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PubMed2006

Generalized linear models with ordinally-observed covariates.

An ordinally-observed variable is a variable that is only partially observed through an ordinal surrogate. Although statistical models for ordinally-observed response variables are well known, relatively little attention has been given to the problem of ordinally-observed regressors. In this paper I show that if surrogates to ordinally-observed covariates are used as regressors in a generalized linear model then the resulting measurement error in the covariates can compromise the consistency of point estimators and standard errors for the effects of fully-observed regressors. To properly account for this measurement error when making inferences concerning the fully-observed regressors, I propose a general modelling framework for generalized linear models with ordinally-observed covariates. I discuss issues of model specification, identification, and estimation, and illustrate these with examples.

Analysis of Variance↗
PubMed1996

A linear model fails to predict orientation selectivity of cells in the cat visual cortex.

1. Postsynaptic potentials (PSPs) evoked by visual stimulation in simple cells in the cat visual cortex were recorded using in vivo whole-cell technique. Responses to small spots of light presented at different positions over the receptive field and responses to elongated bars of different orientations centred on the receptive field were recorded. 2. To test whether a linear model can account for orientation selectivity of cortical neurones, responses to elongated bars were compared with responses predicted by a linear model from the receptive field map obtained from flashing spots. 3. The linear model faithfully predicted the preferred orientation, but not the degree of orientation selectivity or the sharpness of orientation tuning. The ratio of optimal to non-optimal responses was always underestimated by the model. 4. Thus non-linear mechanisms, which can include suppression of non-optimal responses and/or amplification of optimal responses, are involved in the generation of orientation selectivity in the primary visual cortex.

Animals↗
PubMed2004

Multilevel linear modelling for FMRI group analysis using Bayesian inference.

Functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and/or multiple subjects. A hierarchical approach can be taken to modelling such data with a general linear model (GLM) at each level of the hierarchy introducing different random effects variance components. Inferring on these models is nontrivial with frequentist solutions being unavailable. A solution is to use a Bayesian framework. One important ingredient in this is the choice of prior on the variance components and top-level regression parameters. Due to the typically small numbers of sessions or subjects in neuroimaging, the choice of prior is critical. To alleviate this problem, we introduce to neuroimage modelling the approach of reference priors, which drives the choice of prior such that it is noninformative in an information-theoretic sense. We propose two inference techniques at the top level for multilevel hierarchies (a fast approach and a slower more accurate approach). We also demonstrate that we can infer on the top level of multilevel hierarchies by inferring on the levels of the hierarchy separately and passing summary statistics of a noncentral multivariate t distribution between them.

Bayes Theorem↗
PubMed2000

General linear models for multicenter clinical trials.

The use of generalized linear models (GLM) in the analysis of multicenter clinical trials is commonplace. Currently, diverse opinion exists as to the proper modeling approach in this setting. This paper provides a description of the technical backdrop underlying the model selection and discusses the pros and cons of the usual parameter estimators. Arguments are given favoring a model incorporating a term for interaction effect while attenuating the effects of small centers.

Clinical Trials as Topic↗
PubMed1994

Use of log-linear models for assessing differential item functioning in a measure of psychological functioning.

Log-linear models are used to investigate contingency tables that cross-classify respondents according to item response, mental health status (MHS), and the background variables of ethnicity and gender. Specifically, log-linear models are used to examine item validity, defined as an item response by MHS interaction, and differential item functioning (DIF), defined as an interaction between item response and a background variable. The investigation focused on a set of items that measure subjective well-being and coping behavior. Female (n = 627) and male (n = 338) respondents represented 3 ethnic groups: African American, Anglo-American, and Hispanic/Latino. Strong evidence of item validity and some evidence of DIF was found. Most of the interaction between item response and either ethnicity or gender occurred among respondents with diminished mental health.

Adaptation, Psychological↗
PubMed2006

Multiscale hybrid linear models for lossy image representation.

