'I made some mistakes . . . but I love them dearly' the views of parents of children in informal kinship care

In-depth semi-structured interviews with 30 parents of children living with relatives in informal kinship care arrangements revealed the parents' views of the reasons for the informal kinship care arrangements, quality of their relationships with the children and their caregivers, their current and future roles in their children's lives, feelings experienced when with and away from the children, positive and negative aspects of kinship care, future goals and dreams for their children, and their assessments of their own strengths and challenges. Results of these interviews suggest several implications for social work practice and research.     

A Characterization of the Normal Family of Distributions Based on the Bias of the Maximum Likelihood Estimator

This paper characterizes the family of Normal distributions within the class of exponential families of distributions, via the structure of the bias of the maximum likelihood estimator Θ _n of the canonical parameter Θ . More specifically, when E _θ ( Θ n ) – Θ = (1/ n ) Q ( Θ ) + o (1/ n ), the equality Q ( Θ ) = 0 proves to be a property of the Normal distribution only. The same conclusion is obtained for the one-dimensional case bt assuming that Q ( Θ ) is a polynomial of Θ .     

Conditional Generalized Liouville Distributions on the Simplex

Liouville and generalized Liouville distributions on the simplex have been proposed for modeling compositional data and have been shown to be free from the extreme independence structure that characterizes the Dirichlet class. In this article, generalized Liouville distributions are shown to be rich enough to distinguish some lesser modes of independence as well. Unfortunately, it is noted that the applicability of the Liouville family will be limited, owing to the lack of invariance with respect to the chosen fill-up value. As an alternative, a new family of simplex distributions is proposed, one that admits invariance with respect to choice of fill-up value, as well as the ability to differentiate among many forms of independence.     

Some aspects of statistical inference on the lagrange (generalized) poisson distribution

A generalization of the Poisson distribution was defined by Consul and Jain (Ann. Math. Statist., 41, (1970)) and was obtained as a particular family of Lagrange distributions by Consul and Shenton (SIAM. J. Appl. Math., 23, (1972)). The distribution is subsequently named the generalized Poisson distribution (GPD). This GPD reduces to the Poisson distribution for ? = 0. When the data have a one-way layout structure, the asymptotically locally optimal Neyman's C(d) test is constructed and compared with the conditional test on the hypothesis H_o? = 0. Within the framework of the generalized linear models an appropriate link function is given, and the asymptotic distributions of the estimated parameters are derived.     

Response transformations in repeated measures and growth curve models

This article describes estimation and inference procedures for the parameters of the Box-Cox and foided-power transformations in repeated measures and growth curve models. Procedures for computing maximum likelihood estimates of the transformation and covariance parameters under several covanance structures (omnibus sphericity, local sphericity, and unstructured) are described. Lack of fit statistics and hypothesis tests for comparing these structures also are described. The procedures are illustrated on three data sets. Software for performing the analyses in the SAS System is described and is available from the authors.     

Note on sums of a random number of random variables with exponential family distributions

With the help of the result that exponential-type families are determined by their mean value functions it is shown that stochastic independence of the random variables S_N and N-S_N characterizes the Poisson and Bernoulli distributions simultaneously.     

Sufficient Reduction in Multivariate Surveillance

The relation between change points in multivariate surveillance is important but seldom considered. The sufficiency principle is here used to clarify the structure of some problems, to find efficient methods, and to determine appropriate evaluation metrics. We study processes where the changes occur simultaneously or with known time lags. The surveillance of spatial data is one example where known time lags can be of interest. A general version of a theorem for the sufficient reduction of processes that change with known time lags is given. A simulation study illustrates the benefits or the methods based on the sufficient statistics.     

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.