score or raw score) possesses this fundamental monotone likelihood ratio property.     

An evaluation of touch-screen input for a HyperCard-based digit-span task

The touch screen appears to be an ideal input device for human subjects in many research applications in psychology. Nonetheless, the research on relative merits of input devices is inconclusive. The present experiments were carried out to compare touch-screen, mouse, and voice responses on a HyperCard-based digit-span task. The results indicated that touch-screen input has no advantage in comparison to the use of a mouse, but that it produces better performance than voice response does. The latter finding, however, may be an artifact of visual cues embedded in this implementation of the digit-span task.     

Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models

Using the theory of pseudo maximum likelihood estimation the asymptotic covariance matrix of maximum likelihood estimates for mean and covariance structure models is given for the case where the variables are not multivariate normal. This asymptotic covariance matrix is consistently estimated without the computation of the empirical fourth order moment matrix. Using quasi-maximum likelihood theory a Hausman misspecification test is developed. This test is sensitive to misspecification caused by errors that are correlated with the independent variables. This misspecification cannot be detected by the test statistics currently used in covariance structure analysis.For helpful comments on a previous draft of the paper we are indebted to Kenneth A. Bollen, Ulrich L. Küsters, Michael E. Sobel and the anonymous reviewers of Psychometrika. For partial research support, the first author wishes to thank the Department of Sociology at the University of Arizona, where he was a visiting professor during the fall semester 1987.     

A new proof for monotone likelihood ratio for the sum of independent bernoulli random variables

By use of an inequality of Marcus and Lopes for elementary symmetric functions, a new proof is presented for the following result by Ghurye and Wallace: Given that the independent random variablesX _j are Bernoulli with success probabilityp _j () strictly between 0 and 1 and nondecreasing in, the sum X _j has monotone likelihood ratio.     

Derivation of learning process statistics for a general markov model

A Markov learning model may be stated in the form of a transition matrix, starting vector, and response probability vector. Utilizing these and some general properties of absorbing Markov chains, general expressions are derived for several statistics of the learning process which can be applied to any model of this form. Included are derivations for the mean learning curve, number of total errors, trial numbers of the first success and the last error, and the number of error runs. As an illustration, all derivations are worked out for the simple two-state one-element model.     

Increasing and decreasing intrinsic interest with contingent rewards: A test of cognitive evaluation theory

The study examined Deci's (Deci, E. L. Intrinsic motivation. New York: Plenum Press, 1975) hypotheses regarding the effects of contingent rewards on intrinsic task interest. Seventy-two male university students worked on a series of puzzles and were given either a high value reward ($1.50) or a low value reward ($.45). The money was given either contingent upon the simple execution of the task (task-contingent), contingent upon the ostensible attainment of a performance criterion level (criterion-contingent), or noncontingent and unexpected (control). Compared to the high payment control subjects, subjects who received the task-contingent high reward rated the task as less interesting, while subjects who received the criterion-contingent high reward rated it as more interesting. Also, subjects expressed less interest in the task after receiving the high task-contingent reward than the low task-contingent reward, but indicated greater interest after receiving the high criterion-contingent reward than the low criterion-contingent reward. It was concluded that substantial support was obtained for Deci's (1975) cognitive evaluation theory.     

A maximum likelihood approach to test validation with missing and censored dependent variables

A maximum likelihood approach is described for estimating the validity of a test (x) as a predictor of a criterion variable (y) when there are both missing and censoredy scores present in the data set. The missing data are due to selection on a latent variable (y _s ) which may be conditionally related toy givenx. Thus, the missing data may not be missing random. The censoring process in due to the presence of a floor or ceiling effect. The maximum likelihood estimates are constructed using the EM algorithm. The entire analysis is demonstrated in terms of hypothetical data sets.     

An SAS/IML procedure for maximum likelihood factor analysis

Maximum likelihood factor analysis (MLFA), originally introduced by Lawley (1940), is based on a firm mathematical foundation that allows hypothesis testing when normality is assumed with large sample sizes. MLFA has gained in popularity since Jöreskog (1967) implemented an iterative algorithm to estimate parameters. This article presents a concise program using matrix language SAS/LML with the optimization subroutine NLPQN to obtain MLFA solutions. The program is pedagogically useful because it shows the step-by-step computational processes for MLFA, whereas almost all other statistical packages for MLFA are in “black boxes.” It is also demonstrated that this approach can be extended to other multivariate methods requiring numerical optimizations, such as the widely used structural equation modeling. Researchers may find this program useful in conducting Monte Carlo simulation studies to investigate the properties of multivariate methods that involve numerical optimizations.     

An alternative test for multisample sphericity

A test for multisample sphericity based on the efficient scores criterion is obtained as an alternative to the likelihood ratio test developed by Mendoza.     

An automated odor test for rats

The odor-testing apparatus described consists of a circular open-field area opening into four glass tubes, each with an odor source at the far end. When a rat is introduced, each tube is blocked by a grid; when the rat has touched each grid (sampled each odor), the tubes automatically open and recording of preference behavior starts. Two measures of preference are recorded by a photocell outside each tube, the number of visits and the time spent near the odor source. A uniformity test with food odor in all tubes showed that the apparatus did not promote position bias. In two separate sensitivity tests, one with food odor and one with estrous female urine odor, male rats significantly preferred an attractive odor in one tube to odorless controls. The apparatus yields relatively sensitive and reliable odor preference determinations by ensuring sampling of each odor before data are recorded and by eliminating visual, auditory and gustatory cues.     

An alternative scoring method for the Motivation Sources Inventory: a case for ratio analysis

Previously published research is examined, and an alternative scoring method for the Motivation Sources Inventory is proposed. The new method, ratio analysis, provides an empirical assessment more consistent with the theoretical framework of the inventory. Theoretical and empirical support for ratio analysis is provided.     

Maximum likelihood estimation of the joint covariance matrix for sections of tests given to distinct samples with application to test equating

Consider an old testX consisting ofs sections and two new testsY andZ similar toX consisting ofp andq sections respectively. All subjects are given testX plus two variable sections from either testY orZ. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X ₁, ...,X _s ,Y ₁, ...,Y _p ,Z ₁, ...,Z _q ) and describe an application of these estimation techniques to linear, observed-score, test equating.The author is indebted to Paul W. Holland and Donald B. Rubin for their encouragement and many helpful comments and suggestions that contributed significantly to the development of this paper.This research was supported by the Program Statistics Research Project of the ETS Research Statistics Group.     

An algorithm for generating artificial test clusters

An algorithm for generating artificial data sets which contain distinct nonoverlapping clusters is presented. The algorithm is useful for generating test data sets for Monte Carlo validation research conducted on clustering methods or statistics. The algorithm generates data sets which contain either 1, 2, 3, 4, or 5 clusters. By default, the data are embedded in either a 4, 6, or 8 dimensional space. Three different patterns for assigning the points to the clusters are provided. One pattern assigns the points equally to the clusters while the remaining two schemes produce clusters of unequal sizes. Finally, a number of methods for introducing error in the data have been incorporated in the algorithm.