In this paper, we introduce a simple and efficient representation for natural images. We view an image (in either the spatial domain or the wavelet domain) as a collection of vectors in a high-dimensional space. We then fit a piece-wise linear model (i.e., a union of affine subspaces) to the vectors at each downsampling scale. We call this a multiscale hybrid linear model for the image. The model can be effectively estimated via a new algebraic method known as generalized principal component analysis (GPCA). The hybrid and hierarchical structure of this model allows us to effectively extract and exploit multimodal correlations among the imagery data at different scales. It conceptually and computationally remedies limitations of many existing image representation methods that are based on either a fixed linear transformation (e.g., DCT, wavelets), or an adaptive uni-modal linear transformation (e.g., PCA), or a multimodal model that uses only cluster means (e.g., VQ). We will justify both quantitatively and experimentally why and how such a simple multiscale hybrid model is able to reduce simultaneously the model complexity and computational cost. Despite a small overhead of the model, our careful and extensive experimental results show that this new model gives more compact representations for a wide variety of natural images under a wide range of signal-to-noise ratios than many existing methods, including wavelets. We also briefly address how the same (hybrid linear) modeling paradigm can be extended to be potentially useful for other applications, such as image segmentation.

Algorithms↗
PubMed1988

Genetic analysis of dystocia and calf mortality in Israeli-Holsteins by threshold and linear models.

Calvings of 106,751 Israeli Holstein heifers were analyzed for dystocia and calf mortality, scored dichotomously, and a composite trait, scored trichotomously. Dystocia was also studied with 146,973 second and third parity records. Models fitted included herd-year-season, sex of calf, calving age, calving month, sire of cow, sire of calf, and groups of sire of cow and of calf. Herd-year-season, sire of cow and calf, and residuals were random with diagonal variance-covariance matrices. Herd-year-season variance was assume to be 10% of the residual component. Other variance components were estimated by REML for linear models and by the counterpart of REML for threshold models. Heritability estimates were two to five times greater in threshold than in linear models, but correlations between corresponding sire evaluations were all greater than .9. Linear model sire evaluations were skewed positively, whereas threshold model evaluations had symmetrical distributions. Heritability for dystocia was greater in first than in later parities. Correlations between first and later parity sire evaluations were less than .5. Thus, the genetic control of dystocia seems to be different for heifers and cows. Correlations between sire of cow and calf evaluations were less than .3. Correlations between dystocia and calf mortality evaluations were about .7.

Animals↗
PubMedDate not supplied

[Analysis of mortality time trend using generalized linear models].

In this work it is shown how generalized linear models allow one to describe different patterns of temporary evolution of mortality data, while at the same time allow for an easy interpretation. As a practical application, the evolution of the female breast cancer mortality in Catalonia from 1986 to 2000 is analyzed. Remarkably, the mortality from breast cancer first increases and then decreases for all age groups. Moreover, the year in which the cancer rate starts decreasing is more recent in the older age groups.

Breast Neoplasms↗
PubMed2002

Reconsidering the use of the general linear model with single-case data.

Using a low point estimate of autocorrelation to justify analyzing single-case data with the general linear model (GLM) is questioned. Monte Carlo methods are used to examine the degree to which bias in the estimate of autocorrelation depends on the complexity of the linear model used to describe the data. A method is then illustrated for determining the range of autocorrelation parameters that could reasonably have led to the observed autocorrelation. The argument for using a GLM analysis can be strengthened when the GLM analysis functions appropriately across the range of plausible autocorrelations. For situations in which the GLM analysis does not function appropriately across this range, a method is provided for adjusting the confidence intervals to ensure adequate coverage probabilities for specified levels of autocorrelation.

Analysis of Variance↗
PubMed2005

Multilevel generalized linear models for modelling age-related gender difference in violent behaviour and associated factors in the general household population.

