Latent class analysis risk profiles: An effective method to predict a first re-report of maltreatment?

Recurrence of child maltreatment is a significant concern causing substantial individual, family and societal cost. Variable-based approaches to identifying targets for intervention may not reflect the reality that families may experience multiple co-occurring risks. An alternative approach was tested using baseline data from the National Survey of Child and Adolescent Well-being (NSCAW) I and II to develop Latent Class Analysis models of family risk classes using variables derived from prior studies of re-reporting. The samples were collected approximately 10 years apart offering a chance to test how the approach might be impacted by demographic or policy shifts. The association between baseline classes and later re-reports was tested using both samples. A two-class model of high versus low presence of baseline risk resulted that was strongly associated with later likelihood of re-report and results were relatively stable across the two studies. Person-centered approaches may hold promise in the early identification of families that require a more comprehensive array of supports to prevent re-reports of maltreatment.     

Profile likelihood approaches for semiparametric copula and frailty models for clustered survival data

ABSTRACT

In clustered survival data, the dependence among individual survival times within a cluster has usually been described using copula models and frailty models. In this paper we propose a profile likelihood approach for semiparametric copula models with different cluster sizes. We also propose a likelihood ratio method based on profile likelihood for testing the absence of association parameter (i.e. test of independence) under the copula models, leading to the boundary problem of the parameter space. For this purpose, we show via simulation study that the proposed likelihood ratio method using an asymptotic chi-square mixture distribution performs well as sample size increases. We compare the behaviors of the two models using the profile likelihood approach under a semiparametric setting. The proposed method is demonstrated using two well-known data sets.     

Managing stakeholder pressures: Toward a typology of corporate social performance profiles

Why do some firms ignore some stakeholders while courting others? We propose two key drivers of firms' social postures and derive from this analysis a novel typology of corporate social performance (CSP) profiles. Although we expect that other drivers exist, we argue that a useful starting point for understanding any given CSP profile is to consider the pressure exerted on an organization by its stakeholders in conjunction with its level of resource endowment. Our preliminary typology identifies six distinct CSP profiles that reflect different opportunities and risks for stakeholder management: the CSP Vanguard, Opportunist, Generalist, Minimalist, Specialist, and Laggard. All else equal, the first two CSP profiles imply more nonmarket opportunities than risk, whereas we expect Laggards and Specialists to face greater risk in their responses to social and environmental issues. According to our framework, Generalists and Minimalists probably operate between these two extremes of business risk. Our conceptual analysis seeks to advance research and practice for more strategic stakeholder management.     

Phase I monitoring of social network with baseline periods using poisson regression

Social network analysis is an important analytic tool to forecast social trends by modeling and monitoring the interactions between network members. This paper proposes an extension of a statistical process control method to monitor social networks by determining the baseline periods when the reference network set is collected. We consider probability density profile (PDP) to identify baseline periods using Poisson regression to model the communications between members. Also, Hotelling T² and likelihood ratio test (LRT) statistics are developed to monitor the network in Phase I. The results based on signal probability indicate a satisfactory performance for the proposed method.     

Adjustment of the Profile Likelihood for a Class of Normal Regression Models

We apply the method of McCullagh & Tibshirani (1990) to a generalization of the model for variance components in which the parameter of interest can appear in both the mean and variance. We obtain the exact adjusted profile log-likelihood score function. For the variance components model, we obtain the adjusted profile log-likelihood and show that it equals the restricted log-likelihood of Patterson & Thompson (1971). We discuss an example due to Kempton (1982) of a regression model with autoregressive terms in which the parameter of interest appears in both the mean and variance.     

The score function and a comparison of various adjustments of the profile likelihood

Several adjustments of the profile likelihood have the common effect of reducing the bias of the associated score function. Hence expansions for the adjusted score functions differ by a term, D_ξ, that has small asymptotic order (n ^?½). The effect of D_ξ on other quantities of interest is studied. In particular, we find the bias and variance of the adjusted maximum-likelihood estimate to be relatively unaffected, while differences in the Bartlett correction depend on D_ξ in a simple way.     

