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PubMed1992

Aspects of general linear modelling of migration.

"This paper investigates the application of general linear modelling principles to analysing migration flows between areas. Particular attention is paid to specifying the form of the regression and error components, and the nature of departures from Poisson randomness. Extensions to take account of spatial and temporal correlation are discussed as well as constrained estimation. The issue of specification bears on the testing of migration theories, and assessing the role migration plays in job and housing markets: the direction and significance of the effects of economic variates on migration depends on the specification of the statistical model. The application is in the context of migration in London and South East England in the 1970s and 1980s."

Demography↗

PubMed2000

A robust mixed linear model analysis for longitudinal data.

This paper describes robust procedures for estimating parameters of a mixed effects linear model as applied to longitudinal data. In addition to fixed regression parameters, the model incorporates random subject effects to accommodate between-subjects variability and autocorrelation for within-subject variability. Robust empirical Bayesian estimation of subject effects is briefly discussed. As an illustration, the procedures are applied to data from a multiple sclerosis clinical trial.

Adjuvants, Immunologic↗

PubMed1985

Some extensions of a linear model for categorical variables.

The Grizzle-Starmer-Koch (GSK) model is extended to include the traditional log-linear model and a general class of Poisson and conditional Poisson distributions. Estimators of the model parameters are defined under general exact and stochastic linear constraints.

Analysis of Variance↗

PubMed2003

Non-linear models for the relation between cardiovascular risk factors and intake of wine, beer and spirits.

It is generally accepted that moderate consumption of alcohol is associated with a reduced risk of coronary heart disease (CHD). It is not clear however whether this benefit is derived through the consumption of a specific beverage type, for example, wine. In this paper the associations between known CHD risk factors and different beverage types are investigated using a novel approach with non-linear modelling. Two types of model are proposed which are designed to detect differential effects of beverage type. These may be viewed as extensions of Box and Tidwell's power-linear model. The risk factors high density lipoprotein cholesterol, fibrinogen and systolic blood pressure are considered using data from a large longitudinal study of British civil servants (Whitehall II). The results for males suggest that gram for gram of alcohol, the effect of wine differs from that of beer and spirits, particularly for systolic blood pressure. In particular increasing wine consumption is associated with slightly more favourable levels of all three risk factors studied. For females there is evidence of a differential relationship only for systolic blood pressure. These findings are tentative but suggest that further research is required to clarify the similarities and differences between the results for males and females and to establish whether either of the models is the more appropriate. However, having clarified these issues, the apparent benefit of consuming wine instead of other alcoholic beverages may be relatively small.

Adult↗

PubMed2005

[The application of hierarchical linear modelling for rehabilitation center comparisons in quality assurance and rehabilitation research].

For a fair comparison of rehabilitation centres with respect to the effects of the treatment provided (e. g. for the purpose of quality assurance programmes), it is essential that those factors which influence the outcome of rehabilitation treatment and over which the rehabilitation centres have no control (the so-called "confounders", such as co-morbidity and age of the patients on commencement of treatment) are included in the statistical analysis. Simple linear regression models without random effects and without interaction terms are frequently used for this purpose. However, this method has certain limitations which can be avoided if hierarchical linear modelling (HLM) is employed. HLM has the advantage over standard regression analysis methods in that it can be used to take into account the multi-level structure of a comparison problem, allows predictors to be introduced at the level of the centres and also makes it possible to model variations of regression coefficients for the centres. When the HLM technique is used, separate linear models can be produced for the various hierarchically structured data levels of the question (e. g. the levels "patients" and "centres" for rehabilitation centres, for example). Moreover, it can be empirically tested with HLMs whether the rehabilitation coefficients (e. g. effects of mean age of patients on the outcome of rehabilitation) differ significantly between the centres. In this article, we describe the use of hierarchical linear modelling on the basis of data obtained from the quality assurance programme of the statutory health insurance schemes in the field of medical rehabilitation ("QS-Reha").

Benchmarking↗

PubMed2007

Dose-time-response cumulative multinomial generalized linear model.

