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PubMed1991

Using log-linear models to test for associations among congenital malformations.

Log-linear models can be used to test for pairwise associations and higher order interactions among anatomically distinct birth defects or congenital malformations. A log-linear model, including terms for every possible pairwise association among seven severe and easily detectable congenital malformations, was examined using data on 16,217 infants registered in the Metropolitan Atlanta Congenital Defects Program between 1968 and 1986. The resulting model showed clear patterns of strong association between some congenital malformations and not others, and the presence of 3-way interaction terms where the association between two malformations depended on the presence of a third. Examining a more parsimonious log-linear model showed overlapping patterns of pairwise association involving anal-rectal atresia and omphalocele, anal-rectal atresia and limb deficiency, and anal-rectal atresia and tracheaesophageal fistula. A second common pattern involved a triangular cluster with a hierarchical relationship among the three malformations (where there was a strong association between the first and second malformations and between the first and third malformations, but the association between the second and third was only seen in the absence of the first). Three such overlapping triangular clusters were identified from these data: neural tube defects, oral clefts, and omphalocele; neural tube defects, oral clefts, and limb deficiency; and limb deficiency, diaphragmatic hernia, and neural tube defects.(ABSTRACT TRUNCATED AT 250 WORDS)

Abnormalities, Multiple↗
PubMed1999

On the approximation rate of hierarchical mixtures-of-experts for generalized linear models.

We investigate a class of hierarchical mixtures-of-experts (HME) models where generalized linear models with nonlinear mean functions of the form psi (alpha + xT beta) are mixed. Here psi (.) is the inverse link function. It is shown that mixtures of such mean functions can approximate a class of smooth functions of the form psi (h(x)), where h(.) epsilon W2;K infinity (a Sobolev class over [0, 1]s), as the number of experts m in the network increases. An upper bound of the approximation rate is given as O(m-2/s) in Lp norm. This rate can be achieved within the family of HME structures with no more than s-layers, where s is the dimension of the predictor x.

Algorithms↗
PubMed1986

Evaluation of linear models of surface spectral reflectance with small numbers of parameters.

Recent computational models of color vision demonstrate that it is possible to achieve exact color constancy over a limited range of lights and surfaces described by linear models. The success of these computational models hinges on whether any sizable range of surface spectral reflectances can be described by a linear model with about three parameters. In the first part of this paper, I analyze two large sets of empirical surface spectral reflectances and examine three conjectures concerning constraints on surface reflectance: that empirical surface reflectances fall within a linear model with a small number of parameters, that empirical surface reflectances fall within a linear model composed of band-limited functions with a small number of parameters, and that the shape of the spectral-sensitivity curves of human vision enhance the fit between empirical surface reflectances and a linear model. I conclude that the first and second conjectures hold for the two sets of spectral reflectances analyzed but that the number of parameters required to model the spectral reflectances is five to seven, not three. A reanalysis of the empirical data that takes human visual sensitivity into account gives more promising results. The linear models derived provide excellent fits to the data with as few as three or four parameters, confirming the third conjecture. The results suggest that constraints on possible surface-reflectance functions and the "filtering" properties of the shapes of the spectral-sensitivity curves of photoreceptors can both contribute to color constancy. In the last part of the paper I derive the relation between the number of photoreceptor classes present in vision and the "filtering" properties of each class. The results of this analysis reverse a conclusion reached by Barlow: the "filtering" properties of human photoreceptors are consistent with a trichromatic visual system that is color constant.

Analysis of Variance↗
PubMed1986

Log-linear modeling of consonant confusion data.

Log-linear models, in conjunction with the G2 statistic, were developed and applied to several existing sets of consonant confusion data. Significant interactions of consonant error patterns were found with signal-to-noise ratio (S/N), presentation level, vowel context, and low-pass and high-pass filtering. These variables also showed significant interactions with error patterns when categorized on the basis of feature classifications. Patterns of errors were significantly altered by S/N for place of articulation (front, middle, back), voicing, frication, and nasality. Low-pass filtering significantly affected error patterns when categorized by place of articulation, duration, or nasality; whereas, high-pass filtering only affected voicing and frication error patterns. This paper also demonstrates the utility of log-linear modeling techniques in applications to confusion matrix analysis: specific effects can be tested; variant cells in a matrix can be isolated with respect to a particular model of interest; diagonal cells can be eliminated from the analysis; and the matrix can be collapsed across levels of variables, with no violation of independence. Finally, log-linear techniques are suggested for development of parsimonious and predictive models of speech perception.

Humans↗
PubMed1975

Models for cultural inheritance: a general linear model.

