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Results for “Linear Models”

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PubMed1990

One-sided significance tests for generalized linear models under dichotomous response.

Dichotomous response models are common in many experimental settings. Often, concomitant explanatory variables are recorded, and a generalized linear model, such as a logit model, is fit. In some cases, interest in specific model parameters is directed only at one-sided departures from some null effect. In these cases, procedures can be developed for testing the null effect against a one-sided alternative. These include Bonferroni-type adjustments of univariate Wald tests, and likelihood ratio tests that employ inequality-constrained multivariate theory. This paper examines such tests of significance. Monte Carlo evaluations are undertaken to examine the small-sample properties of the various procedures. The procedures are seen to perform fairly well, generally achieving their nominal sizes at total sample sizes near 100 experimental units. Extensions to the problem of one-sided tests against a control or standard are also considered.

Biometry↗

PubMed2004

fMRI analysis with the general linear model: removal of latency-induced amplitude bias by incorporation of hemodynamic derivative terms.

Functional magnetic resonance imaging (fMRI) data are often analyzed using the general linear model employing a hypothesized neural model convolved with a hemodynamic response function. Mismatches between this hemodynamic model and the data can be induced by spatially varying delays or slice-timing differences. It is common practice to desensitize the analysis to such delays by incorporation of the hemodynamic model plus its temporal derivative. The rationale often used is that additional variance will be captured and regressed out from the data. Though this is true, it ignores the potential for amplitude bias induced by small model mismatches due to, for example, variable hemodynamic delays and is not helpful for "random effects" analyses which typically do not account for the first level variance at all. Amplitude bias is due to the use of only the nonderivative portion of the model in the final test for significant amplitudes. We propose instead testing an amplitude value that is a function of both the nonderivative and the derivative terms of the model. Using simulations, we show that the proposed amplitude test does not suffer from delay-induced bias and that a model incorporating temporal derivatives is a more natural test for amplitude differences. The proposed test is applied in a random-effects analysis of 100 subjects. It reveals increased amplitudes in areas consistent with the task, with the largest increases in regions with greater hemodynamic delays.

Acoustic Stimulation↗

PubMed2003

Hierarchical linear models for the quantitative integration of effect sizes in single-case research.

In this article, the calculation of effect size measures in single-case research and the use of hierarchical linear models for combining these measures are discussed. Special attention is given to meta-analyses that take into account a possible linear trend in the data. We show that effect size measures that have been proposed for this situation appear to be systematically affected by the duration of the experiment and fail to distinguish between effects on level and slope. To avoid these flaws, we propose to perform a multivariate meta-analysis on the standardized ordinary least squares regression coefficients from the study-specific regression equations describing the response variable.

Algorithms↗

PubMed1999

Exact tests of goodness of fit of log-linear models for rates.

We propose Metropolis-Hastings sampling methods for estimating the exact conditional p-value for tests of goodness of fit of log-linear models for mortality rates and standardized mortality ratios. We focus on two-way tables, where the required conditional distribution is a multivariate noncentral hypergeometric distribution with known noncentrality parameter. Two examples are presented: a 2 x 3 table, where the exact results, obtained by enumeration, are available for comparison, and a 9 x 7 table, where Monte Carlo methods provide the only feasible approach for exact inference.

Biometry↗

PubMedDate not supplied

Ensemble of linear models for predicting drug properties.

We propose a new classification method for the prediction of drug properties, called random feature subset boosting for linear discriminant analysis (LDA). The main novelty of this method is the ability to overcome the problems with constructing ensembles of linear discriminant models based on generalized eigenvectors of covariance matrices. Such linear models are popular in building classification-based structure-activity relationships. The introduction of ensembles of LDA models allows for an analysis of more complex problems than by using single LDA, for example, those involving multiple mechanisms of action. Using four data sets, we show experimentally that the method is competitive with other recently studied chemoinformatic methods, including support vector machines and models based on decision trees. We present an easy scheme for interpreting the model despite its apparent sophistication. We also outline theoretical evidence as to why, contrary to the conventional AdaBoost ensemble algorithm, this method is able to increase the accuracy of LDA models.

ATP Binding Cassette Transporter, Subfamily B, Mem↗

PubMed1986

Double-inhibitor and uncoupler-inhibitor titrations. 1. Analysis with a linear model of chemiosmotic energy coupling.

The results of double-inhibitor and uncoupler-inhibitor titrations have been simulated and analyzed with a linear model of delocalized protonic coupling using linear nonequilibrium thermodynamics. A detailed analysis of the changes of the intermediate delta muH induced by different combinations of inhibitors of the proton pumps has been performed. It is shown that with linear flow-force relationships the published experimental results of uncoupler-inhibitor titrations are not necessarily inconsistent with, and those of double-inhibitor titrations are inconsistent with, a delocalized chemiosmotic model of energy coupling in the presence of a negligible leak. Also shown and discussed are how the results are affected by a nonnegligible leak and to what extent the shape of the titration curves can be used to discriminate between localized and delocalized mechanisms of energy coupling.

Adenosine Triphosphatases↗

PubMed1990

On the uniqueness of quasi-static solutions of some linear models of left ventricular mechanics.

