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PubMed1992

Linear models of surface and illuminant spectra.

We describe procedures for creating efficient spectral representations for color. The representations generalize conventional tristimulus representations, which are based on the peripheral encoding by the human eye. We use low-dimensional linear models to approximate the spectral properties of surfaces and illuminants with respect to a collection of sensing devices. We choose the linear-model basis functions by minimizing the error in approximating sensor responses for collections of surfaces and illuminants. These linear models offer some conceptual simplifications for applications such as printer calibration; they also perform substantially better than principal-components approximations for computer-graphics applications.

Algorithms↗

PubMed1985

Observations on sire evaluation with categorical data using heteroscedastic mixed linear models.

The ability of three mixed linear models to rank sires correctly for dichotomous and ordered tetrachotomous traits was studied using simulated half-sib progeny data. The models differed in the assumptions made regarding homogeneity of residual variance. Ranking ability was assessed by estimating the realized response to truncation selection (20% of the candidates selected) upon sire evaluations in populations consisting of 50 such sires. Results suggested that weighting for unequal residual variances, in spite of reducing apparent prediction error variance, impairs the ability of best linear unbiased prediction to identify superior sires. This is consistent with theoretical arguments stemming from threshold models.

Animals↗

PubMed1975

Simultaneous estimation of parameters in different linear models and applications to biometric problems.

Empirical Bayes procedure is employed in simultaneous estimation of vector parameters from a number of Gauss-Markoff linear models. It is shown that with respect to quadratic loss function, empirical Bayes estimators are better than least squares estimators. While estimating the parameter for a particular linear model, a suggestion has been made for distinguishing between the loss due to decision maker and the loss due to individual. A method has been proposed but not fully studied to achieve balance between the two losses. Finally the problem of predicting future observations in a linear model has been considered.

Bayes Theorem↗

PubMed1991

Testing for association between disease and linked marker loci: a log-linear-model analysis.

One approach frequently used for identifying genetic factors involved in the process of a complex disease is the comparison of patients and controls for a number of genetic markers near a candidate gene. The analysis of such association studies raises some specific problems because of the fact that genotypic and not gametic data are generally available. We present a log-linear-model analysis providing a valid method for analyzing such studies. When studying the association of disease with one marker locus, the log-linear model allows one to test for the difference between allelic frequencies among affected and unaffected individuals, Hardy-Weinberg (H-W) equilibrium in both groups, and interaction between the association of alleles at the marker locus and disease. This interaction provides information about the dominance of the disease susceptibility locus, with dominance defined using the epidemiological notion of odds ratio. The degree of dominance measured at the marker locus depends on the strength of linkage disequilibrium between the marker locus and the disease locus. When studying the association of disease with several linked markers, the model becomes rapidly complex and uninterpretable unless it is assumed that affected and unaffected populations are in H-W equilibrium at each locus. This hypothesis must be tested before going ahead in the analysis. If it is not rejected, the log-linear model offers a stepwise method of identification of the parameters causing the difference between populations. This model can be extended to any number of loci, alleles, or populations.

Alleles↗

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↗

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↗

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↗

PubMed1992

Methods for estimating the parameters of a linear model for ordered categorical data.

In many empirical analyses, the response of interest is categorical with an ordinal scale attached. Many investigators prefer to formulate a linear model, assigning scores to each category of the ordinal response and treating it as continuous. When the covariates are categorical, Haber (1985, Computational Statistics and Data Analysis 3, 1-10) has developed a method to obtain maximum likelihood (ML) estimates of the parameters of the linear model using Lagrange multipliers. However, when the covariates are continuous, the only method we found in the literature is ordinary least squares (OLS), performed under the assumption of homogeneous variance. The OLS estimates are unbiased and consistent but, since variance homogeneity is violated, the OLS estimates of variance can be biased and may not be consistent. We discuss a variance estimate (White, 1980, Econometrica 48, 817-838) that is consistent for the true variance of the OLS parameter estimates. The possible bias encountered by using the naive OLS variance estimate is discussed. An estimated generalized least squares (EGLS) estimator is proposed and its efficiency relative to OLS is discussed. Finally, an empirical comparison of OLS, EGLS, and ML estimators is made.

Abnormalities, Drug-Induced↗

PubMed1992

Categorical data analysis in primary care research: log-linear models.

Primary care researchers often wish to perform multiple variable analyses using variables measured at a nominal or ordinal level. This paper provides a step-by-step description of log-linear modeling, an approach uniquely well suited to explore and describe interactions among three or more nominal or ordinal variables. The method of log-linear analysis is illustrated with the use of an example from a primary care research project in which the relationships among hypertension, diet, and sodium were examined. The advantages and disadvantages of log-linear models and logistic regression are compared and available computer software programs discussed.

Humans↗

PubMed1991

A log-linear modeling framework for selective mixing.

Nonrandom mixing can significantly alter the diffusion path of an infectious disease such as AIDS that requires intimate contact. Recent attempts to model this effect have sought a general framework capable of representing both simple and arbitrarily complicated mixing structures, and of solving the balancing problem in a nonequilibrium multigroup population. Log-linear models are proposed here as a general framework for solving the first problem. This approach offers several additional benefits: The parameters used to govern the mixing have a simple, intuitive interpretation, the framework provides a statistically sound basis for the estimation of these parameters from mixing-matrix data, and the resulting estimates are easily integrated into compartmental models for diffusion. A modified selection model is proposed to solve the second problem of generalizing the selection process to nonequilibrium populations. The distribution of contacts under this model is derived and is found to satisfy the assumptions of statistical inference for log-linear models. Together these techniques provide an integrated and flexible framework for modeling the role of selective mixing in the spread of disease.

