Generalized Linear Latent Variable Modeling for Multi-Group Studies

ABSTRACT

Latent variable modeling is commonly used in behavioral, social, and medical science research. The models used in such analysis relate all observed variables to latent common factors. In many applications, the observations are highly non normal or discrete, e.g., polytomous responses or counts. The existing approaches for non normal observations can be considered lacking in several aspects, especially for multi-group samples situations. We propose a generalized linear model approach for multi-sample latent variable analysis that can handle a broad class of non normal and discrete observations, and that furnishes meaningful interpretation and inference in multi-group studies through maximum likelihood analysis. A Monte Carlo EM algorithm is proposed for parameter estimation. The convergence assessment and standard error estimation is addressed. Simulation studies are reported to show the usefulness of the our approach. An example from a substance abuse prevention study is also presented.     

On the optimality of the sample variance

The present paper explores the structure of linear exponential families for which the sample variance is a uniformly minimum variance unbiased estimator.     

Maximum likelihood ridge displays

I illustrate likelihood methods for estimating the consequences of shrinkage along any ridge path as well as methods for picking a two-hyperparameter path of optimal curvature and the optimal point on that path. In addition to my published "classical" methods, I also illustrate both the empirical Bayes and the random coefficient maximum likelihood approaches. Traces of risks for known parameters and losses for simulated responses are followed by traces of estimates that can reveal the same general information.     

PROPERTIES OF THE MINIMUM POINT OF AN UNBALANCED TWO-SIDED RANDOM WALK

In this paper, properties of minimum point of a unbalanced two-sided random walk are investigated. Under the condition that the parameters at both sides tend to zero at the same order, probabilities that the minimum point is on which side, and the second order expansions for the first two moments of the minimum point are obtained. Applications of these results are very promising. First, they can be used to study the properties of the maximum likelihood estimator for the change point in the large sample case; second, they can be used to study inference problems after CUSUM test.     

Third-Order Asymptotic Distributions of Classic Test Statistics for One-Parameter Exponential Family Models

ABSTRACT

In this article we derive third-order asymptotic expansions for the non null distribution functions of four classic statistics under a sequence of local alternatives in one-parameter exponential family models. Our results are quite general and cover a wide range of important distributions.     

Generalized polya eggenberger family of distributions and its relation to lagrangian katz family

Janardan (1973) introduced the generalized Polya Eggenberger family of distributions (GPED) as a limiting distribution of the generalized Markov-Polya distribution (GMPD). Janardan and Rao (1982) gave a number of characterizing properties of the generalized Markov-Polya and generalized Polya Eggenberger distributions. Here, the GPED family characterized by four parameters, is formally defined and studied. The probability generating function, its moments, and certain recurrence relations with the moments are provided. The Lagrangian Katz family of distributions (Consul and Famoye (1996)) is shown to be a sub-class of the family of GPED (or GPED ₁ ) as it is called in this paper). A generalized Polya Eggenberger distribution of the second kind (GPED ₂ ) is also introduced and some of it's properties are given. Recurrence relations for the probabilities of GPED ₁ and GPED ₂ are given. A number of other structural and characteristic properties of the GPED ₁ are provided, from which the properties of Lagrangian Katz family follow. The parameters of GMPD ₁ are estimated by the method of moments and the maximum likelihood method. An application is provided.     

A one-sided test for testino homogeneity of scale parameters against simple ordered alternative

In an earlier paper the authors (1997) extended the results of Hayter (1990) to the two parameter exponential probability model. This paper addressee the extention to the scale parameter case under location-scale probability model. Consider k (k≧3) treatments or competing firms such that an observation from with treatment or firm follows a distribution with cumulative distribution function (cdf) F_i(x)=F[(x-μ_i)/Q_i], where F(·) is any absolutely continuous cdf, i=1,…,k. We propose a test to test the null hypothesis H₀:θ₁=…=θ_k against the simple ordered alternative H₁:θ₁≦…≦θ_k, with at least one strict inequality, using the data X_i,j, i=1,…k; j=1,…,n₁. Two methods to compute the critical points of the proposed test have been demonstrated by talking k two parameter exponential distributions. The test procedure also allows us to construct simultaneous one sided confidence intervals (SOCIs) for the ordered pairwise ratios θ_j/θ_i, 1≦i<j≦k. Statistical simulation revealed that: 9i) actual sizes of the critical points are almost conservative and (ii) power of the proposed test relative to some existing tests is higher.     

Transformed generalized linear models

The estimation of data transformation is very useful to yield response variables satisfying closely a normal linear model. Generalized linear models enable the fitting of models to a wide range of data types. These models are based on exponential dispersion models. We propose a new class of transformed generalized linear models to extend the Box and Cox models and the generalized linear models. We use the generalized linear model framework to fit these models and discuss maximum likelihood estimation and inference. We give a simple formula to estimate the parameter that index the transformation of the response variable for a subclass of models. We also give a simple formula to estimate the r$r$th moment of the original dependent variable. We explore the possibility of using these models to time series data to extend the generalized autoregressive moving average models discussed by Benjamin et al. [Generalized autoregressive moving average models. J. Amer. Statist. Assoc. 98, 214–223]. The usefulness of these models is illustrated in a simulation study and in applications to three real data sets.     

Family violence laws: Traditional narratives and the (in)visibility of lesbian relationships and lesbian-parented families

Abstract

Feminist advocacy and activism over the last 40 years broke historic ground in shining a light on “domestic” or “family” violence, traditionally conceptualized as male violence against female intimate partners and their children. This has resulted in a large body of research, particularly in the United States, United Kingdom, Australia, and similar jurisdictions, around the gendered nature of family violence and violence within heterosexual relationships and heterosexual-parented families. As a consequence, the predominant narrative—in political, policy, and advocacy settings—is largely heteronormative. Less research has focused on family violence in non-heterosexual relationships. The data that do exist have employed different methodological approaches and there are limitations on the extent to which they can be compared to the data on violence within heterosexual relationships. However, the existing research does demonstrate that family violence within lesbian, gay, bisexual, transgender, and intersex (LGBTI) communities is a significant issue. Even so, the current narrative does not acknowledge this, and predominantly reflects heterosexual norms of intimate relationships and family structures in society. LGBTI relationships are described as “invisible” in policy and practice responses to family violence, due to the failure to acknowledge violence in such communities. This article explores these claims in relation to lesbian relationships in the context of Australian legislative responses to family violence. It considers the extent to which family violence laws in two Australian jurisdictions recognize and frame lesbian identity in intimate relationships and lesbian-parented families. This is considered in light of the emerging conceptualization of family violence in lesbian relationships and lesbian-parented families, as evidenced by the wider scholarly literature on the nature and dynamics of such violence.     

Some Reflections on the Legacies of Michael White: An Australian Perspective

This article, which appears in a special 30‐year anniversary edition of the Australian and New Zealand Journal of Family Therapy, reflects on the legacies of the work of Michael White. It begins by looking back on Michael's time as editor of the Australian Journal of Family Therapy. Of the many themes that were discussed in the Editorials and Letters to the Editor section of this journal in the early 1980s, this article focuses on three in particular to explore the legacies of the work of Michael White. The author describes how Michael has bequeathed not only a profound body of work, but also a distinctive spirit of originating, and ways of working that consider the effects of social issues and that examine the politics of experience. It is the author's hope that this approach to considering Michael White's legacies honours his work and also honours the contributions of the Australian and New Zealand Journal of Family Therapy in its 30th year.