General Linear Model Approach Research Articles

Robust Design via Generalized Linear Models

A single data transformation may fail to satisfy all the required properties necessary for an analysis. With generalized linear models (GLMs), the identification of the mean-variance relationship and the choice of the scale on which the effects are to be measured can be done separately, overcoming the shortcomings of the data-transformation approach. GLMs also provide an extension of the response surface approach. In this paper, we set out the current status of the GLM approach to the analysis of data from quality-improvement experiments and discuss its merits.

Analysis of rainfall variability using generalized linear models: A case study from the west of Ireland

In the early 1990s a cluster of extreme flood events occurred in the south Galway region of western Ireland, and this led to speculation of changing rainfall patterns in the area. In this paper we illustrate the use of generalized linear models (GLMs) to test for such changes and quantify their structure. GLMs, long established in the statistical literature, provide a flexible and rigorous formal framework within which to distinguish between possible climate change scenarios and are able to deal with high levels of variability, such as those typically associated with daily rainfall sequences. The study indicates that the GLM approach provides a powerful tool for interpreting historical rainfall records.

Sources of intermittent demand for aircraft spare parts within airline operations

Owing to the sporadic nature of demand for aircraft maintenance repair parts, airline operators perceive difficulties in parts demand forecasting. In this paper we investigate the sources of demand lumpiness, as a function of flying hours, that may affect the parts demand rate. Experimental results of demand lumpiness, measured by the square coefficient of variation (CV 2) and the average inter-demand interval (ADI), are examined and clarified through statistical analysis. The general linear model approach is used to explain the variation attributable to the various experimental factors and their interactions. Actual historical data for hard-time and condition-monitoring components from an airlines operator are used. This study shows that aircraft utilization rate can be a major source of lumpiness since it increases and decreases the square coefficient of variation and the average inter-demand interval respectively for the observed demand. This assumes a strictly linear relationship between demand and flying hours/landings.

Insulin resistance and five-year progression of carotid intimal-medial wall thickness:

0026 Insulin resistance (IR) is thought to be an important risk factor for atherosclerosis. It is unclear, however, whether the effect is independent of other cardiovascular (CV) risk factors that cluster with IR, e.g., obesity, hypertension (HTN), and hyperlipidemia. IRAS is a multi-ethnic epidemiologic cohort study investigating the association between IR and CV disease. IR was measured by the frequently sampled intravenous glucose tolerance test with minimal model analysis in 773 non-diabetic persons aged 60 years (range 44 - 75) who participated in the baseline IRAS examination (1992-4). Intimal-medial thickness (IMT) of the carotid arteries was measured by B-mode ultrasonography as an index of atherosclerosis at baseline and at the 5-year follow-up exam (1998-9). Both scans were read at the follow-up time point to eliminate possible reader drift. We modeled change in IMT on IR, adjusting for baseline IMT using a general linear models approach. The models adjusted progressively for demographic variables and CV risk factors. Overall, common carotid (CCA) IMT increased 30 μm (s.e. = 8 μm). Average IR at baseline was 2.2 units (range 0 - 14.2). Adjusting for age, sex, ethnicity, clinic and baseline measurement, CCA IMT increased 20 μm (p=0.007) for a 2 unit increase in IR (change from 25th to 75th percentile). Further adjustment for baseline HDL, LDL, smoking, HTN and glycemia attenuated the effect (17 μm, p=0.05). Adjustment for BMI and waist-hip ratio explained some of the effect (13 μm, p=0.13). No significant association was observed between IR and progression in the internal carotid artery. Analyses incorporating hierarchical measurement error models for IMT were performed to confirm these results. As expected in these analyses, the IR effect was somewhat attenuated, but not eliminated. In summary, IR is associated with progression of carotid atherosclerosis, but this effect may be mediated through the associated cluster of CV risk factors.