A theory of cultural evolution is proposed based on a general linear mode of cultural transmission. The trait of an individual is assumed to depend on the values of the same trait in other individuals of the same, the previous or earlier generation. The transmission matrix W has as its elements the proportional contributions of each individual (i) of one generation to each individual (j) of another. In addition, there is random variation (copy error or innovation) for each individual. Means and variances of a group of N individuals change with time and will stabilize asymptotically if the matrix W is irreducible and aperiodic. The rate of convergence is geometric and is governed by the largest non-unit eigenvalue of W. Groups fragment and evolve independently if W is reducible. The means of independent groups vary at random at a predicted rate, a phenomenon termed "random cultural drift". Variances within a group tend to be small, assuming cultural homogeneity. Transmission matrices of the teacher/leader type, and of parental type have been specifically considered, as well as social hierarchies. Various limitations, extensions, and some chances of application are discussed.

Cultural Evolution↗
PubMed2026

Scaling linear-model breeding values to the liability scale: an application to pig binary traits.

In commercial pig production, many important traits are recorded as binary phenotypes. For such traits, threshold models offer an appropriate framework but are computationally intensive. Thus, linear models are widely used to obtain genomic estimated breeding values (GEBV); however, these are on the observed scale (phenotypic). This creates the need for a robust method to approximate GEBV from linear models to the liability scale. A recently proposed approximation showed good concordance for low-prevalence traits (<5%) but has not yet been tested for a wider range of prevalence values and for models with more than one random effect. We aimed to evaluate the performance of this approximation for pig binary traits with prevalences ranging from <5% to >86%, in both animal and maternal animal models. Data were available for five fitness traits (FT1-FT5), with up to 233k animals with phenotypes, of which 204k animals were genotyped with a 25k SNP array. Variance component estimates were obtained using threshold models. Classical animal models were used for FT1-FT3, and maternal animal models for FT4 and FT5. Variance components on the observed scale were then obtained by multiplying estimates from a threshold model by the square of the height of the standard normal density evaluated at the threshold. GEBV were predicted using single-step genomic best linear unbiased prediction under both linear and threshold models. The approximation tested involved scaling the GEBV using the height of the ordinate of the standard normal distribution evaluated at the threshold as a scaling factor. The agreement between GEBV from the scaled linear model and the threshold model on the probability scale was evaluated using Pearson and Spearman correlations, mean squared error (MSE), regression parameters, overlapping coefficient (OVL), distribution overlap, and classification accuracy (CACC). Correlations between linear and threshold GEBV ranged from 0.94 (low-prevalence traits) to 0.99 (high-prevalence traits) for the direct GEBV and were 0.99 for the maternal GEBV. MSE were close to zero. The OVL exceeded 0.83 for all traits. CACC ranged from 95.10% to 98.33% for the direct GEBV and from 92.54% to 97.42% for the maternal GEBV. Regardless of model and trait prevalence, this approximation yielded GEBV that are highly consistent with threshold model GEBV, providing a reliable, practical approach for large-scale pig genetic evaluations for binary traits using linear models.

Animals↗
PubMed1986

A general multivariate approach to linear modeling in human genetics.

The general linear structural equation model is applied to problems in human genetics where there may be more than one measured phenotype per individual. A modeling convention, termed conditional associations, is developed to extend the general linear model so that it can handle the unique problems in human genetic models that arise from the pairing up of individuals or families under assortment between mates and the assortative placement of adoptees. Formulas are presented to generate expected covariance matrices for assortment or assortative placement on many variables simultaneously. It is demonstrated that all linear models in human genetics can be reduced in form to two fundamental equations. An algorithm is presented that will allow the application of these two equations to linear modeling in human genetics.

Adoption↗
PubMed2005

Reconstruction of gene regulatory networks under the finite state linear model.

We study the Finite State Linear Model (FSLM) for modelling gene regulatory networks proposed by A. Brazma and T. Schlitt in [4]. The model incorporates biologically intuitive gene regulatory mechanism similar to that in Boolean networks, and can describe also the continuous changes in protein levels. We consider several theoretical properties of this model; in particular we show that the problem whether a particular gene will reach an active state is algorithmically unsolvable. This imposes some practical difficulties in simulation and reverse engineering of FSLM networks. Nevertheless, our simulation experiments show that sufficiently many of FSLM networks exhibit a regular behaviour and that the model is still quite adequate to describe biological reality. We also propose a comparatively efficient O(2(K)n(K+1)M(2K)m log m) time algorithm for reconstruction of FSLM networks from experimental data. Experiments on reconstruction of random networks are performed to estimate the running time of the algorithm in practice, as well as the number of measurements needed for successful network reconstruction.

Algorithms↗
PubMed2003

Application of multilevel models to morphometric data. Part 1. Linear models and hypothesis testing.

