Linear Models II : Analysis of Variance; PCA of Response Variables

2004 ◽  
pp. 301-318
Keyword(s):  
Analysis Of Variance ◽  
Linear Models ◽  
Response Variables

scholarly journals Estimating Bayes factors from minimal summary statistics in repeated measures analysis of variance designs

2020 ◽  
Vol 17 (1) ◽  
Author(s):  
Thomas Faulkenberry
Keyword(s):  
Analysis Of Variance ◽  
Repeated Measures ◽  
Bayes Factor ◽  
Linear Models ◽  
Repeated Measurements ◽  
Bayes Factors ◽  
Complex Method ◽  
Summary Statistics ◽  
Minimal Set ◽  
Repeated Measures Analysis

In this paper, I develop a formula for estimating Bayes factors directly from minimal summary statistics produced in repeated measures analysis of variance designs. The formula, which requires knowing only the F-statistic, the number of subjects, and the number of repeated measurements per subject, is based on the BIC approximation of the Bayes factor, a common default method for Bayesian computation with linear models. In addition to providing computational examples, I report a simulation study in which I demonstrate that the formula compares favorably to a recently developed, more complex method that accounts for correlation between repeated measurements. The minimal BIC method provides a simple way for researchers to estimate Bayes factors from a minimal set of summary statistics, giving users a powerful index for estimating the evidential value of not only their own data, but also the data reported in published studies.

Recategorisation of body mass index to achieve andrological predictive power: a study in more than 20 000 patients

2020 ◽  
Vol 32 (7) ◽  
pp. 648 ◽  
Author(s):  
Nicolás Ramírez ◽  
Rosa Inés Molina ◽  
Andrea Tissera ◽  
Eugenia Mercedes Luque ◽  
Pedro Javier Torres ◽  
...  
Keyword(s):  
Body Mass Index ◽  
Body Mass ◽  
Analysis Of Variance ◽  
Predictive Power ◽  
Linear Models ◽  
Semen Quality ◽  
Normal Weight ◽  
Morbidly Obese ◽  
Chi Squared ◽  
Underweight Patients

The aim of this study was to recategorise body mass index (BMI) in order to classify patients according to their risk of semen abnormalities. Patients (n=20563) presenting at an andrology laboratory were classified into five groups according to BMI: underweight (BMI <20kg m−2), normal weight (BMI 20–24.9kg m−2), overweight (BMI 25–29.9kg m−2), obese (BMI 30–39.9kg m−2) and morbidly obese (BMI >40kg m−2). Semen quality was evaluated to determine: (1) differences between groups using analysis of variance (ANOVA); (2) the chances of semen abnormalities (using generalised linear models, Chi-squared tests and odds ratios); (3) reference BMI values with andrological predictive power (multivariate conglomerate analyses and multivariate analysis of variance (MANOVA)); and (4) expected values of abnormalities for each new group resulting from BMI recategorisation. Morbidly obese and underweight patients exhibited the highest decrease in semen quality and had higher chances of semen abnormalities. The smallest number of sperm abnormalities was found at a BMI of 27kg m−2. Four reference values were identified, recategorising BMI into four groups according to their risk of semen abnormalities (from lowest to highest risk): Group1,BMI between 20 and 32kg m−2; Group2, BMI <20 and BMI >32–37kg m−2; Group3, BMI >37–42kg m−2; and Group4, BMI >42kg m−2. A BMI <20 or >32kg m−2 is negatively associated with semen quality; these negative associations on semen quality increase from a BMI >37kg m−2 and increase even further for BMI >42kg m−2. The BMI recategorisation in this study has andrological predictive power.

Applying Log-Linear Models in Educational Research

1988 ◽  
Vol 32 (1) ◽  
pp. 3-24 ◽  
Author(s):  
John J. Kennedy
Keyword(s):  
Educational Research ◽  
Analysis Of Variance ◽  
Logit Model ◽  
Contingency Table ◽  
Goodness Of Fit ◽  
Qualitative Data ◽  
Linear Models ◽  
Linear Modelling ◽  
Acceptable Model ◽  
Log Linear

This didactic illustrates the Goodman-Kennedy approach to log-linear modelling within the context of two educational research examples. The first example lends itself to a symmetrical analysis. To qualitative data presented within a 2 × 2 × 2 contingency table, general log-linear models are specified and assessed for goodness of fit. Subsequently an acceptable model is identified and interpreted. In a second example, an asymmetrical logit-model analysis is performed on data in a 2 × 2 × 5 table. It is shown that a subset of general models can be fitted to observed data and that resultant component chi-squares can be used to assess logit response in a manner that is analogous to the analysis of variance.

Unusually Small F-Statistic in Analysis of Variance and Regression Analysis

2016 ◽  
Vol 3 (3) ◽  
pp. 45-59
Author(s):  
Ceyhun Ozgur
Keyword(s):  
Regression Analysis ◽  
Lower Limit ◽  
Analysis Of Variance ◽  
Control Chart ◽  
Linear Models ◽  
Statistical Significance ◽  
P Value ◽  
Mean Square ◽  
Process Change ◽  
The Mean

All textbooks and articles dealing with classical tests in the context of linear models stress the implications of a significantly large F-ratio since it indicates that the mean square for whatever effect is being evaluated contains significantly more than just error variation. In general, though, with one minor exception, all texts and articles, to the authors' knowledge, ignore the implications of an F-ratio that is significantly smaller than one would expect due to chance alone. Why this is so difficult to explain since such an occurrence is similar to a range value falling below the lower limit on a control chart for variation or a p-value falling below the lower limit on a control chart for proportion defective. In both of those cases the small value represents an unusual and significant occurrence and, if valid, a process change that indicates an improvement. Therefore, it behooves the quality manager to determine what that change is in order to have it continue. In the case of a significantly small F-ratio some problem may be indicated that requires the designer of the experiment to identify it, and to take “corrective action.” While graphical procedures are available for helping to identify some of the possible problems that are discussed they are somewhat subjective when deciding if one is looking at an actual effect; e.g., interaction, or whether the result is merely due to random variation. A significantly small F-ratio can be used to support conclusions based on the graphical procedures by providing a level of statistical significance as well as serving as a warning flag or warning that problems may exist in the design and/or analysis.

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