It is preferable to use longitudinal data when studying patterns of violence and antisocial behaviour over the lifespan together with the associated risk factors in the general population. From the statistical modelling perspective, random samples of cross-sectional data, representative of the population, can be a reliable alternative. Sampling, weighting, and possible geographical clustering of the behaviour must be considered in the analysis together with correct choice of model as a function of age, although cohort effects and age effects are not separated from the analysis. This paper demonstrates the use of multilevel generalized linear models in the British National Survey of Psychiatric Morbidity in 2000. A multilevel logistic model as a special case of a generalized linear model with individual weightings was adapted for a dichotomous measure of violence and extended to Poisson and negative binomial outcomes. Three types of age function, discrete age effects, continuous age effects, and piecewise polynomial function of age intervals were evaluated for goodness of fit, and for their practical advantages and disadvantages. Models were developed for possible risk factors in relation to specific age groups of interest.

Adolescent↗
PubMed2004

limmaGUI: a graphical user interface for linear modeling of microarray data.

SUMMARY: limmaGUI is a graphical user interface (GUI) based on R-Tcl/Tk for the exploration and linear modeling of data from two-color spotted microarray experiments, especially the assessment of differential expression in complex experiments. limmaGUI provides an interface to the statistical methods of the limma package for R, and is itself implemented as an R package. The software provides point and click access to a range of methods for background correction, graphical display, normalization, and analysis of microarray data. Arbitrarily complex microarray experiments involving multiple RNA sources can be accomodated using linear models and contrasts. Empirical Bayes shrinkage of the gene-wise residual variances is provided to ensure stable results even when the number of arrays is small. Integrated support is provided for quantitative spot quality weights, control spots, within-array replicate spots and multiple testing. limmaGUI is available for most platforms on the which R runs including Windows, Mac and most flavors of Unix. AVAILABILITY: http://bioinf.wehi.edu.au/limmaGUI.

Computer Graphics↗
PubMed1992

[Mathematical simulation of intracranial condition--Part 1. Linear model stimulation].

We developed a linear mathematical model of the intracranial vessels, which reflects changes of the pulse wave (pulse pressure) of intracranial pressure after ligation of the internal jugular vein. The model composed of eight major variables: 1. resistance of arteries, 2. resistance of small arteries and capillary vessels, 3. resistance of veins, 4. resistance of internal jugular and vertebral veins, 5. compliance of arteries, 6. compliance of small arteries and capillary vessels, 7. compliance of veins and 8. intracranial compliance. All variables are presumed to have linear elements and replaced with electrical elements. The model of neck dissection is expressed as the change of resistance of the internal jugular and vertebral veins. Intracranial condition is expressed as the pulse wave (pulse pressure) of intracranial pressure and driving pressure. After unilateral ligation of the internal jugular vein, the pulse wave of intracranial pressure increased 24% and, after bilateral ligation of the internal jugular vein, it increased 55%. After unilateral ligation of the internal jugular vein, the pulse wave of intracranial pressure increased 27%, and, after bilateral ligation, it increased 79%. When intracranial compliance is normal, the respective ratios of pulse wave of intracranial pressure and driving pressure to cross-sectional area decreased, whereas those after increase of intracranial compliance increased.

Cerebrovascular Circulation↗
PubMed1998

Hospital- and patient-related characteristics determining maternity length of stay: a hierarchical linear model approach.

OBJECTIVES: The purpose of this study was to identify factors related to pregnancy and childbirth that might be predictive of a patient's length of stay after delivery and to model variations in length of stay. METHODS: California hospital discharge data on maternity patients (n = 499,912) were analyzed. Hierarchical linear modeling was used to adjust for patient case mix and hospital characteristics and to account for the dependence of outcome variables within hospitals. RESULTS: Substantial variation in length of stay among patients was observed. The variation was mainly attributed to delivery type (vaginal or cesarean section), the patient's clinical risk factors, and severity of complications (if any). Furthermore, hospitals differed significantly in maternity lengths of stay even after adjustment for patient case mix. CONCLUSIONS: Developing risk-adjusted models for length of stay is a complex process but is essential for understanding variation. The hierarchical linear model approach described here represents a more efficient and appropriate way of studying interhospital variations than the traditional regression approach.

