Bayesian structural equation modeling for the health index

There are many factors which could influence the level of health of an individual. These factors are interactive and their overall effects on health are usually measured by an index which is called as health index. The health index could also be used as an indicator to describe the health level of a community. Since the health index is important, many research have been done to study its determinant. The main purpose of this study is to model the health index of an individual based on classical structural equation modeling (SEM) and Bayesian SEM. For estimation of the parameters in the measurement and structural equation models, the classical SEM applies the robust-weighted least-square approach, while the Bayesian SEM implements the Gibbs sampler algorithm. The Bayesian SEM approach allows the user to use the prior information for updating the current information on the parameter. Both methods are applied to the data gathered from a survey conducted in Hulu Langat, a district in Malaysia. Based on the classical and the Bayesian SEM, it is found that demographic status and lifestyle are significantly related to the health index. However, mental health has no significant relation to the health index.     

The Performance of Randomization Tests that Use Permutations of Independent Variables

ABSTRACT

In this article we evaluate the performance of a randomization test for a subset of regression coefficients in a linear model. This randomization test is based on random permutations of the independent variables. It is shown that the method maintains its level of significance, except for extreme situations, and has power that approximates the power of another randomization test, which is based on the permutation of residuals from the reduced model. We also show, via an example, that the method of permuting independent variables is more valuable than other randomization methods because it can be used in connection with the downweighting of outliers.     

Evaluation of Linear Trend Tests Using Resampling Techniques

A number of parametric and non-parametric linear trend tests for time series are evaluated in terms of test size and power, using also resampling techniques to form the empirical distribution of the test statistics under the null hypothesis of no linear trend. For resampling, both bootstrap and surrogate data are considered. Monte Carlo simulations were done for several types of residuals (uncorrelated and correlated with normal and nonnormal distributions) and a range of small magnitudes of the trend coefficient. In particular for AR(1) and ARMA(1, 1) residual processes, we investigate the discrimination of strong autocorrelation from linear trend with respect to the sample size. The correct test size is obtained for larger data sizes as autocorrelation increases and only when a randomization test that accounts for autocorrelation is used. The overall results show that the type I and II errors of the trend tests are reduced with the use of resampled data. Following the guidelines suggested by the simulation results, we could find significant linear trend in the data of land air temperature and sea surface temperature.     

A Statistical Reanalysis of the Classical Rutherford's Experiment

Modified chi-squared and some newly developed tests for the Poisson, binomial, and an approximated Feller's distribution are discussed. A reanalysis of the classical Rutherford's experimental data on alpha decay is done. Previous analyses of the data were not correct from the point of view of the theory of statistical testing. Tests used show that the data contradict to both Poisson and binomial distribution and do not contradict to a precise “binomial” approximation of Feller's distribution that takes into account a counter's dead time. This gives a plausible statistically correct confirmation of the well-established exponential law of radioactive decay.     

A Nonparametric Test for Symmetry Based on Freeman and Halton's Ideas on Contingency Tables

In this article, we propose a nonparametric method to test for symmetry in bivariate data. By using the extension of Fisher's exact treatment for 2 × 2 contingency tables proposed by Freeman and Halton (1951 Freeman , G. H. , Halton , J. H. ( 1951 ). Note on an exact treatment of contingency tables, goodness of fit and other problems of significance . Biometrika 38 : 141 – 149 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), we can test the hypothesis of equal distribution for two samples of integer valued variables. Then, by counting the number of observations belonging to each cell of a symmetric, appropriately built grid, we can produce the two samples of integers required to use this test for equal distribution. The resulting test for symmetry is potentially extendible to higher dimensions. A simulation study is performed to compare with some known tests (Bowker, 1948 Bowker , A. H. ( 1948 ). A test for symmetry in contingency tables . Journal of the American Statistical Association 43 : 572 – 574 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Hollander, 1971 Hollander , M. ( 1971 ). A nonparametric test for bivariate symmetry . Biometrika 58-1 : 203 – 212 .[Crossref], [Web of Science ®] , [Google Scholar]; and its improvement given in Krampe and Kuhnt, 2007 Krampe , A. , Kuhnt , S. ( 2007 ). Bowker's test for symmetry and modifications within the algebraic framework . Computational Statistics and Data Analysis 51 : 4124 – 4142 .[Crossref], [Web of Science ®] , [Google Scholar]). Our proposal represents a competitive option as a test for symmetry.     

New Section on Social Statistics

The analysis of a general k-factor factorial experiment having unequal numbers of observations per cell is complex. For the special case of a 2 ^k experiment with unequal numbers of observations per cell, the method of unweighted means provides a simple vehicle for analysis that requires no matrix inversion and can be used with existing software programs for the analysis of balanced data. All numerator sums of squares for testing main effects and interactions are χ² with one degree of freedom. In addition, for tests having one degree of freedom in any factorial experiment, the method of unweighted means may be modified to yield exact tests.     

Error rate for testing a contrast after a significant F test

In statistical applications an experimenter often tests a particular contrast after a significant F test for the equality of means. This paper evaluates the overall error rate for this testing .procedure.     

Computation of exact and approximate probability values for a matched pairs permutation test

An algorithm is presented for computing the probability value associated with a recently-developed test of statistical inference for matched pairs. The exact probability value is provided for small samples; otherwise, an approximate probability value is computed.     

Repeated measurements,log likelihood ratio tests and small samples

Various models have previously been proposed for data comprising m repeated measurements on each of N subjects. Log likelihood ratio tests may be used to help choose between possible models, but these tests are based on distributions which in theory apply only asymptotically. With small N , the log likelihood ratio approximation is unreliable, tending to reject the simpler of two models more often than it should. This is shown by reference to three datasets and analogous simulated data. For two of the three datasets, subjects fall into two groups. Log likelihood ratio tests confirm that for each of these two datasets group means over time differ. Tests suggest that group covariance structures also differ.     

A Note on the Variances of the Tests of Kendall,Jonckheere, and Terpstra

Recently, some papers have been appearing that have noticed some mistakes in the calculations in the statistical software in simple and classical tests (Wilcoxon–Mann-Whitney and Log-Rank). This article examines the variance formulas for the Kendall test, the Jonckheere test, and the Terpstra test. We show in this article that these variances (in spite of what is said in the literature and in the statistical software), in the presence of ties and r ≥ 3 groups, are only equal approximately and are exactly equal for two groups and ties as we prove in the Appendix.