In toxicological and pharmaceutical experiments, a type of quantal bioassay experiment is designed in which a response, such as mortality, in a group of animals is recorded over time points under different dose levels in the course of the experiment. The application of the typical logit and probit analyses is no longer valid in this situation because it neglects the dependency on time and also the possible interaction of time and dose concentration on the response in the experiment. In this paper, a dose-time-response model is proposed for this type of experiment and a cumulative multinomial generalized linear model that incorporates time and the other experimental conditions as covariates is developed by the theory of maximum likelihood estimation. Both the point estimator and confidence bands for ED50(t), the concentration of a toxicant that will kill 50% of the animals by a specific time, t; as well as LT50(d), the time to 50% mortalities for a specific concentration, d, is then formulated in closed form from the newly proposed dose-time-response model. Finally, the newly proposed model is considered for a real data set to demonstrate the application.

Algorithms↗

PubMed2001

Analysis of a linear model for electrical stimulation of axons--critical remarks on the "activating function concept".

A comprehensive description of a linear model of an axon of infinite length exposed to an external voltage is presented. The steady-state transmembrane potential is derived as a function proportional to the convolution product of the second spatial difference sn of the external potential (the "activating function") and the impulse response psin of a spatial low-pass filter. The impulse response psin represents the influence of the axon and is fully characterized by the axon's length constant lambda. A closed-form solution of the cable equation can be given in the spatial Fourier domain. Due to a "spectral acceleration effect", the overall transmembrane potential approximates the steady-state considerably faster than an exponential with the axon's membrane time constant tau. The effect is increasingly pronounced, the smaller the distance between the electrode and the axon. Regarding myelinated fibers and practically relevant electrode/axon distances and pulse widths, the transmembrane potential at the end of a stimulation pulse can be substantially better approximated by the steady-state condition than by the initial response as claimed by the "activating function concept." Quantitative limits for the range of validity of the activating function concept are derived.

Axons↗

PubMed2007

Bayesian comparison of spatially regularised general linear models.

In previous work (Penny et al., [2005]: Neuroimage 24:350-362) we have developed a spatially regularised General Linear Model for the analysis of functional magnetic resonance imaging data that allows for the characterisation of regionally specific effects using Posterior Probability Maps (PPMs). In this paper we show how it also provides an approximation to the model evidence. This is important as it is the basis of Bayesian model comparison and provides a unified framework for Bayesian Analysis of Variance, Cluster of Interest analyses and the principled selection of signal and noise models. We also provide extensions that implement spatial and anatomical regularisation of noise process parameters.

Artifacts↗

PubMed2000

Suitability of log-linear models to evaluate the microbiological quality of baby clams (Chamelea gallina L.) harvested in the Adriatic Sea.

The presence of fecal coliforms or Escherichia coli in baby clams (Chamelea gallina L.) is considered an indicator related to their safety because they can be correlated with the presence of pathogenic bacteria. For this reason the Italian regulation has defined limits for these microorganisms. The presence of these microbial indicators is dependent on various environmental variables. In this work all the variables considered are categorical and, consequently, the traditional approach of predictive microbiology was not applicable. The data were summarized by means of a cross-tabulation and analyzed using the log-linear model technique. This statistical technique is widely used in social and economic studies but only partially developed in food microbiology. The suitability of the log-linear model to analyse microbiological data in relation to environmental variables was evaluated. In particular, the microbiological quality of baby clams harvested in five different areas of the Adriatic Sea coast in Emilia Romagna (Italy) was considered. The influence of the season and geographical origin on microbiological standards was assessed. A logit model was developed to predict the frequencies, depending on geographical origin and season, of samples with concentrations of the indicator organisms below or above the legal standards provided by Italian regulation.

Animals↗

PubMed2003

Adjusting power for a baseline covariate in linear models.