Modelling a non-normal response for quality improvement

Efforts to improve quality require that the factors affecting it be identified. This allows either removal of root-causes for low quality or finding optimal settings for the investigated product or process. When the common assumptions of the normal scenario are not met, two alternative approaches are commonly pursued: normalization of data and the use of generalized linear models (GLM). Recently, a third alternative has been developed, that models a response subject to self-generated random variation and externally generated systematic and random variation. It is assumed that the relationship between the response and the externally generated variation is uniformly convex (or concave). A unique feature of the new model is that both its structure and the parameters' values are determined solely by the data on hand (no theory-based arguments are required). Here, we compare the effectiveness of the new methodology relative to current approaches when applied to response modelling in quality improvement efforts. We do this by using published data sets which have been formerly analysed within the framework of either the normalizing approach or the GLM approach (or both). The relative merits of the new methodology are demonstrated and discussed.

Statistical Training in Psychology: A National Survey and Commentary on Undergraduate Programs

We surveyed a national sample of U.S. undergraduate psychology programs regarding the structure and content of statistical training. Results revealed considerable diversity in approaches and offerings. Contemporary trends in data analysis (e.g., power and effect size analysis, confidence interval estimation, general linear model approaches) as well as measurement issues appear to receive relatively little attention in the core sequence. Respondents tended to view such topics as appropriate for more advanced courses, which they said were infrequently required. We discuss options for addressing issues of course sequencing, content focus, and advanced-level offerings in the major.

Accounting for the correlation between fellow eyes in regression analysis.

Regression techniques that appropriately use all available eyes have infrequently been applied in the ophthalmologic literature, despite advances both in the development of statistical models and in the availability of computer software to fit these models. We considered the general linear model and polychotomous logistic regression approaches of Rosner and the estimating equation approach of Liang and Zeger, applied to both linear and logistic regression. Methods were illustrated with the use of two real data sets: (1) impairment of visual acuity in patients with retinitis pigmentosa and (2) overall visual field impairment in elderly patients evaluated for glaucoma. We discuss the interpretation of coefficients from these models and the advantages of these approaches compared with alternative approaches, such as treating individuals rather than eyes as the unit of analysis, separate regression analyses of right and left eyes, or utilization of ordinary regression techniques without accounting for the correlation between fellow eyes. Specific advantages include enhanced statistical power, more interpretable regression coefficients, greater precision of estimation, and less sensitivity to missing data for some eyes. We concluded that these models should be used more frequently in ophthalmologic research, and we provide guidelines for choosing between alternative models.

Multivariate case-control study of survival following transurethral resection of prostate

Although prevalence of perioperative mortality following transurethral resection of the prostate (TURP) has steadily declined as reported in several review studies, it has been suggested that with extended follow-up after TURP, mortality exceeds that of an age-matched population. The sample selected for this study was drawn from a data base of 2,005 men who entered a urologic health-screening program. The sample included a group of 25 patients who underwent TURP and a group of 50 age-matched control patients with symptoms of prostatism. Patients were followed for six years, a total of 450 observed person-years. Multivariate analyses based on a general linear model approach for the dependent variable of survival were used to assess gains in predictive efficiency due to combinations of TURP versus control, time, and patient variables. F-ratio hypothesis tests of coefficients of multiple determination for the models indicated that TURP did account for a significant amount of the variability of survival but only after five years of follow-up. However, a far larger proportion of the variance in survival was explained by other patient variables of age, preoperative risk, comorbidity factors, and postoperative urinary disease after all effects due to TURP, follow-up years, and operation cohort years were held constant in the survival prediction equation.

Software for advanced ANOVA courses: A survey

In response to a survey of faculty regarding their commercial software preferences for advanced analysis of variance courses, it was found that the most frequently used packages were SAS, SPSSx, and BMDP, all originally mainframe packages. The fourth choice, SYSTAT, was written for microcomputers but is currently also available for other host computers. Difficulty for students was the most frequently cited reason fornot using one of these four packages. The most important criteria for choosing software packages were variety of designs, accuracy, and ease of use. Cost was a factor only for microcomputer licenses. Packages using the general linear model approach were paramount to some, while others would not consider such packages. Instructors decried the lack of the “ideal program,” but the diversity of their desires makes it clear that no program could be ideal for all of them. Many faculty seemed unaware of newer software packages or of the extent to which older packages (particularly Minitab) have been modified; some had their choices constrained by departmental limitations. Better dissemination of information about statistical software is needed, whether it be from software publishers or through the professional literature.