Morphometric data usually have a hierarchical structure (i.e., cells are nested within patients), which should be taken into consideration in the analysis. In the recent years, special methods of handling hierarchical data, called multilevel models (MM), as well as corresponding software have received considerable development. However, there has been no application of these methods to morphometric data yet. In this paper we report our first experience of analyzing karyometric data by means of MLwiN - a dedicated program for multilevel modeling. Our data were obtained from 34 follicular adenomas and 44 follicular carcinomas of the thyroid. We show examples of fitting and interpreting MM of different complexity, and draw a number of interesting conclusions about the differences in nuclear morphology between follicular thyroid adenomas and carcinomas. We also demonstrate substantial advantages of multilevel models over conventional, single-level statistics, which have been adopted previously to analyze karyometric data. In addition, some theoretical issues related to MM as well as major statistical software for MM are briefly reviewed.

Adenoma↗
PubMed1998

Interaction effects of client and treatment program characteristics on retention: an exploratory analysis using hierarchical linear models.

This paper applied a hierarchical linear modeling approach to explore the interaction effects of treatment program and client characteristics on client retention in treatment for drug users. Program characteristics included services provision, funding sources, and staff-client gender congruence, and client characteristics included gender, age at admission, and drug use level prior to admission. The same model was applied separately to three modalities: residential, methadone maintenance, and outpatient drug-free programs. Data were obtained from 59 treatment programs and 3,764 of their clients who had discharge records. The most noteworthy significant interaction effect detected was program's funding source and client's gender on treatment retention in the outpatient drug-free modality. For example, female clients remained less time in the programs that accepted only public funding than in the programs that accepted both public and private funding. Male clients remained in the treatment an average of 25.3 fewer days than female clients in drug-free programs that only accepted public fund, but stayed about the same time as females if the programs received mixed funding.

Adult↗
PubMed2004

Multiple regression of cost data: use of generalised linear models.

OBJECTIVE: Choosing an appropriate method for regression analyses of cost data is problematic because it must focus on population means while taking into account the typically skewed distribution of the data. In this paper we illustrate the use of generalised linear models for regression analysis of cost data. METHODS: We consider generalised linear models with either an identity link function (providing additive covariate effects) or log link function (providing multiplicative effects), and with gaussian (normal), overdispersed poisson, gamma, or inverse gaussian distributions. These are applied to estimate the treatment effects in two randomised trials adjusted for baseline covariates. Criteria for choosing an appropriate model are presented. RESULTS: In both examples considered, the gaussian model fits poorly and other distributions are to be preferred. When there are variables of prognostic importance in the model, using different distributions can materially affect the estimates obtained; it may also be possible to discriminate between additive and multiplicative covariate effects. CONCLUSIONS: Generalised linear models are attractive for the regression of cost data because they provide parametric methods of analysis where a variety of non-normal distributions can be specified and the way covariates act can be altered. Unlike the use of data transformation in ordinary least-squares regression, generalised linear models make inferences about the mean cost directly.

Costs and Cost Analysis↗
PubMed1999

A general maximum likelihood analysis of variance components in generalized linear models.

This paper describes an EM algorithm for nonparametric maximum likelihood (ML) estimation in generalized linear models with variance component structure. The algorithm provides an alternative analysis to approximate MQL and PQL analyses (McGilchrist and Aisbett, 1991, Biometrical Journal 33, 131-141; Breslow and Clayton, 1993; Journal of the American Statistical Association 88, 9-25; McGilchrist, 1994, Journal of the Royal Statistical Society, Series B 56, 61-69; Goldstein, 1995, Multilevel Statistical Models) and to GEE analyses (Liang and Zeger, 1986, Biometrika 73, 13-22). The algorithm, first given by Hinde and Wood (1987, in Longitudinal Data Analysis, 110-126), is a generalization of that for random effect models for overdispersion in generalized linear models, described in Aitkin (1996, Statistics and Computing 6, 251-262). The algorithm is initially derived as a form of Gaussian quadrature assuming a normal mixing distribution, but with only slight variation it can be used for a completely unknown mixing distribution, giving a straightforward method for the fully nonparametric ML estimation of this distribution. This is of value because the ML estimates of the GLM parameters can be sensitive to the specification of a parametric form for the mixing distribution. The nonparametric analysis can be extended straightforwardly to general random parameter models, with full NPML estimation of the joint distribution of the random parameters. This can produce substantial computational saving compared with full numerical integration over a specified parametric distribution for the random parameters. A simple method is described for obtaining correct standard errors for parameter estimates when using the EM algorithm. Several examples are discussed involving simple variance component and longitudinal models, and small-area estimation.

Adrenergic beta-Antagonists↗
PubMedDate not supplied

Non-linear models for the analysis of longitudinal data.

