scholarly journals Instantaneous Geometric Rates via Generalized Linear Models

2017 ◽  
Vol 17 (2) ◽  
pp. 358-371 ◽  
Author(s):  
Andrea Discacciati ◽  
Matteo Bottai
Keyword(s):  
Clinical Trial ◽  
Randomized Clinical Trial ◽  
Linear Model ◽  
Generalized Linear Models ◽  
Generalized Linear Model ◽  
Renal Carcinoma ◽  
Linear Models ◽  
Rate Model ◽  
Model Framework ◽  
Link Functions

The instantaneous geometric rate represents the instantaneous probability of an event of interest per unit of time. In this article, we propose a method to model the effect of covariates on the instantaneous geometric rate with two models: the proportional instantaneous geometric rate model and the proportional instantaneous geometric odds model. We show that these models can be fit within the generalized linear model framework by using two nonstandard link functions that we implement in the user-defined link programs log_igr and logit_igr. We illustrate how to fit these models and how to interpret the results with an example from a randomized clinical trial on survival in patients with metastatic renal carcinoma.

scholarly journals Comparison of Generalized Linear Model and Generalized Linear Mixed Model – An Application to Low Birth Weight Data

2020 ◽  
pp. 31-37
Author(s):  
Michael Fosu Ofori ◽  
Stephen B. Twum ◽  
Jackson A. Y. Osborne
Keyword(s):  
Linear Model ◽  
Generalized Linear Models ◽  
Generalized Linear Model ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Models ◽  
Generalized Linear Mixed Model ◽  
Correlated Data ◽  
Parameter Estimates ◽  
Over Dispersion

Background: Generalized Linear models are mostly fitted to data that are not correlated. However, very often data that are collected from health and epidemiological studies are correlated either as a result of the sampling methods or the randomness associated with the collection of such data. Therefore, fitting generalized linear models to such data that produce only fixed effects could lead to over dispersion in the model estimates. Objectives: The objective of this study is to fit both generalized linear and generalized linear mixed models to a correlated data and compare the results of the two models. Methods: Logistic regression is employed in fitting the generalized linear model since the dependent variable in the study is bivariate whilst the GLIMMIX model in SAS is used to fit the generalized linear mixed model. Results: The generalized linear model produces over dispersion with higher errors among the parameter estimates than the generalized linear mixed model. Conclusion: In dealing with a more correlated data, generalized linear mixed model, which can handle both fixed and random effects, is preferable to generalized linear model.

Posterior contraction in sparse generalized linear models

Biometrika ◽  
2020 ◽  
Author(s):  
Seonghyun Jeong ◽  
Subhashis Ghosal
Keyword(s):  
Generalized Linear Models ◽  
Bayesian Methods ◽  
Generalized Linear Model ◽  
Linear Models ◽  
Continuous Distribution ◽  
Fractional Power ◽  
Regression Coefficients ◽  
Link Function ◽  
Convergence Properties ◽  
Set Up

Summary We study posterior contraction rates in sparse high-dimensional generalized linear models using priors incorporating sparsity. A mixture of a point mass at zero and a continuous distribution is used as the prior distribution on regression coefficients. In addition to the usual posterior, the fractional posterior, which is obtained by applying Bayes theorem with a fractional power of the likelihood, is also considered. The latter allows uniformity in posterior contraction over a larger subset of the parameter space. In our set-up, the link function of the generalized linear model need not be canonical. We show that Bayesian methods achieve convergence properties analogous to lasso-type procedures. Our results can be used to derive posterior contraction rates in many generalized linear models including logistic, Poisson regression and others.

An analysis of error structure in modeling the stock–recruitment data of gadoid stocks using generalized linear models

2004 ◽  
Vol 61 (1) ◽  
pp. 134-146 ◽  
Author(s):  
Yan Jiao ◽  
David Schneider ◽  
Yong Chen ◽  
Joe Wroblewski
Keyword(s):  
Linear Model ◽  
Generalized Linear Model ◽  
Linear Models ◽  
Model Error ◽  
Future Research ◽  
Error Structure ◽  
Gamma Distributions ◽  
Error Distributions ◽  
Acceptable Model ◽  
Stock Recruitment

When modeling the stock–recruitment (S–R) relationship, the Cushing, Ricker, and other S–R models are fitted to the observed S–R data by estimating parameters with assumptions made concerning the model error structure. Using a generalized linear model approach, we explored and identified the appropriate model error structure in modeling S–R data for gadoid stocks. The S–R parameter estimation was found to be influenced by the choice of error distributions assumed in the analysis. In modeling S–R data for gadoid stocks, the Beverton–Holt model was found to be more sensitive to the assumption of model error distribution than the Cushing and Ricker models. The lognormal and gamma distributions had higher probability of being acceptable model error distributions. Cluster analyses and summary statistics of error distributions in S–R modeling did not show consistent patterns in the identification of an acceptable model error structure among species, geographic distributions, and sample sizes. A better understanding of the factors and mechanisms resulting in differences in the choice of appropriate model error distributions for different populations is needed in future research. We recommend that the generalized linear model be used to identify acceptable model error structures in quantifying S–R relationships.