A Nonparametric Test Statistic for the General Linear Model

Puri and Sen (1969Puri and Sen (1985) presented a nonparametric test statistic based on a general linear model approach that is appropriate for testing a wide class of hypotheses. The two forms of this statistic, pure- and mixed-rank, differ according to whether the original predictor values or their ranks are used. Both forms permit the use of standard statistical packages to perform the analyses. The applicability of these statistics in testing a number of hypotheses is highlighted, and an example of their use is given. A simulation study for the multivariate-multiple-regression case is used to examine the distributional behavior of the pure- and mixed-rank statistics and an important competitor, the rank transformation of Conover and Iman (1981). The results suggest that the pure- and mixed-rank statistics are superior with respect to minimizing liberal Type I error rates, whereas the Conover and Iman statistic produces larger power values.

Applied Regression Analysis and Other Multivariable Methods

Applied Regression Analysis and Other Multivariable Methods

Multivariate parabolic bioassay

A general linear model approach to quantitative parabolic bioassays with multivariate responses is proposed. The point and interval estimator of the relative potency and an associated test for validity is presented. The relationships with known univariate methods are illustrated.

Analysis of the Unbalanced Two‐Period Cross‐Over Design with Negligible Residual Effects

The analysis of variance proposed by Grizzle (1965) for the unbalanced two‐period crossover design when residual effects are omitted is shown to be appropriate only when the numbers of subjects in both treatment sequences, A : B and B : A, are equal. Following a general linear model approach, a valid analysis of variance is developed for the general unbalanced case.Explicit general expressions, both in algebraic and matrix form, are presented and a numerical example is given to illustrate the details of the analysis.

A general caxedorical data memddology for evaluating medical diagnostic tests

Measures of sensitivity, predictive accuracy, and agreement are currently used to evaluate the efficiency of diagnostic tests reported on dichotomous scales. This paper presents a unified approach to the evaluation of diagnostic tests in terns of generalized Lnuices of sensitivity, misclassification, predictive accuracy and inaccuracy, classification agreement and prediction agreement for polytomous measurement scales. It Is sufficiently general to accommodate additional complications of study design factors such as multiple testing, known and unknown disease prevalence distributions, and multiple subpopulations defined by the cross-classification of independent factors. Estimation and hypothesis testing are developed within a general linear models approach to the analysis of categorical data from repeated measurement lesigns using weighted least squares computations. This methodology is illustrated within the context of data from a. large cotmiunity-based epidemiologic study of obstructive airways diseas...

EFFECT‐SIZE ESTIMATION: A COMMENTARY ON WOLF AND BASSLER

Wolf and Bassler [10] have presented a general linear model approach to the estimation of a variance‐accounted‐for measure of effect magnitude. This commentary questions the usefulness of such a measure, citing its inconsistency with contrast estimates, problems with its interpretation in nonorthogonal designs, and its susceptibility to extraneous influence unrelated to observed differences among group means. In addition, it questions whether the term “importance” should be applied to such a measure.

Linear Model Analysis of Categorical Data with Incomplete Response Vectors

The general linear model approach to the analysis of categorical data described by Grizzle et al. [1969] is extended to situations where: (1) missing data for certain individuals arise at random as a result of non-response or deleted incorrect response; (2) supplemental samples pertaining to various subsets of variables have been obtained due to cost considerations and/or special interest in these variables. The problems discussed are distinct from those involving 'incomplete contingency tables' containing a priori empty cells. The extension is presented through a series of examples which show how the approach can be used to handle a wide variety of non-standard data configurations. Applications to categorical data mixed models and split plot designs are emphasized.