Lognormal Regression Model Research Articles

Life duration of foreign multinational subsidiaries: Evidence from UK northern manufacturing industry 1970–93

Duration analysis is employed to examine the survival of 252 foreign manufacturing plants in the UK Northern region during 1970–93. Contrary to expectations, the hazard function is approximately inverse quadratic rather than monotonic decreasing. Greenfield entrants face a lower risk of failure than acquisition entrants, particularly early in life. Acquisitions of older plants exhibit stronger survival than acquisitions of recently established plants, so that the age of (indigenous) acquired plant at the point of foreign takeover appears to matter to the survival of acquisition entrants. Plant size and industrial concentration also emerge as important. Home country of parent firm and location within region are unimportant. Consistent with the inverse U-shaped hazard function, the lognormal regression model provides a reasonably satisfactory fit to the data, certainly tighter than the Weibull model.

Minimax approach to accelerated life tests

This article explores how the minimax approach to designing experiments applies to the Weibull and lognormal regression models used in accelerated life testing (ALT). When tackling these problems, the local optimal approach assumes the parameters in the information matrix known, while in the Bayes approach, prior distributions are imposed on them. By contrast, the minimax strategy searches for the design that minimizes the maximum of the optimality function criteria over the parameter region of interest. For an offshoot of the criterion based on minimizing the volume of the joint statistical-confidence region for the model parameters (D-optimality), the authors prove that the restricted minimax designs coincide with the local optimal designs at the 'lower left corner' of the parameter region. Extensive simulation shows that this phenomenon also holds for the criterion based on maximizing the precision of estimation of a prespecified quantile of the life distribution. Based on their findings, they recommend that the locally optimal designs be used, but for the most extreme set of feasible parameters instead of implementing them for the best guess for the parameters, as is usually done.

Log-normal regression modeling through recursive partitioning

This article discusses a method for fitting log-normal regression models to censored survival data through binary decision trees. Recursive partitioning is performed by analysis of the distributions of residuals and cross-validation estimates of the average squared error. Several forms of strata selection and bootstrapping are examined to study their relative effectiveness. If the Newton — Raphson method for determining the maximum likelihood estimates fails because of heavy censoring, a method relying only on the first derivatives of the log likelihood function is used. The proposed method helps to identify the local effect of the covariates. The methods are illustrated with real and simulated data. Especially, a data set having categorical variables and missing values is used for modeling the tree-structured log-normal regression.

Estimating the distribution of times from HIV seroconversion to aids using multiple imputation

Multiple imputation is a model based technique for handling missing data problems. In this application we use the technique to estimate the distribution of times from HIV seroconversion to AIDS diagnosis with data from a cohort study of 4954 homosexual men with 4 years of follow-up. In this example the missing data are the dates of diagnosis with AIDS. The imputation procedure is performed in two stages. In the first stage, we estimate the residual AIDS-free time distribution as a function of covariates measured on the study participants with data provided by the participants who were seropositive at study entry. Specifically, we assume the residual AIDS-free times follow a log-normal regression model that depends on the covariates measured at enrolment on the seropositive participants. In the second stage we impute the date of AIDS diagnosis for the participants who seroconverted during the course of the study and are AIDS-free with use of the log-normal distribution estimated in the first stage and the covariates from each seroconverter's latest visit. The estimated proportions developing AIDS within 4 and within 7 years of seroconversion are 15 and 36 per cent respectively, with associated 95 per cent confidence intervals of (10, 21) and (26, 47) per cent. We discuss the Bayesian foundations of the multiple imputation technique and the statistical and scientific assumptions.

Improved estimation in Lognormal regression models

Lognormal regression model with unknown error variance is considered. We give a class of estimators of the regression coefficients vector improving upon traditional estimator when the number of independent variables is at least three. The relationship between these estimators on one hand and James-Stein type estimators of the normal mean and improved estimators of the normal variance on another hand is discussed.

A method of selecting the levels of regressor variables in lognormal regression model

Kupper and Meydrech and Myers and Lahoda introduced the mean squared error (MSE) approach to study response surface designs, Duncan and DeGroot derived a criterion for optimality of linear experimental designs based on minimum mean squared error. However, minimization of the MSE of an estimator maxr renuire some knowledge about the unknown parameters. Without such knowledge construction of designs optimal in the sense of MSE may not be possible. In this article a simple method of selecting the levels of regressor variables suitable for estimating some functions of the parameters of a lognormal regression model is developed using a criterion for optimality based on the variance of an estimator. For some special parametric functions, the criterion used here is equivalent to the criterion of minimizing the mean squared error. It is found that the maximum likelihood estimators of a class of parametric functions can be improved substantially (in the sense of MSE) by proper choice of the values of regressor var...

Analysing geographic variations in mortality using poisson regression: The example of ischaemic heart disease in England and Wales 1969–1973

This paper describes how Poisson regressions techniques can be used to examine the relationship between mortality and possible explanatory variables over a series of areas in cases where the number of deaths involved is relatively low. As an example an analysis is carried out on deaths from ischaemic heart disease among young adults in the county boroughs of England and Wales during 1969–1973. The results of the study indicate that the number of deaths was higher for males than females and was positively related to age, the size of the ‘at risk’ population and crowding, but negatively associated with water hardness and the size of the New Commonwealth population. A comparison of the Poisson and log-normal regression models clearly shows that the latter provides an inferior goodness of fit and unreliable results. It is therefore concluded that when the number of deaths is small there are both theoretical and practical advantages in using Poisson regression to analyse mortality data.

A simple lagrange multiplier test for lognormal regression

In the spirit of diagnostic testing, this study proposes a simple Lagrange multiplier test for the appropriateness of the lognormal regression model. The alternative hypothesis covers the class of Box-Cox truncated regression models considered by Poirier (1978). The simplicity of the test arises from the absence of any truncation under the null hypothesis.