The analysis of covariance provides a common approach to adjusting for a baseline covariate in medical research. With Gaussian errors, adding random covariates does not change either the theory or the computations of general linear model data analysis. However, adding random covariates does change the theory and computation of power analysis. Many data analysts fail to fully account for this complication in planning a study. We present our results in five parts. (i) A review of published results helps document the importance of the problem and the limitations of available methods. (ii) A taxonomy for general linear multivariate models and hypotheses allows identifying a particular problem. (iii) We describe how random covariates introduce the need to consider quantiles and conditional values of power. (iv) We provide new exact and approximate methods for power analysis of a range of multivariate models with a Gaussian baseline covariate, for both small and large samples. The new results apply to the Hotelling-Lawley test and the four tests in the "univariate" approach to repeated measures (unadjusted, Huynh-Feldt, Geisser-Greenhouse, Box). The techniques allow rapid calculation and an interactive, graphical approach to sample size choice. (v) Calculating power for a clinical trial of a treatment for increasing bone density illustrates the new methods. We particularly recommend using quantile power with a new Satterthwaite-style approximation.

Bone Density↗

PubMed1996

Interpretive work in short-term individual psychotherapy: an analysis using hierarchical linear modeling.

"Work" and "resistance" responses to interpretation in short-term individual (STI) psychotherapy were examined using a hierarchical linear modeling (HLM) procedure. The relationships between interpretation characteristics and patient responses within therapy were considered. Process data were drawn from 60 STI therapy cases, 30 patients with low quality of object relations (QOR), and 30 patients with high QOR. In 4 instances, the relationships between technique and response were found to vary significantly across cases. One was identified for low QOR patients, and 3 were identified for high QOR patients. Individual differences in initial disturbance and outcome were used to account for the variation of technique-response relationships. Significant findings were limited to the high QOR sample. Initial disturbance was directly related to work in response to a transference-oriented approach. The transference focus-work relationship was found to be inversely related to outcome. The results extend previous findings regarding transference technique in STI therapy with high QOR patients. Through capitalizing on within-case variation, HLM can be used to illuminate process-outcome relationships in psychotherapy.

Adolescent↗

PubMed2005

Comparison between linear models and survival analysis for genetic evaluation of clinical mastitis in dairy cattle.

Clinical mastitis was analyzed with mixed linear models (LM) and survival analysis (SA) using data from the first 3 lactations of >200,000 Swedish Holstein cows having their first calving between 1995 and 2000. The model for both methods included fixed effects of year-month and age at calving, fixed regressions of proportions of heterosis and North American Holstein genes, and random effects of herd-year at calving and sire. For the LM, clinical mastitis was defined as a binary trait measured from 10 d before to 150 d after calving. For the SA, clinical mastitis was defined either as the time period from 10 d before calving to the day of first treatment or culling because of mastitis (uncensored record) or from 10 d before to the day of next calving, culling for reasons other than mastitis, movement to a new herd, or to lactation d 240 (censored record). The heritability estimates from SA (0.03 to 0.04) were higher than those obtained with the LM (0.01 to 0.03). Consequently, the accuracies of estimated transmitting abilities were also higher for the trait analyzed with SA. The difference between estimates from the 2 methods was greater for later lactations. This study reveals the potential of analyzing clinical mastitis data with SA.

Animals↗

PubMed2003

Estimation of general linear model coefficients for real-time application.

An algorithm using an orthogonalization procedure to estimate the coefficients of general linear models (GLM) for functional magnetic resonance imaging (fMRI) calculations is described. The idea is to convert the basis functions or explanatory variables of a GLM into orthogonal functions using the usual Gram-Schmidt orthogonalization procedure. The coefficients associated with the orthogonal functions, henceforth referred to as auxiliary coefficients, are then easily estimated by applying the orthogonality condition. The original GLM coefficients are computed from these estimates. With this formulation, the estimates can be updated when new image data become available, making the approach applicable for real-time estimation. Since the contribution of each image data is immediately incorporated into the estimated values, storing the data in memory during the estimation process becomes unnecessary, minimizing the memory requirements of the estimation process. By employing Cholesky decomposition, the algorithm is a factor of two faster than the standard recursive least-squares approach. Results of the analysis of an fMRI study using this approach showed the algorithm's potential for real-time application.

Algorithms↗

PubMed2002

Personality change over 40 years of adulthood: hierarchical linear modeling analyses of two longitudinal samples.