We review two models describing the material properties of heart muscle: the fluid-fiber model and the fluid-fiber-collagen model. We show that the fluid-fiber description gives rise to non-uniqueness when used in ventricular modeling while the fluid-fiber-collagen description does not. We derive a general cavity pressure-volume relation for an extended class family of linear models of the heart's left ventricle.

Biomechanical Phenomena↗

PubMed2004

A note on inference of trait associations with SNP haplotypes and other attributes in generalized linear models.

Recently, Lake et al. [Human Heredity 2003;55:56-65] have proposed an approach based on the EM algorithm for maximum-likelihood inference of trait associations with haplotypes and environmental cofactors in generalized linear models. In this short report, we describe an extension to accommodate missing SNP genotype information. We also discuss differences in the calculation of standard errors between their implementation and our own. Finally, we present results indicating that inference is robust to low levels of dependence between haplotypes and nongenetic factors, but that biased inference can result when there is moderate to strong dependence. Overall, the method is found to perform well in the models we considered.

Algorithms↗

PubMed2001

Mixed multivariate generalized linear models for assessing lower-limb arterial stenoses.

Experiments and observational studies often involve gathering information on several response variables, enabling us to model their dependence on observable predictor variables. Despite associations between the response variables, they are often analysed separately using general and generalized linear models. This paper investigates applications of multivariate regression analysis to improve the accuracy of predictions and decisions, in the specific context of diagnosing arterial stenoses in human legs. Two basic models are developed for this application, using (i) four binary responses and (ii) a mixture of two binary and two normal responses. The results clearly demonstrate the potential advantages offered by this approach.

Arterial Occlusive Diseases↗

PubMed2001

Hierarchical linear modeling of FIM instrument growth curve characteristics after spinal cord injury.

OBJECTIVE: To examine the recovery of aspects of functional independence as a continuous process using growth curve analysis. DESIGN: Retrospective database review of functional outcome assessment data from inception cohort. SETTING: Inpatient rehabilitation unit; community. PATIENTS: A total of 142 subjects (79.6% men; age range, 18-77yr; mean age +/- standard deviation, 36.2 +/- 15.5yr) who were admitted to a rehabilitation unit between March 1986 and November 1994 with a minimum of 4 postinjury FIM assessments. Neurologic subgroups included 63 individuals with paraplegia, 36 with low tetraplegia, 24 with high tetraplegia, and 19 with incomplete injury. MAIN OUTCOME MEASURE: FIM instrument. RESULTS: Growth curve analyses with hierarchical linear modeling using a decelerating recovery function yielded a reliable model in which longer rehabilitation length of stay was associated with a more rapid rate of recovery but lower plateau. Neurologic injury category had expected effects on rate and degree of recovery. Level of impairment-specific results included an age effect in which older age was associated with lower level of plateau. In specific neurologic groups there was a significant gender effect, in which men made more rapid recovery than women, and a significant effect of level of education, in which higher education was associated with more rapid rate of recovery. Rate of FIM recovery was reliably modeled in the sample with incomplete injuries, but none of the demographic predictors was significant. CONCLUSIONS: Functional recovery can be modeled as a decelerating rather than simple linear function. The study of predictors of recovery characteristics, including rate of recovery and plateau, offers a valuable way of understanding rehabilitative needs and outcomes. Gender and education effects on the recovery process are intriguing and warrant further investigation.

Adult↗

PubMed1984

Log-linear-model analysis of the association between disease and genotype.

In this paper, log-linear-model analysis is employed to provide further insight into the disease-genotype association problem, as discussed by Norwood and Hinkelmann (1978, Biometrics 34, 593-602). It is shown how this approach can take account of the structure of the data when testing hypotheses about the type of association, by specifying the form of recurrence risks and allowing estimation of such recurrence risks by maximum likelihood. The notation of conditional recurrence risk is introduced and its usefulness is illustrated.

Alleles↗

PubMed1978

Strategies for the selection of log-linear models.

In a multidimensional contingency table strategies have been proposed to build log-linear models using either stepwise methods or standardized estimates of the parameters of the saturated model. Brown (1976) proposed a two-step procedure to screen effects and then test a subset of models. Alternate methods of model building are discussed with respect to the final choice of model and with respect to intermediate information available to the data analyst during the selection process.

Depression↗

PubMed1991

Using generalized linear models (GLMs) to model errors in motor performance.