On a ‘Level-Sensitive’ Headcount Ratio: Revisiting Shorrocks’ Poverty Index

It is often argued that indicators of achievement or deprivation should be measured such that they display a property of ‘level-sensitivity’, whereby a given change in the indicator acquires a greater significance the higher (lower) the level of achievement (deprivation) at which the change occurs. In this note, it is shown that a level-sensitive headcount ratio of poverty can be derived from an application of the very useful graphical device called ‘a deprivation profile’ advanced by Anthony Shorrocks (in: Jenkins et al. (eds.) The Distribution of Welfare and Household Production: International Perspectives, 1996).     

An EM type estimation procedure for the destructive exponentially weighted Poisson regression cure model under generalized gamma lifetime

In this paper, we assume the number of competing causes to follow an exponentially weighted Poisson distribution. By assuming the initial number of competing causes can undergo destruction and that the population of interest has a cure fraction, we develop the EM algorithm for the determination of the MLEs of the model parameters of such a general cure model. This model is more flexible than the promotion time cure model and also provides an interesting and realistic interpretation of the biological mechanism of the occurrence of an event of interest. Instead of assuming a particular parametric distribution for the lifetime, we assume the lifetime to belong to the wider class of generalized gamma distribution. This allows us to carry out a model discrimination to select a parsimonious lifetime distribution that provides the best fit to the data. Within the EM framework, a two-way profile likelihood approach is proposed to estimate the shape parameters. An extensive Monte Carlo simulation study is carried out to demonstrate the performance of the proposed estimation method. Model discrimination is carried out by means of the likelihood ratio test and information-based methods. Finally, a data on melanoma is analyzed for illustrative purpose.     

Phase I monitoring of generalized linear model-based regression profiles

In some industrial applications, the quality of a process or product is characterized by a relationship between the response variable and one or more independent variables which is called as profile. There are many approaches for monitoring different types of profiles in the literature. Most researchers assume that the response variable follows a normal distribution. However, this assumption may be violated in many cases. The most likely situation is when the response variable follows a distribution from generalized linear models (GLMs). For example, when the response variable is the number of defects in a certain area of a product, the observations follow Poisson distribution and ignoring this fact will cause misleading results. In this paper, three methods including a T²-based method, likelihood ratio test (LRT) method and F method are developed and modified in order to be applied in monitoring GLM regression profiles in Phase I. The performance of the proposed methods is analysed and compared for the special case that the response variable follows Poisson distribution. A simulation study is done regarding the probability of the signal criterion. Results show that the LRT method performs better than two other methods and the F method performs better than the T²-based method in detecting either small or large step shifts as well as drifts. Moreover, the F method performs better than the other two methods, and the LRT method performs poor in comparison with the F and T²-based methods in detecting outliers. A real case, in which the size and number of agglomerates ejected from a volcano in successive days form the GLM profile, is illustrated and the proposed methods are applied to determine whether the number of agglomerates of each size is under statistical control or not. Results showed that the proposed methods could handle the mentioned situation and distinguish the out-of-control conditions.     

LEVERAGE ADJUSTMENTS FOR DISPERSION MODELLING IN GENERALIZED NONLINEAR MODELS

For normal linear models, it is generally accepted that residual maximum likelihood estimation is appropriate when covariance components require estimation. This paper considers generalized linear models in which both the mean and the dispersion are allowed to depend on unknown parameters and on covariates. For these models there is no closed form equivalent to residual maximum likelihood except in very special cases. Using a modified profile likelihood for the dispersion parameters, an adjusted score vector and adjusted information matrix are found under an asymptotic development that holds as the leverages in the mean model become small. Subsequently, the expectation of the fitted deviances is obtained directly to show that the adjusted score vector is unbiased at least to O(1/n) . Exact results are obtained in the single‐sample case. The results reduce to residual maximum likelihood estimation in the normal linear case.