Adult↗
PubMed2002

Linear modeling of steady-state behavioral dynamics.

The observed steady-state behavioral dynamics supported by unsignaled periods of reinforcement within repeating 2,000-s trials were modeled with a linear transfer function. These experiments employed improved schedule forms and analytical methods to improve the precision of the measured transfer function, compared to previous work. The refinements include both the use of multiple reinforcement periods that improve spectral coverage and averaging of independently determined transfer functions. A linear analysis was then used to predict behavior observed for three different test schedules. The fidelity of these predictions was determined.

Animals↗
PubMed2004

On the use of multivariable piecewise-linear models for predicting human response to anesthesia.

The standard modeling paradigm used to describe the relationship between input anesthetic agents and output patient endpoint variables are single-input single-output pharmacokinetic-pharmacodynamic (PK-PD) compartment models. In this paper, we propose the use of multivariable piecewise-linear models to describe the relations between inputs that include anesthesia, surgical stimuli and disturbances to a variety of patient output variables. Subspace identification methods are applied to clinical data to construct the models. A comparison of predicted and measured responses is completed, which includes predictions from PK-PD models, and piecewise-linear time-invariant models.

Adult↗
PubMed2004

Conditional estimation for generalized linear models when covariates are subject-specific parameters in a mixed model for longitudinal measurements.

The relationship between a primary endpoint and features of longitudinal profiles of a continuous response is often of interest, and a relevant framework is that of a generalized linear model with covariates that are subject-specific random effects in a linear mixed model for the longitudinal measurements. Naive implementation by imputing subject-specific effects from individual regression fits yields biased inference, and several methods for reducing this bias have been proposed. These require a parametric (normality) assumption on the random effects, which may be unrealistic. Adapting a strategy of Stefanski and Carroll (1987, Biometrika74, 703-716), we propose estimators for the generalized linear model parameters that require no assumptions on the random effects and yield consistent inference regardless of the true distribution. The methods are illustrated via simulation and by application to a study of bone mineral density in women transitioning to menopause.

Biometry↗
PubMed1994

Diagnostics for the multivariate linear model analysis of 2 x 2 crossover designs.

The multivariate linear model Y = X beta + epsilon is used to analyze data in 2 x 2 crossover designs with either univariate or multivariate response. Diagnostics are performed on estimating the effect of interest formulated as C beta U and on testing the general linear hypothesis C beta U = k. The multivariate Cook's distance is extended to be the influence measure by incorporating the contrast matrix C and the transformation matrix U, and magnitude of F(1)-F, the difference between the F approximation of a multivariate test statistic, is proposed as a measure to detect influential observations for testing the hypothesis C beta U = k. Both measures prove to be very useful because the diagnostics are now associated with estimating and testing effects of interest in the context of the experimental design.

Biopharmaceutics↗
PubMed1984

Covariate analysis of competing-risks data with log-linear models.

A general system of log-linear modeling is proposed for analysis of competing-risks data with discrete covariates. The instantaneous cause-specific failure rates, approximated by step-functions, are analyzed by techniques for multidimensional contingency tables. Censored observations are accommodated. Counts of failures of each type, and the amount of follow-up, are summarized in two arrays in which each cell denotes a distinct combination of failure type, time interval and covariate value. Maximum likelihood estimators for the parameters of the model are derived by iterative proportional fitting; the resulting estimates of the number of failures in each cell are used for goodness-of-fit tests. The principal advantages of this approach are its simple display of data, its computational ease for the fitting and comparison of models and its provision of explicit goodness-of-fit tests. Interpretation of the models is facilitated by reference to several alternative models for survivorship and competing risks. The basic model is extended to incorporate stochastic covariates whose values change during follow-up, and to accommodate quantitative covariates.

Analysis of Variance↗