Because of differences in design factors, experiments in human motor performance sometimes produce a wide range in variability or consistency in a subject's individual errors. These differences in variation often lead to heterogeneity in the variance-covariance matrices between group factors, which prohibits the use of repeated-measures (RM) ANOVA or MANOVA techniques to analyze the error data. Provided certain conditions are met, however, each subject's individual errors can be collapsed into the summary error measures, constant error (CE) and variable error (VE), which can still provide a more than adequate description of the subjects' performance. This article proposes the appropriate conditions and the corresponding generalized linear models (GLMs) with which a subject's individual errors, recorded in short-term motor memory research, can be combined into the summary measures, CE and VE, which can be analyzed subsequently as the dependent variables in the experimental design. The CE scores can be modeled using GLMs without requiring the assumption of homogeneity of variances. Similarly, the VE scores can be modeled as a GLM, using a log-linear regression model that assumes a gamma distribution, rather than using a traditional analysis of variance (ANOV A) model that assumes an inappropriate normal error distribution for these scores. An example reveals that the analysis of VE scores, unlike the analysis of CE scores, is able to differentiate between group practice methods. These differences tend to be underestimated by traditional ANOVA methods, however. Differences between the ANOV A and GLM analyses of the VE scores are further clarified by simulation. Based on differences like those observed in the example, when simulated VE scores were analyzed, assuming both a normal and a gamma distribution, the power of the gamma tests was found to be superior to the normal analyses in all but a small range of cases, in which such differences were found to be negligible. Hence, it is only by declaring the VE scores to have a GLM with a gamma distribution that the anticipated group practice differences can be properly identified.

Journal Article↗

PubMed2003

Log-linear models for assessing gene-age interaction and their application to case-control studies of the apolipoprotein E (apoE) gene in Alzheimer's disease.

Case-control studies provide a powerful approach for detecting disease-susceptibility genes or assessing gene-environment interactions. We investigated the situation in which the gene being studied plays a role in several diseases, and the allele frequency among subjects free of the disease of interest consequently decreases with age as subjects die from other diseases. The logistic model is one approach frequently used for analyzing case-control data, but it cannot accommodate this dependence of genotype and age. Using a log-linear model, we therefore proposed a hierarchical procedure that could be used as a valid method for assessing interactions in such situations. We then applied this procedure to observed data on Alzheimer's disease and the apolipoprotein E gene in Japan. We were able to derive an appropriate inference on whether the interaction was a gene-age interaction or merely a bias due to death from other diseases.

Age Factors↗

PubMed1983

Dependence of the linear model for the nerve compound action potential on the single fibre action potential waveform.

The linear model of the nerve compound action potential (CAP) depends on the assumed waveform for the single fibre action potential (SFAP). A general method has been developed to investigate the influence of the unknown features of the SFAP on the estimation of nerve fibre conduction velocity (CV) distribution. A SFAP waveform is considered consistent with the model and the experimental data if recorded and reconstructed CAPS fit and the distribution is physically meaningful. Experimental CAPS were monopolarly recorded using surface electrodes over the median nerve at the wrist. To fit the model, SFAP waveforms must satisfy some internal relationship. The most important feature is that the ratio between positive and negative areas of the SFAP is almost one and does not vary in different subjects and recording sites. Many SFAP waveforms fit the model, and the relative conduction velocity distributions may be very different. These must be regarded as conventional distributions. As for inter-subject comparison, the dependence of the method on the recording site has been reduced by choosing the place where stimulus intensity and relative motor response amplitude have given values. In this recording environment CV distributions of normal subjects can be properly compared using the same SFAP and deviations from normality evidenced.

Action Potentials↗

PubMed1976

The linear model: a statistical tool applied to psychophysical research in dental prosthetics.

The construction of a linear model is described, and its function in analysing variations in the perception of comfortable mandibular occlusal positions is explained. In principle, the model combines analyses of variance and regression in a number of simple computer operations. Data from a clinical study were used to demonstrate the analytical capacity of a specific model, designed to estimate the effect of factors, which were supposed to influence the perception of comfortable mandibular positions.

Adult↗

PubMed1984

Comparison of the responses of auditory nerve fibers to consonant-vowel syllables with predictions from linear models.

The responses of cat auditory-nerve fibers to synthesized consonant-vowel syllables were compared with predictions from linear models based on individual fibers' threshold tuning curves. Comparisons with the linear predictions provided information about the specific effects of peripheral nonlinearities on the representation of speech sounds. Spectral peaks, such as the formants of vowels, were more prominently represented in synchronized discharge patterns than in the linear predictions. Suppression of responses to other spectral peaks and to stimulus components between spectral peaks accounted for the differences. While profiles of fibers' synchronized responses were usually dominated by a single formant, predicted linear responses often included broad responses having two or more formants as well as components near the fibers' characteristic frequencies. In contrast, when no stimulus peak fell within a fiber's response area, the agreement between the neural response and the linear prediction was quite good. The results suggest that one role for peripheral nonlinearities in the auditory system may be to enhance the neural representation of spectral features such as formants.

Animals↗

PubMed1994

A four-parameter linear model for analysing cardiorespiratory data in post-operative cardiac patients.

This paper investigates the possibility of characterizing the differences between normal- and high-risk postoperative cardiac patients on the basis of four parameters related to a simple linear model of cardiorespiratory performances. The model comprises three subsystems representing cardiac, vascular and respiratory functions, respectively. These parameters, determined from physiological variables measured in the Intensive Care Unit, seem useful for clinical evaluation of patient status. In fact, their values quantify the improved cardiovascular and respiratory response that normal-risk patients exhibit to increasing metabolic needs after hypothermic treatment, with less utilization of blood oxygen reserve. In addition, a set of three parameters derived from the proposed four allows a prediction of patient class membership with an error lower than 7% when used with a Bayes quadratic classifier.

Cardiac Surgical Procedures↗