Generalized linear models

Multiple Regression A general linear model is one expressed as... 

Data were subjected to analysis of variance and regression analysis using the general linear model procedure of the Statistical Analysis System (40). Means were compared using Waller-Duncan procedure with a K ratio of 100. Polynomial equations were best fitted to the data based on significance level of the terms of the equations and values. 

Univariate and Multivariate General Linear Models Theory and Applications Using SAS Software by Neil H.Timm andTammy A. Mieczkowski... 

Statistical analyses were performed with SPSS 8.0. We used a Wilcoxon signed ranks test to test for seasonality. To test for individuality we used a general linear model (GLM) with either individual or colony as a fixed factor. All tests were... 

The sequence of meal consumption was determined by random assignment of diets to subjects. Statistical analysis was performed by a General Linear Models Procedure (20) using split-plot in time analysis with the following non-orthogonal contrasts ... 

I In the context of the I I General Linear Model I I use the MAXIMUM I ABSOLUTE STUDENTIZEDI RESIDUAL to detect I inconsistency. Keep in I jmind that inconsi.stency I is RELATIVE to the I assumed form of the I model. 

Values followed by asterisk are significantly different from the control at the 0.05 level according to the general linear model procedure. 

McCulloch P, Nelder JA. 1989. Generalized linear models. 2nd ed. New York Chapman HalVCRC. 

Traditionally, the determination of a difference in costs between groups has been made using the Student s r-test or analysis of variance (ANOVA) (univariate analysis) and ordinary least-squares regression (multivariable analysis). The recent proposal of the generalized linear model promises to improve the predictive power of multivariable analyses. 

Blough DK, Madden CW, Hornbrook MC. Modehng risk using generalized linear models. J Health Econ 1999 18 153-71. 

Laframboise T, Harrington D, Weir BA. PLASQ a generalized linear model-based procedure to determine allelic dosage in cancer cells from SNP array data. Biostatistics 2007 8 323-336. 

The analysis of variance (ANOVA) gives information on the significant effects. Data were analyzed using the general linear model (GLM) procedure from the Statistical Analysis System (SAS Institute, Cary, NC). A discussion and explanation of the statistics involved are given by Davies [19]. 

Analysis of variance appropriate for a crossover design on the pharmacokinetic parameters using the general linear models procedures of SAS or an equivalent program should be performed, with examination of period, sequence and treatment effects. The 90% confidence intervals for the estimates of the difference between the test and reference least squares means for the pharmacokinetic parameters (AUCo-t, AUCo-inf, Cmax should be calculated, using the two one-sided t-test procedure). 

Figure 3. Relationship between leaf area (A), epidermal cell density (B), stomatal density (C) and stomatal index (D) versus altitude for Nothofagus solandri leaves growing on the slope of Mt. Ruapehu, New Zealand (collected in 1999). Black diamonds indicate the mean of ten counting fields on each leaf, white squares are the averages of five to eight leaves per elevation, with error bars of 1 S.E.M. Nested mixed-model ANOVA with a general linear model indicates significant differences for all factors (p = 0.000). Averages per elevation were used for regression analysis A. y = -0.0212 + 73.1 R2 = 0.276 p = 0.147. B. y = 1.70 + 3122 R2 = 0.505 p = 0.048. C. y = 0.164 + 360 R2 = 0.709 p = 0.009. D. linear (dashed) y = 0.004 + 9.33 R2 = 0.540 p = 0.038 non-linear (solid) y = 0.00001 2 - 0.0206 + 21.132 R2 = 0.770.

Table 1. Stomatal density (SD), epidermal cell density (ED) and stomatal index (SI) of sun and shade leaves of Nothofagus solandri var. cliffortioides. Sun and shade leaves were collected at three localities (Fig. 2) Horrible Bog (HOR), Kawatiri Junction (KJ) and St. Arnaud (SA). Values are means of five leaves per light level (seven counts per leaf). The complete data set (total) was analyzed with a nested mixed-model ANOVA based on a general linear model, for comparisons within the individual localities a fully nested ANOVA was used.

Table 2. Stomatal density (SD), Epidermal cell density (ED) and stomatal index (SI) of modern Quercus kelloggii leaves, assigned to light regime during growth by degree of undulation, and p-values from a pairwise comparison using a nested mixed-model ANOVA based on a general linear model.

Monda, D.P., Galat, D.L., Finger, S.E. and Kaiser, M S. (1995) Acute toxicity of ammonia (NH3-N) in sewage effluent to Chironomus riparius II. Using a generalized linear model, Archives of Environmental Contamination and Toxicology 28 (3), 385-390. 

Fahrmeir, L., Tutz, G. Multivariate Statistical Modelling based on Generalized Linear Models, Springer, Berlin, Heidelberg, New York, 1994... 

The classic two-way ANOVA does demand a balanced data set. It can therefore be a pain if a piece of data is lost. However, there is a technique called a general linear model that will achieve the same ends as the two-way ANOVA, without the need for perfectly balanced data. Many statistical packages offer the technique. 

Engel, J. and Huele, A. F. (1996). A generalized linear modeling approach to robust design. 

Lee, Y. and Nelder, J. A. (1998). Generalized linear models for analysis of quality-improvement experiments. Canadian Journal of Statistics, 26, 95-105. 

Myers, R. H., Montgomery, D. C., and Vining, G. G. (2002). Generalized Linear Models with Applications in Engineering and the Sciences. John Wiley and Sons, New York. 

Pan, G. and Taam, W. (2002). On generalized linear model method for detecting dispersion effects in unreplicated factorial designs. Journal of Statistical Computation and Simulation, 72, 431-450. 

A promising new use of prior distributions for subset selection is in the formulation of optimality criteria for the construction of designs that allow model discrimination. This technique is discussed in Section 6. The chapter concludes with a discussion, including possible extensions of the techniques to generalized linear models. 

A statistical analysis based on General Linear Model (GLM) was developed to analyse the influence of loading and off-axis angle on damage of composite laminates. The void content in the composite specimens acted as stress raiser resulting in cracks initiation, propagation and failure as tensile loads progressively applied. Analysis of Variance (ANOVA) was performed for void contents to check the statistical differences caused by the experimental errors. 

Solving set of Eq. (7) we ean find value s of eoeffieients. Results are tabulated in Table. Table 1. General linear model coefficients and p-valnes... 

Regression Analysis. The GLM (General Linear Models) procedure of SAS was used to fit the experimental data to Equation 3. This procedure provides estimates of coefficients and intercept GLM also tests hypotheses and indicates the overall quality of the correlation. Output from the GLM procedure is shown in Tables IV, V, and VI numbers, which are listed to 6 decimal places in the original output, have been rounded off to If- places. 

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