Normative personality change over 40 years was shown in 2 longitudinal cohorts with hierarchical linear modeling of California Psychological Inventory data obtained at multiple times between ages 21-75. Although themes of change and the paucity of differences attributable to gender and cohort largely supported findings of multiethnic cross-sectional samples, the authors also found much quadratic change and much individual variability. The form of quadratic change supported predictions about the influence of period of life and social climate as factors in change over the adult years: Scores on Dominance and Independence peaked in the middle age of both cohorts, and scores on Responsibility were lowest during peak years of the culture of individualism. The idea that personality change is most pronounced before age 30 and then reaches a plateau received no support.

Adolescent↗

PubMed1994

On tests against one-sided hypotheses in some generalized linear models.

One-sided hypotheses arise naturally in many situations. When testing against such hypotheses, it is desirable to take the available one-sided information into account, rather than simply applying a two-sided test. What we expect to gain by applying a one-sided test instead of a two-sided test is an increase in the power of the test. We consider various tests of one-sided hypotheses in a class of models that includes generalized linear and Cox regression models. The tests are likelihood ratio, Wald, score, generalized distance, and a Pearson chi-square. It is shown that these test statistics are asymptomatically equivalent in terms of local power; this is a generalization of the well-known corresponding result for two-sided alternatives. Two examples are also discussed. They are on (1) testing for interaction in binomial response models, and (2) comparison of treatments with ordinal categorical responses.

Aminacrine↗

PubMed1986

A log-linear model for binary pedigree data.

A pedigree model for binary data, motivated by log-linear modelling, has been developed to examine evidence for familial aggregation in disease status. From an epidemiological point of view a convenient way to express disease concordance between a pair of relatives is in terms of the odds ratio. For a rare disease this is almost equivalent to the relative risk of one family member being affected given that the other is affected, and in extending this to pedigrees it is assumed that these relative risks are multiplicative. In applying the model to the breast cancer data, pedigrees on a rare disease ascertained through an affected proband, it has been shown that estimation of concordance is dependent critically on knowing the probability that a sampled individual is affected. Therefore known population estimates of prevalence or cumulative risk, and an appropriate ascertainment correction, need to be invoked for the model to give proper estimates of disease concordance. The model is flexible in that measured ancillary risk factors, including genetic marker information, can be incorporated into the analysis. Therefore in future studies this information should be collected on all individuals, not just those affected. Suggested statistics for examining a fitted model are presented.

Alanine Transaminase↗

PubMed2004

Linear models and empirical bayes methods for assessing differential expression in microarray experiments.

The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated two-color experiment using a simple hierarchical parametric model. The purpose of this paper is to develop the hierarchical model of Lonnstedt and Speed (2002) into a practical approach for general microarray experiments with arbitrary numbers of treatments and RNA samples. The model is reset in the context of general linear models with arbitrary coefficients and contrasts of interest. The approach applies equally well to both single channel and two color microarray experiments. Consistent, closed form estimators are derived for the hyperparameters in the model. The estimators proposed have robust behavior even for small numbers of arrays and allow for incomplete data arising from spot filtering or spot quality weights. The posterior odds statistic is reformulated in terms of a moderated t-statistic in which posterior residual standard deviations are used in place of ordinary standard deviations. The empirical Bayes approach is equivalent to shrinkage of the estimated sample variances towards a pooled estimate, resulting in far more stable inference when the number of arrays is small. The use of moderated t-statistics has the advantage over the posterior odds that the number of hyperparameters which need to estimated is reduced; in particular, knowledge of the non-null prior for the fold changes are not required. The moderated t-statistic is shown to follow a t-distribution with augmented degrees of freedom. The moderated t inferential approach extends to accommodate tests of composite null hypotheses through the use of moderated F-statistics. The performance of the methods is demonstrated in a simulation study. Results are presented for two publicly available data sets.

Journal Article↗

PubMed1991

Estimating standardized parameters from generalized linear models.

Although the traditional unrestricted ('non-parametric') estimators of directly standardized rates and rate differences remain unbiased in sparse data, they tend to suffer from instability (low precision). As a result, many authors have proposed more precise estimators based on parametric models for the rates. This paper provides a general approach for constructing estimators of standardized parameters using generalized linear models, and shows that, in some common special cases, these model-based ('smoothed') estimators can have an exceptionally simple form.

Adult↗