Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Linear Models”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 recordsLinked to original sources
PubMed1983

The analysis of dependence in cross-classifications having ordered categories, using log-linear models for frequencies and log-linear models for odds.

To analyse the dependence of a qualitative (dichotomous or polytomous) response variable upon one or more qualitative explanatory variables, log-linear models for frequencies are compared with log-linear models for odds, when the categories of the response variable are ordered and the categories of each explanatory variable may be either ordered or unordered. The log-linear models for odds express the odds (or log odds) pertaining to adjacent response categories in terms of appropriate multiplicative (or additive) factors. These models include the 'null log-odds model', the 'uniform log-odds model', the 'parallel log-odds model', and other log-linear models for the odds. With these models, the dependence of the response variable (with ordered categories) can be analyzed in a manner analogous to the usual multiple regression analysis and related analysis of variance and analysis of covariance. Application of log-linear models for the odds sheds light on earlier applications of log-linear models for the frequencies in contingency tables with ordered categories.

Biometry↗
PubMed1993

[From multiple regression analysis to logistic model, proportional hazard model and log linear model. Its concept and application].

Recently logistic model, proportional hazard model and log linear model have been used frequently in the medical literatures. Here, each model is reviewed briefly from basics to its application, pointing out pitfalls in its application, some of which are common to any regression analysis. The logistic model is especially useful for the analysis of retrospective data where odds ratio is utilized to evaluate the outcome probability. On the other hand, proportional hazard model is useful when we analyze censored data, utilizing hazard function. Log linear model has been used where contingency table has more than three independent variables, the situation where its applicability in clinical medicine is wide. Familiarity with these statistical methods would enable us to evaluate data more effectively and efficiently and ultimately to read literature more easily.

Models, Statistical↗
PubMed1998

A large class of models derived from generalized linear models.

Generalized linear models may be extended in several ways. This paper describes five such extensions: (i) generalized additive models; (ii) the use of quasi-likelihood; (iii) joint modelling of mean and dispersion; (iv) introduction of extra random components to give hierarchical generalized linear models; (v) modelling of correlated responses within subjects in longitudinal models. These extensions are largely independent, and so can be combined in many ways to produce a large class of models. Finally, a further extension to dynamic forms of the models is sketched.

Linear Models↗
PubMed2004

Comparison between a Weibull proportional hazards model and a linear model for predicting the genetic merit of US Jersey sires for daughter longevity.

Predicted transmitting abilities (PTA) of US Jersey sires for daughter longevity were calculated using a Weibull proportional hazards sire model and compared with predictions from a conventional linear animal model. Culling data from 268,008 Jersey cows with first calving from 1981 to 2000 were used. The proportional hazards model included time-dependent effects of herd-year-season contemporary group and parity by stage of lactation interaction, as well as time-independent effects of sire and age at first calving. Sire variances and parameters of the Weibull distribution were estimated, providing heritability estimates of 4.7% on the log scale and 18.0% on the original scale. The PTA of each sire was expressed as the expected risk of culling relative to daughters of an average sire. Risk ratios (RR) ranged from 0.7 to 1.3, indicating that the risk of culling for daughters of the best sires was 30% lower than for daughters of average sires and nearly 50% lower than than for daughters of the poorest sires. Sire PTA from the proportional hazards model were compared with PTA from a linear model similar to that used for routine national genetic evaluation of length of productive life (PL) using cross-validation in independent samples of herds. Models were compared using logistic regression of daughters' stayability to second, third, fourth, or fifth lactation on their sires' PTA values, with alternative approaches for weighting the contribution of each sire. Models were also compared using logistic regression of daughters' stayability to 36, 48, 60, 72, and 84 mo of life. The proportional hazards model generally yielded more accurate predictions according to these criteria, but differences in predictive ability between methods were smaller when using a Kullback-Leibler distance than with other approaches. Results of this study suggest that survival analysis methodology may provide more accurate predictions of genetic merit for longevity than conventional linear models.

