https://rss.onlinelibrary.wiley.com/doi/pdf/10.2307/2347897

Multivariate normal probabilities with error bound

Publisher Summary Item response theory (IRT) deals with the statistical analysis of data in which responses of each of the number of respondents to each of the number of items or trials are assigned to define mutually exclusive categories. This chapter presents the best known item response models specifying the probability of response in each category as a function of parameters attributed to items and of a latent value attributed to the respondent. The extension of these models to more than one latent variable and possible respondent-level covariates is also discussed in the chapter. A further critical assumption in IRT is that item responses, given the respondent's location in the latent space, are statistically independent. It is important in IRT because it allows straightforward calculation of the likelihood of the model parameters, given the item responses of a sample of respondents. When the number of respondents is large, it leads to efficient, likelihood-based methods for IRT analysis in a wide variety of applications, including not only the measurement of individual differences, such as in education or clinical psychology, but also the estimation of group effects or population quantiles without the explicit calculation of respondent locations or “scores.”

Item response theory in a general framework

Non-linear regression with discrete explanatory variables, with an application to the earnings function

The purpose was to investigate whether an HIV-prevention curriculum and a health maintenance curriculum produced different rates of change in reported consistent condom use and to explore what mediating variables predicted reported consistent condom use over time. A longitudinal crossover research design with extended posttest observations was used with a sample of 279 African American women. After pretesting, women received the designated curriculum and were posttested at completion, 3, 6, and 9 months. After the 9-month posttest, the curriculum was switched, and the above procedure was repeated. Using SAS macro GLIMMIX, the data revealed that the HIV curriculum yielded higher consistent condom use than did the health maintenance curriculum and that the mediating variables that predicted consistent condomuse over time were self-efficacy for low-risk HIV behavior, HIV-related community behavior, and social norms. Enhancing consistent condom use over time may require the promotion and reinforcement of thes...

Condom use predictors for low-income African American women.

Known methods are described for evaluating the multivariate normal distribution function in general and in a number of special cases. Methods are presented for evaluation of the one-dimensional normal distribution function and its inverse.

Evaluation of the normal distribution function

Algorithm as 2: The Normal Integral

Algorithm AS 10: The Use of Orthogonal Polynomials

Ascop—A Statistical Computing Procedure

Input/output/ (I/O) is analysed in terms of the transfer of items of various types having various internal and external representations between various internal and external positions. Ways of describing representation and position are discussed, for both character and binary data. Three basic properties of good I/O facilities for statistical computing are stated, and the facilities offered by four existing programming languages are matched against them. Finally extensions to Fortran are proposed that would provide the properties sought.

Input/Output in Statistical Programming

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Papers

Algorithm as 2: The Normal Integral

Algorithm AS 10: The Use of Orthogonal Polynomials

Ascop—A Statistical Computing Procedure

Input/Output in Statistical Programming