Generalized Mantel-Haenszel Estimators for Simultaneous Differential Item Functioning Tests

The Mantel-Haenszel estimator is one of the most popular techniques for measuring differential item functioning (DIF). A generalization of this estimator is applied to the context of DIF to compare items by taking the covariance of odds ratio estimators between dependent items into account. Unlike the Item Response Theory, the method does not rely on the local item independence assumption which is likely to be violated when one item provides clues about the answer of another item. Furthermore, we use these (co)variance estimators to construct a hypothesis test to assess DIF for multiple items simultaneously. A simulation study is presented to assess the performance of several tests. Finally, the use of these DIF tests is illustrated via application to two real data sets.

The Effect of Clenching and Occlusal Instability on Body Weight Distribution, Assessed by a Postural Platform

The purpose of this research project was to investigate whether or not clenching and occlusal instability of Angle's Class I malocclusion have an effect on body weight distribution in healthy adult subjects. Twenty adults (fourteen males and six females, ages 27-40, mean age 31.7 years, SD 3.32) were included in this study. The MatScan (Tekscan Inc., Boston, MA) system was used to measure the body weight distribution changes of the subjects. Four body weight distribution measurements were taken for each subject while (1) the mandible was in the rest position (no tooth contact) (RES), (2) subject was clenching (maximum intercuspation of the teeth with heavy occlusal forces) (CL), (3) subject was clenching on the right side (with 1 mm disocclusion on the left side) (CLR), and (4) subject was clenching on the left side (with 1 mm disocclusion on the right side) (CLL). The lateral and the anteroposterior body weight distribution changes during the different clenching conditions (both sides, right, and left) were compared to those at which the mandible was at the rest position. The statistical significance of these results was tested with a Chi-Squared test (p<0.05). Based on the findings of the present study it was concluded that clenching and occlusal instability are associated with lateral body weight distribution changes.

Methods for parameter identification in oscillatory networks and application to cortical and thalamic 600 Hz activity

Directed information transfer in the human brain occurs presumably by oscillations. As of yet, most approaches for the analysis of these oscillations are based on time-frequency or coherence analysis. The present work concerns the modeling of cortical 600 Hz oscillations, localized within the Brodmann Areas 3b and 1 after stimulation of the nervus medianus, by means of coupled differential equations. This approach leads to the so-called parameter identification problem, where based on a given data set, a set of unknown parameters of a system of ordinary differential equations is determined by special optimization procedures. Some suitable algorithms for this task are presented in this paper. Finally an oscillatory network model is optimally fitted to the data taken from ten volunteers.

Testing for Marginal Independence between Two Categorical Variables with Multiple Responses

Questions that ask respondents to "choose all that apply" from a set of items occur frequently in surveys. Categorical variables that summarize this type of survey data are called both pick any/c variables and multiple-response categorical variables. It is often of interest to test for independence between two categorical variables. When both categorical variables can have multiple responses, traditional Pearson chi-square tests for independence should not be used because of the within-subject dependence among responses. An intuitively constructed version of the Pearson statistic is proposed to perform the test using bootstrap procedures to approximate its sampling distribution. First- and second-order adjustments to the proposed statistic are given in order to use a chi-square distribution approximation. A Bonferroni adjustment is proposed to perform the test when the joint set of responses for individual subjects is unavailable. Simulations show that the bootstrap procedures hold the correct size more consistently than the other procedures.

Permutation analysis of data with multiple binary category choices

In many studies, respondents may mark all answers that apply when responding to a multiple-choice question, i.e., a cafeteria or multiple-response question. One exact and two approximate permutation methods are described to analyze multiple-response questions. The methods provide the probability, under the null hypothesis, that the multiple binary responses do not differ among specified groups.

Testing for conditional multiple marginal independence

Survey respondents are often prompted to pick any number of responses from a set of possible responses. Categorical variables that summarize this kind of data are called pick any/c variables. Counts from surveys that contain a pick any/c variable along with a group variable (r levels) and stratification variable (q levels) can be marginally summarized into an r x c x q contingency table. A question that may naturally arise from this setup is to determine if the group and pick any/c variable are marginally independent given the stratification variable. A test for conditional multiple marginal independence (CMMI) can be used to answer this question. Since subjects may pick any number out of c possible responses, the Cochran (1954, Biometrics 10, 417-451) and Mantel and Haenszel (1959, Journal of the National Cancer Institute 22, 719-748) tests cannot be used directly because they assume that units in the contingency table are independent of each other. Therefore, new testing methods are developed. Cochran's test statistic is extended to r x 2 x q tables, and a modified version of this statistic is proposed to test CMMI. Its sampling distribution can be approximated through bootstrapping. Other CMMI testing methods discussed are bootstrap p-value combination methods and Bonferroni adjustments. Simulation findings suggest that the proposed bootstrap procedures and the Bonferroni adjustments consistently hold the correct size and provide power against various alternatives.

On the first-order Rao-Scott correction of the Umesh-Loughin-Scherer statistic

Decady and Thomas (2000, Biometrics 56, 893-896) propose a first-order corrected Umesh-Loughin-Scherer statistic to test for association in an r x c contingency table with multiple column responses. Agresti and Liu (1999, Biometrics 55, 936-943) point out that such statistics are not invariant to the arbitrary designation of a zero or one to a positive response. This paper shows that, in addition, the proposed testing procedure does not hold the correct size when there are strong pairwise associations between responses.

A simple test of association for contingency tables with multiple column responses

Loughin and Scherer (1998, Biometrics 54, 630-637) investigated tests of association in two-way tables when one of the categorical variables allows for multiple-category responses from individual respondents. Standard chi-squared tests are invalid in this case, and they developed a bootstrap test procedure that provides good control of test levels under the null hypothesis. This procedure and some others that have been proposed are computationally involved and are based on techniques that are relatively unfamiliar to many practitioners. In this paper, the methods introduced by Rao and Scott (1981, Journal of the American Statistical Association 76, 221-230) for analyzing complex survey data are used to develop a simple test based on a corrected chi-squared statistic.

Modeling a categorical variable allowing arbitrarily many category choices

This article discusses the modeling of a categorical variable for which subjects can select any number of categories. For c categories, the response variable consists of a cross-classification of c binary components, one pertaining to each category. Using data from a survey (Loughin, T. M. and Scherer, P. N., 1998, Biometrics, 54, 630 637) in which Kansas farmers indicated their primary sources of veterinary information, we discuss simultaneous logit modeling of the binary components of the multivariate response. The use of maximum likelihood or quasi-likelihood fitting provides chi-squared tests with degrees of freedom df = c(r - 1) for testing the independence between each of the c response components and an explanatory variable with r categories. These tests are alternatives to the weighted chi-squared test and the bootstrap test proposed by Loughin and Scherer for this hypothesis.