Animals↗
PubMed2004

Short-term prediction of Betula airborne pollen concentration in Vigo (NW Spain) using logistic additive models and partially linear models.

Betula pollen is a common cause of pollinosis in localities in NW Spain and between 13% and 60% of individuals who are immunosensitive to pollen grains respond positively to its allergens. It is important in the case of all such people to be able to predict pollen concentrations in advance. We therefore undertook an aerobiological study in the city of Vigo (Pontevedra, Spain) from 1995 to 2001, using a Hirst active-impact pollen trap (VPPS 2000) situated in the city centre. Vigo presents a temperate maritime climate with a mean annual temperature of 14.9 degrees C and 1,412 mm annual total precipitation. This paper analyses two ways of quantifying the prediction of pollen concentration: first by means of a generalized additive regression model with the object of predicting whether the series of interest exceeds a certain threshold; second using a partially linear model to obtain specific prediction values for pollen grains. Both models use a self-explicative part and another formed by exogenous meteorological factors. The models were tested with data from 2001 (year in which the total precipitation registered was almost twice the climatological average overall during the flowering period), which were not used in formulating the models. A highly satisfactory classification and good forecasting results were achieved with the first and second approaches respectively. The estimated line taking into account temperature and a calm S-SW wind, corresponds to the real line recorded during 2001, which gives us an idea of the proposed model's validity.

Allergens↗
PubMed1999

Tutorial in biostatistics. An introduction to hierarchical linear modelling.

Hierarchical linear models are useful for understanding relationships in hierarchical data structures, such as patients within hospitals or physicians within hospitals. In this tutorial we provide an introduction to the technique in general terms, and then specify model notation and assumptions in detail. We describe estimation techniques and hypothesis testing procedures for the three types of parameters involved in hierarchical linear models: fixed effects, covariance components, and random effects. We illustrate the application using an example from the Type II Diabetes Patient Outcomes Research Team (PORT) study and use two popular PC-based statistical computing packages, HLM/2L and SAS Proc Mixed, to perform two-level hierarchical analysis. We compare output from the two packages applied to our example data as well as to simulated data. We elaborate on model interpretation and provide guidelines for model checking.

Adult↗
PubMedDate not supplied

[Introduction of the general linear models].

General linear models can be considered the paradigm of all models used in clinical epidemiology. In these models, the independent variables combine in linear fashion to predict the values of the variable response. Since no model predicts the variable response perfectly, an error term is incorporated into the model to acknowledge what remains to be explained after getting a fit to the data. When this error term is normally distributed with constant variance, the linear models are reasonably appropriate to describe the input/output relationship of interest.

Linear Models↗
PubMed2002

Application of conditional moment tests to model checking for generalized linear models.

Generalized linear models (GLMs) are increasingly being used in daily data analysis. However, model checking for GLMs with correlated discrete response data remains difficult. In this paper, through a case study on marginal logistic regression using a real data set, we illustrate the flexibility and effectiveness of using conditional moment tests (CMTs), along with other graphical methods, to do model checking for generalized estimation equation (GEE) analyses. Although CMTs provide an array of powerful diagnostic tests for model checking, they were originally proposed in the econometrics literature and, to our knowledge, have never been applied to GEE analyses. CMTs cover many existing tests, including the (generalized) score test for an omitted covariate, as special cases. In summary, we believe that CMTs provide a class of useful model checking tools.

Journal Article↗
PubMed1999

Modeling risk using generalized linear models.

Traditionally, linear regression has been the technique of choice for predicting medical risk. This paper presents a new approach to modeling the second part of two-part models utilizing extensions of the generalized linear model. The primary method of estimation for this model is maximum likelihood. This method as well as the generalizations quasi-likelihood and extended quasi-likelihood are discussed. An example using medical expense data from Washington State employees is used to illustrate the methods. The model includes demographic variables as well as an Ambulatory. Care Group variable to account for prior health status.

Adolescent↗
PubMedDate not supplied

Meta-analysis by random effect modelling in generalized linear models.

