scholarly journals Performance bounds for parameter estimates of high-dimensional linear models with correlated errors

2016 ◽  
Vol 10 (1) ◽  
pp. 352-379 ◽  
Author(s):  
Wei-Biao Wu ◽  
Ying Nian Wu
Keyword(s):  
Linear Models ◽  
High Dimensional ◽  
Parameter Estimates ◽  
Performance Bounds ◽  
Correlated Errors

scholarly journals A note on misspecification in general linear models with correlated errors for the analysis of crossover clinical trials

PLoS ONE ◽  
2019 ◽  
Vol 14 (3) ◽  
pp. e0213436 ◽  
Author(s):  
Wei Wang ◽  
Ning Cong ◽  
Tian Chen ◽  
Hui Zhang ◽  
Bo Zhang
Keyword(s):  
Clinical Trials ◽  
Linear Models ◽  
General Linear ◽  
Correlated Errors ◽  
General Linear Models

scholarly journals Omitted Variable Bias in GLMs of Neural Spiking Activity

2018 ◽  
Vol 30 (12) ◽  
pp. 3227-3258 ◽  
Author(s):  
Ian H. Stevenson
Keyword(s):  
Neural Activity ◽  
Single Neuron ◽  
Linear Models ◽  
Theory And Practice ◽  
Parameter Estimates ◽  
Omitted Variables ◽  
History Effects ◽  
Omitted Variable Bias ◽  
Wide Range ◽  
Variable Bias

Generalized linear models (GLMs) have a wide range of applications in systems neuroscience describing the encoding of stimulus and behavioral variables, as well as the dynamics of single neurons. However, in any given experiment, many variables that have an impact on neural activity are not observed or not modeled. Here we demonstrate, in both theory and practice, how these omitted variables can result in biased parameter estimates for the effects that are included. In three case studies, we estimate tuning functions for common experiments in motor cortex, hippocampus, and visual cortex. We find that including traditionally omitted variables changes estimates of the original parameters and that modulation originally attributed to one variable is reduced after new variables are included. In GLMs describing single-neuron dynamics, we then demonstrate how postspike history effects can also be biased by omitted variables. Here we find that omitted variable bias can lead to mistaken conclusions about the stability of single-neuron firing. Omitted variable bias can appear in any model with confounders—where omitted variables modulate neural activity and the effects of the omitted variables covary with the included effects. Understanding how and to what extent omitted variable bias affects parameter estimates is likely to be important for interpreting the parameters and predictions of many neural encoding models.

scholarly journals Drawing inferences for high‐dimensional linear models: A selection‐assisted partial regression and smoothing approach

Biometrics ◽  
2019 ◽  
Vol 75 (2) ◽  
pp. 551-561
Author(s):  
Zhe Fei ◽  
Ji Zhu ◽  
Moulinath Banerjee ◽  
Yi Li
Keyword(s):  
Linear Models ◽  
High Dimensional ◽  
Partial Regression

Variable selection in high-dimensional double generalized linear models

2012 ◽  
Vol 55 (2) ◽  
pp. 327-347 ◽  
Author(s):  
Dengke Xu ◽  
Zhongzhan Zhang ◽  
Liucang Wu
Keyword(s):  
Variable Selection ◽  
Generalized Linear Models ◽  
Linear Models ◽  
High Dimensional

scholarly journals Grouping strategies and thresholding for high dimensional linear models

2013 ◽  
Vol 143 (9) ◽  
pp. 1417-1438 ◽  
Author(s):  
Mathilde Mougeot ◽  
Dominique Picard ◽  
Karine Tribouley
Keyword(s):  
Linear Models ◽  
High Dimensional ◽  
Grouping Strategies

scholarly journals Age and growth rate variation influence the functional relationship between somatic and otolith size

2017 ◽  
Vol 74 (5) ◽  
pp. 680-692 ◽  
Author(s):  
Eloïse C. Ashworth ◽  
Norman G. Hall ◽  
S. Alex Hesp ◽  
Peter G. Coulson ◽  
Ian C. Potter
Keyword(s):  
Growth Rate ◽  
Age And Growth ◽  
Growth Effect ◽  
Parameter Estimates ◽  
Rate Variation ◽  
Fish Length ◽  
Correlated Errors ◽  
Otolith Growth ◽  
Positive Dependence ◽  
Otolith Size

Curves describing the length–otolith size relationships for juveniles and adults of six fish species with widely differing biological characteristics were fitted simultaneously to fish length and otolith size at age, assuming that deviations from those curves are correlated rather than independent. The trajectories of the somatic and otolith growth curves throughout life, which reflect changing ratios of somatic to otolith growth rates, varied markedly among species and resulted in differing trends in the relationships formed between fish and otolith size. Correlations between deviations from predicted values were always positive. Dependence of length on otolith growth rate (i.e., “growth effect”) and “correlated errors in variables” introduce bias into parameter estimates obtained from regressions describing the allometric relationships between fish lengths and otolith sizes. The approach taken in this study to describe somatic and otolith growth accounted for both of these effects and that of age to produce more reliable determinations of the length–otolith size relationships used for back-calculation and assumed when drawing inferences from sclerochronological studies.

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