Acquired Immunodeficiency Syndrome↗

PubMed1991

The evaluation of agreement by means of log-linear models: proxy interviews on reproductive history among floriculture workers in Colombia.

We used data from Colombia to compare responses from husbands and wives concerning the reproductive history of the women. We analyzed agreement in two ways: First, we compared kappa statistics between independent subgroups. Second, we evaluated agreement by means of log-linear models. Men underreported the total number of pregnancies and the number of abortions of their wives. Agreement on the term of the pregnancy was dependent on the ages of the partners. Log-linear modeling provides an attractive alternative to more usual ways of studying agreement.

Adolescent↗

PubMed1985

Confidence intervals for a variance ratio, or for heritability, in an unbalanced mixed linear model.

A procedure is presented for constructing an exact confidence interval for the ratio of the two variance components in a possibly unbalanced mixed linear model that contains a single set of m random effects. This procedure can be used in animal and plant breeding problems to obtain an exact confidence interval for a heritability. The confidence interval can be defined in terms of the output of a least squares analysis. It can be computed by a graphical or iterative technique requiring the diagonalization of an m X m matrix or, alternatively, the inversion of a number of m X m matrices. Confidence intervals that are approximate can be obtained with much less computational burden, using either of two approaches. The various confidence interval procedures can be extended to some problems in which the mixed linear model contains more than one set of random effects. Corresponding to each interval procedure is a significance test and one or more estimators.

Analysis of Variance↗

PubMed1992

Estimating prevalence by group testing using generalized linear models.

A method is described for estimating prevalence by group testing using generalized linear models. This provides a simple way of analysing such data using widely available software. Existing methodology to correct for overdispersion using quasi-likelihoods is applied to the group testing model. The methods are illustrated by an estimation of salmonella contamination in eggs, and of yellow fever virus infection in a mosquito population.

Animals↗

PubMed1986

Bivariate linear models in neurobiology: problems of concept and methodology.

Bivariate linear models, used to describe morphological and functional characteristics between two sets of observations, are examined both in concept and in application. This paper focuses on the underlying assumptions and statistics of the method most frequently used: ordinary linear regression, principal axis and standard major axis. It is shown how the choice of method should depend on: the purpose of the analysis and the a priori assumptions regarding the residual variance. It appears that none of the methods has a universal application. Differences among the models discussed are illustrated by a bivariate morphometric analysis of cerebrocortical regions in primates.

Animals↗

PubMed1992

Log-linear modelling of pairwise interobserver agreement on a categorical scale.

This article uses log-linear models to describe pairwise agreement among several raters who classify a sample on a subjective categorical scale. The models describe agreement structure simultaneously for second-order marginal tables of a multidimensional cross-classification of ratings. Practical difficulties arise in fitting the models, because models refer to pairwise marginal tables of a very large and sparse table. A standard analysis that treats the marginal tables as independent yields consistent estimates of model parameters, but not of the covariance matrix of the estimates. We estimate the covariance matrix using the jackknife. We apply the models to describe agreement between evaluations made by seven pathologists of carcinoma in situ of the uterine cervix, using a five-level ordinal scale. Previous analyses showed differences among the pathologists in their pairwise levels of agreement, but we observe near homogeneity in the dependence structure of their ratings.

Carcinoma in Situ↗

PubMed1989

Log-linear models for the analysis of matched cohort studies.

The application of conditional logistic regression to the analysis of matched case-control studies has now become quite customary. In addition, it is well known that software designed to fit linear logistic and log-linear models can be used in these analyses. The application of conditional logistic regression to cohort designs is described, and an approach is developed that adapts the linear logistic and log-linear models for the analysis of prospectively collected data. Specific situations discussed include matched pairs, 2:1 matching, and studies in which some subjects are pair matched and others matched 2:1. The methods are illustrated with numeric examples.

Case-Control Studies↗

PubMed1990

Application of log-linear model in inference on karyotypic evolution in chronic myelocytic leukemia.

Relationships among additional chromosome abnormalities in chronic myelocytic leukemia (CML) with translocation 9;22 [Philadelphia chromosome (Ph1)-positive CML] were analyzed by log-linear models on 709 karyotypes reported in the literature. Additional abnormalities, such as the gain of chromosome 8 (+8), gain of Philadelphia chromosome (+Ph1), isochromosome of the long arm (q) of chromosome 17 [i(17q)], and the gain of chromosome 19 (+19), were frequently observed. A four-way 2 x 2 x 2 x 2 contingency table was considered with respect to the appearance of these four abnormalities, then the hierarchical log-linear models having at least four main effects were fitted to the observed contingency table. Akaike's information criteria of the models reflected the fitness of the model very well. Parameter estimates of the interaction terms indicated that the combinations of two abnormalities, '+8 and +19', '+Ph1 and +19', and '+8 and i(17q)' were positively associated, while '+Ph1 and i(17q)', and '+19 and i(17q)' were negatively associated. Based on the results of the data analysis, an inference was made on the route of karyotypic evolution in Ph1-positive CML; it statistically supports the hypothesis presented by Heim and Mitelman.

Aneuploidy↗

PubMed1992

On the computation of likelihood ratio and score test based confidence intervals in generalized linear models.

Numerical procedures for calculating likelihood ratio test and score test based confidence intervals in generalized linear models are considered. Newton's method appears to have better convergence properties than the secant method in the likelihood ratio test case. However, the secant method may be easier to program for models with link functions that are not natural. Similarly, the secant method is easier to implement for the computation of score test based intervals. The practical implementation of the procedures in GLIM is illustrated.

Confidence Intervals↗