A simulation study of impacts of error structure on modeling stock–recruitment data using generalized linear models

2004 ◽  
Vol 61 (1) ◽  
pp. 122-133 ◽  
Author(s):  
Yan Jiao ◽  
Yong Chen ◽  
David Schneider ◽  
Joe Wroblewski
Keyword(s):  
Linear Model ◽  
Generalized Linear Model ◽  
Linear Models ◽  
Least Squares Method ◽  
Estimation Of Parameters ◽  
Estimation Errors ◽  
Error Structure ◽  
Stock Recruitment ◽  
Data Points ◽  
The Impact

Stock–recruitment (S–R) models are commonly fitted to S–R data with a least-squares method. Errors in modeling are usually assumed to be normal or lognormal, regardless of whether such an assumption is realistic. A Monte Carlo simulation approach was used to evaluate the impact of the assumption of error structure on S–R modeling. The generalized linear model, which can readily deal with different error structures, was used in estimating parameters. This study suggests that the quality of S–R parameter estimation, measured by estimation errors, can be influenced by the realism of error structure assumed in an estimation, the number of S–R data points, and the number of outliers in modeling. A small number of S–R data points and the presence of outliers in S–R data could increase the difficulty in identifying an appropriate error structure in modeling, which might lead to large biases in the S–R param eter estimation. This study shows that generalized linear model methods can help identify an appropriate error distribution in S–R modeling, leading to an improved estimation of parameters even when there are outliers and the number of S–R data points is small. We recommend the generalized linear model be used for quantifying stock–recruitment relationships.

Summary goodness-of-fit statistics for binary generalized linear models with noncanonical link functions

2015 ◽  
Vol 58 (3) ◽  
pp. 674-690 ◽  
Author(s):  
Jana D. Canary ◽  
Leigh Blizzard ◽  
Ronald P. Barry ◽  
David W. Hosmer ◽  
Stephen J. Quinn
Keyword(s):  
Generalized Linear Models ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Fit Statistics ◽  
Link Functions

scholarly journals An Exploration of Link Functions Used in Ordinal Regression

2020 ◽  
Vol 18 (1) ◽  
pp. 2-15
Author(s):  
Thomas J. Smith ◽  
David A. Walker ◽  
Cornelius M. McKenna
Keyword(s):  
Survey Data ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Simulated Data ◽  
Ordinal Regression ◽  
Research Center ◽  
Link Function ◽  
25Th Anniversary ◽  
Link Functions ◽  
The Web

The purpose of this study is to examine issues involved with choice of a link function in generalized linear models with ordinal outcomes, including distributional appropriateness, link specificity, and palindromic invariance are discussed and an exemplar analysis provided using the Pew Research Center 25th anniversary of the Web Omnibus Survey data. Simulated data are used to compare the relative palindromic invariance of four distinct indices of determination/discrimination, including a newly proposed index by Smith et al. (2017).

Changes in the distribution of Poplar Box (Eucalyptus populnea) on major soil groups: An application of the log-linear model.

1981 ◽  
Vol 3 (1) ◽  
pp. 33 ◽  
Author(s):  
RB Cunningham ◽  
AA Webb ◽  
A Mortlock
Keyword(s):  
Statistical Analysis ◽  
Linear Model ◽  
Generalized Linear Models ◽  
Gradient Analysis ◽  
Linear Models ◽  
Geographic Location ◽  
Significance Tests ◽  
Log Linear ◽  
Eucalyptus Populnea ◽  
Soil Groups

The association of poplar box (Eucalyptus populnea) with five main soil groups is examined. A statistical analysis, using a log- linear model, indicated that the relative frequencies of poplar box sites occumng on major soil groups changed with geographic location. The change in distribution is shown to relate to climate, as indicated by summer and winter moisture indices and the diff- erence between them. This study illustrates the use of log-linear models in ecology; such models, and more generally, Generalized Linear Models, in providing significance tests, have advantages over the non-statistical methods of gradient analysis.

scholarly journals Capturing multiple timescales of adaptation to second-order statistics with generalized linear models: gain scaling and fractional differentiation

2019 ◽  
Author(s):  
Kenneth W. Latimer ◽  
Adrienne L. Fairhall
Keyword(s):  
Generalized Linear Models ◽  
Cortical Neurons ◽  
Generalized Linear Model ◽  
Single Neuron ◽  
Statistical Approach ◽  
Linear Models ◽  
Fractional Differentiation ◽  
Multiple Timescales ◽  
Second Order Statistics ◽  
Gain Adaptation

AbstractSingle neurons can dynamically change the gain of their spiking responses to account for shifts in stimulus variance. Moreover, gain adaptation can occur across multiple timescales. Here, we examine the ability of a simple statistical model of spike trains, the generalized linear model (GLM), to account for these adaptive effects. The GLM describes spiking as a Poisson process whose rate depends on a linear combination of the stimulus and recent spike history. The GLM successfully replicates gain scaling observed in Hodgkin-Huxley simulations of cortical neurons that occurs when the ratio of spike-generating potassium and sodium conductances approaches one. Gain scaling in the GLM depends on the length and shape of the spike history filter. Additionally, the GLM captures adaptation that occurs over multiple timescales as a fractional derivative of the stimulus variance, which has been observed in neurons that include long timescale after hyperpolarization conductances. Fractional differentiation in GLMs requires long spike history that span several seconds. Together, these results demonstrate that the GLM provides a tractable statistical approach for examining single-neuron adaptive computations in response to changes in stimulus variance.

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