Given the importance of longitudinal studies in biomedical research, it is not surprising that considerable attention has been given to linear and generalized linear models for the analysis of longitudinal data. A great deal of attention has also been given to non-linear models for repeated measurements, particularly in the field of pharmacokinetics. In this article, a brief overview of non-linear models for the analysis of repeated measures is given. Particular emphasis is placed on mixed-effects non-linear models and on various estimation procedures proposed for such models. Several of these estimation procedures are compared via a simulation study. In addition, simulation is used to investigate the effects of model misspecification, particularly with respect to one's choice of random-effects. A relatively straightforward measure useful in selecting an appropriate set of random effects is investigated and found to perform reasonably well.

Humans↗
PubMed1983

A case study of linear versus non-linear modelling.

Theories for the facilitation of neurotransmitter release are discussed in a case study of the properties of linear and non-linear models for a phenomenon whose time course can be represented by a sum of decaying exponentials. Particular attention is paid to the effects of a "key factor" on the slopes and amplitudes of the exponentials that can be derived from semilog plots of the data. It is shown that the presence of such effects can give strong evidence for the inappropriateness of linear models. A non-linear model is demonstrated to be capable of describing the changes with extracellular Ca concentration of straight line segments that fit data in semilog plots of facilitation as a function of time. The conclusion is reached that even if data seems to be representable by several independently alterable exponentials one must be cautious in drawing inferences concerning the number, linearity, or independence of the underlying processes.

Action Potentials↗
PubMed2006

Probe-level linear model fitting and mixture modeling results in high accuracy detection of differential gene expression.

BACKGROUND: The identification of differentially expressed genes (DEGs) from Affymetrix GeneChips arrays is currently done by first computing expression levels from the low-level probe intensities, then deriving significance by comparing these expression levels between conditions. The proposed PL-LM (Probe-Level Linear Model) method implements a linear model applied on the probe-level data to directly estimate the treatment effect. A finite mixture of Gaussian components is then used to identify DEGs using the coefficients estimated by the linear model. This approach can readily be applied to experimental design with or without replication. RESULTS: On a wholly defined dataset, the PL-LM method was able to identify 75% of the differentially expressed genes within 10% of false positives. This accuracy was achieved both using the three replicates per conditions available in the dataset and using only one replicate per condition. CONCLUSION: The method achieves, on this dataset, a higher accuracy than the best set of tools identified by the authors of the dataset, and does so using only one replicate per condition.

Algorithms↗
PubMed2000

A double bootstrap method to analyze linear models with autoregressive error terms.

A new method for the analysis of linear models that have autoregressive errors is proposed. The approach is not only relevant in the behavioral sciences for analyzing small-sample time-series intervention models, but it is also appropriate for a wide class of small-sample linear model problems in which there is interest in inferential statements regarding all regression parameters and autoregressive parameters in the model. The methodology includes a double application of bootstrap procedures. The 1st application is used to obtain bias-adjusted estimates of the autoregressive parameters. The 2nd application is used to estimate the standard errors of the parameter estimates. Theoretical and Monte Carlo results are presented to demonstrate asymptotic and small-sample properties of the method; examples that illustrate advantages of the new approach over established time-series methods are described.

Bias↗
PubMed2004

Cross-validation for linear model with unequal variances in genomic analysis.

In recent years, genomic studies are usually conducted to identify genes that may have an impact on clinical outcomes. The identified genes are then used to establish a predictive model for identifying subjects who are most likely to respond to the test treatment in clinical trials. This information is useful in early and later phases of clinical development. The United States Food and Drug Administration (FDA) requires that such a predictive model be validated before it can be used in clinical development. Shao [Shao, J. (1993). Linear model selection by cross-validation. J. Amer. Statist. Assoc. 88(422):486-494] proposed a cross-validation method for linear model with equal variances, which is found useful in genomic studies. In practice, however, genomic data may be obtained from different sources with unequal variances. As a result, Shao's method may not be applied directly. In this paper, we extend Shao's method for cross-validation of a linear model with unequal variances. Along this line, two re-sampling methods were proposed to account for the heterogeneity in variance. Several simulations were performed to evaluate the finite samples performances of the proposed methods. An example concerning a breast cancer research is present to illustrate the use of the proposed methods.

Algorithms↗
PubMed2006

Simple linear models of scanning impedance imaging for fast reconstruction of relative conductivity of biological samples.

Scanning impedance imaging (SH) uses a noncontacting electrical probe held at a known voltage and scanned over a thin sample on a ground plane in a conductive medium to obtain images of current. The current image is related in a nonlinear way to the conductivity of the sample. This paper develops the theory behind SII showing how the measured current relates to the desired conductivity. Also included is the development of a simplified, linear model that is effective in explaining many of the experimental results. Good agreement of the linear model with step-response data over an insulator is shown. The linear model shows that the current is a blurred version of the conductivity. Simple deblurring methods can, therefore, be applied to obtain relative conductivity images from the raw current data. Raw SII data from a flower-petal and a leaf sample are shown as well as relative conductivity images deblurred using the linear model.

Algorithms↗