The meta-analysis of multi-centre trials can be based on either fixed or random effect models. This paper argues for the general use of random effect models, and illustrates the value of non-parametric maximum likelihood (NPML) analysis of such trials. The same general approach unifies administrative 'league table' analyses in epidemiological and other studies. Several examples of the NPML analysis are given, including a 70-centre trial.

Adrenergic beta-Antagonists↗
PubMedDate not supplied

A review of some extensions to generalized linear models.

Although generalized linear models are reasonably well known, they are not as widely used in medical statistics as might be appropriate, with the exception of logistic, log-linear, and some survival models. At the same time, the generalized linear modelling methodology is decidedly outdated in that more powerful methods, involving wider classes of distributions, non-linear regression, censoring and dependence among responses, are required. Limitations of the generalized linear modelling approach include the need for the iterated weighted least squares (IWLS) procedure for estimation and deviances for inferences; these restrict the class of models that can be used and do not allow direct comparisons among models from different distributions. Powerful non-linear optimization routines are now available and comparisons can more fruitfully be made using the complete likelihood function. The link function is an artefact, necessary for IWLS to function with linear models, but that disappears once the class is extended to truly non-linear models. Restricting comparisons of responses under different treatments to differences in means can be extremely misleading if the shape of the distribution is changing. This may involve changes in dispersion, or of other shape-related parameters such as the skewness in a stable distribution, with the treatments or covariates. Any exact likelihood function, defined as the probability of the observed data, takes into account the fact that all observable data are interval censored, thus directly encompassing the various types of censoring possible with duration-type data. In most situations this can now be as easily used as the traditional approximate likelihood based on densities. Finally, methods are required for incorporating dependencies among responses in models including conditioning on previous history and on random effects. One important procedure for constructing such likelihoods is based on Kalman filtering.

Animals↗
PubMed2002

Strip-plot designs, mixed models, and comparisons between linear and non-linear models for microtitre plate bioassays.

By paying careful attention to the experimental units and, randomizing where it is reasonable, we are able to devise designs for cell culture bioassay which are statistically legitimate and practical in the laboratory. These designs, strip-plot layouts, can accommodate linear or non-linear models, fixed or mixed models, and can provide good protection from location effects. Non-linear mixed models using these designs can be extended to address serial dilution error. A statistically based approach which includes randomization and proper design is a powerful tool for identifying subtle effects of factors within and outside bioassays; this attention to statistical detail is a necessary first step towards continuous improvement of biological assays.

Biological Assay↗
PubMed2000

Prediction of pesticide concentrations in the atmosphere using an atmospheric diffusion model (linear source plume model).

The foundational model to predict concentration of pesticides in the atmosphere outside of the sprayed area was developed using the results of measured concentration in the atmosphere, in reference to the atmospheric diffusion model utilized for the air pollution prediction model. The atmospheric diffusion model assumes that the applied area was a topographically flat farmland, that wind direction and wind speeds were constant, and the pesticide was constantly discharged from the emission line sources. Therefore the linear source plume model (LSPLM) was developed. The concentration in the atmosphere was predicted by assigning the property of the pesticides and various conditions of measurements of the model, and compared with the measured them, then the adaptability of the model was examined. As a result, the correlation between the measured value and the predicted value in paddy and forested areas was significant (P < 0.01) although deviations in the order of tens were observed, the measured value and the predicted value were generally in agreement.

Agriculture↗
PubMed1994

Time series models based on generalized linear models: some further results.

This paper considers the problem of extending the classical moving average models to time series with conditional distributions given by generalized linear models. These models have the advantage of easy construction and estimation. Statistical modelling techniques are also proposed. Some simulation results and an illustrative example are reported to illustrate the methodology. The models will have potential applications in longitudinal data analysis.

Biometry↗
PubMed2006

Factors governing the three-dimensional hydrogen-bond network structure of poly(m-phenylene isophthalamide) and a series of its model compounds (4): similarity in local conformation and packing structure between a complicated three-arm model compound and the linear model compounds.

