Showing papers in "Journal of The Royal Statistical Society Series C-applied Statistics in 1981"
TL;DR: In this article, the use of regression models for the analysis of ordered categorical variables is discussed with particular reference to the logistic model and maximum likelihood estimation procedures are established for three common sampling plans including the case where sampling is conditional on the ordered variable.
Abstract: SUMMARY Regression models for the analysis of ordered categorical variables are discussed with particular reference to the logistic model. Maximum likelihood estimation procedures are established for three common sampling plans including the case where sampling is conditional on the ordered variable. This was previously not available. The use of these models in discrimination is discussed and an example given. An original method for the establishment of rating scales based on a coarse direct assessment and related variables is introduced. Mention is made of some difficulties in the application of the models and of their potential use for the analysis of designed experiments with ordered response variables.
190 citations
TL;DR: In this paper, the authors propose a generalized linear model (GLIM-3) to fit mixed-up contingency tables and grouped normal data, which can be used to fit these models.
Abstract: SUMMARY In generalized linear models each observation is linked with a predicted value based on a linear function of some systematic effects. We sometimes require to link each observation with a linear function of more than one predicted value. We embed such models into the generalized linear model framework using composite link functions. The computer program GLIM-3 can be used to fit these models. Illustrative examples are given including a mixed-up contingency table and grouped normal data.
181 citations
TL;DR: An intermediate solution via maximum likelihood which takes account of three sources of variation in death rates: sampling error, explanatory variables and unexplained differences between areas is proposed.
Abstract: One can often gain insight into the aetiology of a disease by relating mortality rates in different areas to explanatory variables. Multiple regression techniques are usually employed but unweighted least squares may be inappropriate if the areas vary in population size. Also a fully weighted regression with weights inversely proportional to binomial sampling variances is usually too extreme. This paper proposes an intermediate solution via maximum likelihood which takes account of three sources of variation in death rates: sampling error explanatory variables and unexplained differences between areas. The method is also adapted for logit (death rates) standardized mortality ratios (SMRs) and log (SMRs). Two [United Kingdom] examples are presented. (EXCERPT)
150 citations
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69 citations
TL;DR: In this article, the authors compare the relative merits of AR and window spectral estimation, the basis of the work being an extensive simulation of series constructed from a variety of models, and provide valuable information on the relative performance of various order determination criteria when applied to different types of models and varying data lengths.
Abstract: SUMMARY a process with a "mixed" spectrum. The paper also includes some discussion of two different methods of estimating the coefficients of AR models (the Burg method and the Yule-Walker approach), and of the performance of various order determination criteria, such as FPE, AIC and CAT. 1. I NTRODUCTION The problem of fitting finite parameter linear models to time series has recently aroused renewed interest, particularly in relation to the use of "automatic" model order determination procedures such as Akaike's AIC and Parzen's CAT criteria. Such models can be used to provide "parametric" estimates of the spectral density function, and, in particular, the method of "autoregressive spectral estimation" has attracted growing interest as an alternative to the more traditional non-parametric "window methods". In this paper we compare the relative merits of AR and "window" spectral estimation, the basis of the work being an extensive simulation of series constructed from a variety of models. The simulation study also provides valuable information on the relative performance of various order determination criteria when applied to different types of models and varying data lengths. Our conclusions are summarized in Section 7.
59 citations
TL;DR: In this article, the relative marginal likelihood function for n 1 is derived and the expressions for the relative conditional and maximum likelihood functions are given, with the first two likelihoods, which account for the uncertainty about the value of the other parameters, are to be preferred to the maximum likelihood function.
Abstract: SUMMARY Consider a sequence of (n1 + n2) independent ordered pairs of observations for which the relationship between variables can be represented by a segmented polynomial regression model with unknown point of change n 1. The relative marginal likelihood function for n 1 is derived and the expressions for the relative conditional and maximum likelihood functions are given. Either of the first two likelihoods, which account for the uncertainty about the value of the other parameters, are to be preferred to the maximum likelihood function, with the relative marginal likelihood function being examined more extensively here. In the case where the segmented regression model can be represented by two polynomials of unknown degrees p and q, a procedure is described for estimating p and q. The use of these methods is illustrated using two observed sets of data and three artificially generated sets.
58 citations
TL;DR: In this paper, the problem of estimating variances by pooling information from a large number of small samples is tackled, and a modified maximum likelihood method is described which gives consistent estimators.