Crystal structure of a three-arm model compound of poly(m-phenylene isophthalamide) (PMIA), N,N',N' '-triphenyl trimesamide Phi(CONHPhi)(3), has been analyzed by the X-ray diffraction method. The torsional angles around the bonds connecting the amide group and the central benzene ring are 24-34 degrees , almost the same as those observed for many kinds of aromatic amide compounds, reflecting mainly the intramolecular energetic balance between the amide and benzene groups. On the other hand, the torsional angles around the bonds connecting the amide group and the outer benzene ring were found to distribute over a wide range of 2-51 degrees due to the additional effect of intermolecular interactions. This is the first example to show experimentally clearly the role of intra- and intermolecular interactions in the control of torsional angle around the benzene-amide linkage. The hydrogen bonds are formed between the amide groups of the neighboring molecules, resulting in the construction of three-dimensional network structure. The local packing structure of the three-arm compound was found to be essentially the same as those observed for PMIA and the linear model compounds, indicating a characteristic structural feature of the meta-linkage-type aromatic amide compounds. The energy calculation was made using the software Polymorph Predictor to extract the energetically most stable crystal structure, which was compared successfully with the X-ray analyzed structure.

Journal Article↗
PubMed1976

A computer program suitable for fitting linear models when the dependent variable is dichotomous, polichotomous or censored survival and non-linear models when the dependent variable is quantitative.

Given a set of measurements of s explanatory variables corresponding to each experimental unit, a computer program, whose methodological background can be found in [2] has been written in FORTRAN IV language in order to perform regression analyses when the dependent variable is: (i) dichotomous; (ii) polichotomous; (iii) censored survival. In the two former the Cox's [6] linear logistic models are used while in the third one it has been resorted to the models suggested by Feigl and Zelen [8]. The statistical estimation procedure is maximum likelihood and among the different algorithms developed to reach this goal, the one published by Van der Voort and Dorpema [3], has been utilized. Furthermore, when the dependent variable is quantitative, the program is suitable to fit any function non-linear in the parameters; the pertinent function and its first and second derivatives must be provided by the user. In the present version, implemented on a Univac 1106 machine, the program fits directly the Gompertz function.

Computers↗
PubMed2005

Design and analysis of two-color microarray experiments using linear models.

OBJECTIVES: A variety of linear models have recently been proposed for the design and analysis of microarray experiments. This article gives an introduction to the most common models and describes their respective characteristics. METHODS: We focus on the application of linear models to logarithmized and normalized microarray data from two-color arrays. Linear models can be applied at different stages of evaluating microarray experiments, such as experimental design, background correction, normalization and hypothesis testing. Both one-stage and two-stage linear models including technical and possibly biological replicates are described. Issues related to selecting robust and efficient microarray designs are also discussed. RESULTS: Linear models provide flexible and powerful tools, which are easily implemented and interpreted. The methods are illustrated with an experiment performed in our laboratory, which demonstrates the value of using linear models for the evaluation of current microarray experiments. CONCLUSIONS: Linear models provide a flexible approach to properly account for variability, both across and within genes. This allows the experimenter to adequately model the sources of variability, which are assumed to be of major influence on the final measurements. In addition, design considerations essential for any well-planned microarray experiments are best incorporated using linear models. Results from such experimental design investigations show that the widely used common reference design is often substantially less efficient than alternative designs and its use is therefore not recommended.

Algorithms↗
PubMed1992

Estimation of restriction maps with known site order using a generalized linear model.

A generalized linear model with Gamma errors is used to estimate the coordinates of a restriction map when the site order is known. This can be conveniently programmed in a wide range of statistical packages (e.g. Genstat 5, Minitab, SAS), and gives maximum likelihood estimates with their associated optimal properties. Regression diagnostics allow the checking of assumptions and help to identify mis-specified, influential or discordant fragment lengths. A specific diagnostic for identifying fragment lengths causing reversal of restriction site order is derived. Exact 'fragment' lengths from DNA sequencing can be conveniently included in an approximate manner by giving them a larger weight than observed restriction fragment lengths. Two examples and the Genstat 5 codes used in their analysis are presented.

Algorithms↗