Abstract: The problem of estimating variances by pooling information from a large number of small samples is tackled. Maximum likelihood methods are shown to be inconsistent, but a modified maximum likelihood method is described which gives consistent estimators. A modified likelihood ratio test of fit is also developed, and the application of these results to immunoassay data is described. Comparison with a regression method shows that if the variance function is given by an exponential model, and the observations are in sets of 2, 3 or 4, the modified maximum likelihood method has much greater efficiency.
53 citations
33 citations
TL;DR: In this article, two alternatives to Hastings' approximation to the inverse of the normal cumulative distribution function are given, one is adequate for the majority of practical problems, while the other is of use in the extreme tails.
Abstract: Two alternatives are given to Hastings' approximation to the inverse of the normal cumulative distribution function: one is adequate for the majority of practical problems, while the other is of use in the extreme tails. Both require fewer constants than Hastings' and have greater accuracy, particularly when measured in terms of relative error.
TL;DR: In this paper, the use of cluster analysis in stratification is considered and a clustering or stratification criterion function is suggested which is derived within the context of multivariate stratified sampling.
Abstract: SUMMARY In this paper the use of cluster analysis in stratification is considered. A clustering or stratification criterion function is suggested which is derived within the context of multivariate stratified sampling. A case study in which the States of Mexico are stratified with respect to nine socio-economic variables is presented.
TL;DR: In this paper, the Box and Cox (1964) power transformation family and robust alternatives developed by Bickel and Doksum (1981) and Carroll (1980) are applied to data sets given by John (1978).
Abstract: : The Box and Cox (1964) power transformation family and robust alternatives developed by Bickel and Doksum (1981) and Carroll (1980) are applied to data sets given by John (1978). The robust methods perform quite well compared to normal theory likelihood methods. (Author)
TL;DR: Exponentially damped polynomial regression models are applied to data arising from the return to biochemical equilibrium after an induced disturbance, and statistical analyses are outlined, and illustrated with human blood glucose levels after alcohol consumption.
Abstract: SUMMARY Exponentially damped polynomial regression models are applied to data arising from the return to biochemical equilibrium after an induced disturbance. Computation and statistical analyses are outlined, and illustrated with human blood glucose levels after alcohol consumption.
TL;DR: A non-parametric discriminant function for categorical or discrete-valued data belonging to at least two a priori classes is constructed by a computer program from the base sample data.
Abstract: SUMMARY A non-parametric discriminant function for categorical or discrete-valued data belonging to at least two a priori classes is constructed by a computer program from the base sample data. There is no limit to the number of data variables measured oh members of the base sample, but each variable can have no more than 10 possible values. The program prints out the discriminant function in the form of a branching key for use by hand; also in the form of a Fortran function which can be punched out on cards by the computer. A simple program to read the same variables for each individual, and then call the function, will classify a prospective series from the same population. The key itself may have a descriptive use, especially when the number of variables is enormous. In this case it may be used as a preliminary analysis which may suggest testable hypotheses about the interactions between some of the variables. The algorithm itself is presented in the algorithms section of this issue of Applied Statistics (Sturt, 1980).
TL;DR: The analysis of time series: An Introduction as discussed by the authors, an Introduction to the Analysis of Time Series: an Introduction, by C. Chatfield. London, Chapman and Hall, 1980. xiv, 268 p.
Abstract: The Analysis of Time Series: An Introduction. 2nd edition. By C. Chatfield. London, Chapman and Hall, 1980. xiv, 268 p. 21·5 cm. £6·50.
TL;DR: The Box and Cox family of power transformations is applied to further generalize a "generalized" functional form of the U.K. demand for money given in a recent paper by Mills as discussed by the authors.
Abstract: The Box and Cox family of power transformations is applied to further generalize a “generalized” functional form of the U.K. demand for money given in a recent paper by Mills (1978). New estimates of the generalized forms estimated by Mills are presented. Deficiencies in the earlier results are indicated, and the general methodological problem discussed.
TL;DR: In this paper, it was shown that a covariance model also yields an exact analysis in the case of mixed-up values and, in fact, is easier to implement on a computer than the correct model.
Abstract: Analysis of covariance is a well‐known technique for obtaining estimates and analysing data from designed experiments with missing values. In this article, we show that a covariance model also yields an exact analysis in the case of mixed‐up values and, in fact, is easier to implement on a computer than the correct model. In addition, while estimators of the coefficients of dummy variables introduced as covariates may be used as estimators of missing or mixed‐up values, we show using the technique of John and Lewis (1976) that only for the case of missing values are these covariate coefficient estimators the best linear unbiased estimators (BLUE's) of the means of these values.