Selection of terms in random coefficient regression models

Rocha, Francisco Marcelo Monteiro da; Singer, Júlio M.

doi:10.1080/02664763.2016.1273884

Cited by 10 publications

(13 citation statements)

References 15 publications

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“…We assume that u i and v i are independent. Following Rocha and Singer(2017) we re-express the linear mixed model as a two-stage random coefficients model Laird(2004),…”

Section: Two-stage Random Effects Model: Definitions and Notationsmentioning

confidence: 99%

“…Typically, an additional random effect is included for each regression coefficient which is expected to vary among subjects and it becomes important to assess the randomness of all or a subset of parameters. A linear mixed model can be regarded as a two-stage model (Laird, 2004) where in the first stage it may be viewed as a set of standard regression models with the matrix of covariates and the random effects design matrix "merged" in a unique matrix and the parameter vector which includes both fixed and random parameters or the sum of both (Rocha and Singer, 2017). In the second stage a specification of the mean and the variance of the random effects are assumed.When faced with this representation, we can ask whether the "enlarged" parameters vector is fixed, random or has both fixed and random elements.…”

Section: Introductionmentioning

confidence: 99%

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An F-Type Multiple Testing Approach for Assessing Randomness of Linear Mixed Models

Barnabani¹

2019

ARMS

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In linear mixed models the assessing of the significance of all or a subset of the random effects is often of primary interest. Many techniques have been proposed for this purpose but none of them is completely satisfactory. One of the oldest methods for testing randomness is the F −test but it is often overlooked in modern applications due to poor statistical power and non-applicability in some important situations. In this work a two-step procedure is developed for generalizing an F −test and improving its statistical power. In the first step, by comparing two covariance matrices of a least squares statistic, we obtain a "repeatable" F −type test. In the second step, by changing the projected matrix which defines the least squares statistic we apply the test repeteadly to the same data in order to have a set of correlated statistics analyzed within a multiple testing approach. The resulting test is sufficiently general, easy to compute, with an exact distribution under the null and alternative hypothesis and, perhaps more importantly, with a strong increase of statistical power with respect to the F −test.

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“…We assume that u i and v i are independent. Following Rocha and Singer(2017) we re-express the linear mixed model as a two-stage random coefficients model Laird(2004),…”

Section: Two-stage Random Effects Model: Definitions and Notationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An F-Type Multiple Testing Approach for Assessing Randomness of Linear Mixed Models

Barnabani¹

2019

ARMS

View full text Add to dashboard Cite

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“…Thus, different structures of random factors may be compared in mixed models (Zuur et al 2009). It should be noted, however, that comparisons between mixed models is an active area of research, as there is no current consensus of how to handle random factors (Müller et al 2013, Schielzeth & Nakagawa 2013, Rocha & Singer 2018. Following the previous reasoning, GLMs are nested within GLMMs (GLMs with random factors), GAMs are nested within GLMMs (GAMs with parametric coefficients and random factors), and GAMMs encompass all these types of models (GLMs, GAMs and GLMMs), which means that all these are nested (Zuur et al 2009).…”

Section: Model Selectionmentioning

confidence: 99%

Advocating better habitat use and selection models in bird ecology

Palacio

2018

Rev. Bras. Ornitol.

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In the last decades, habitat use and selection has emerged as a basic aspect of bird ecology, due to its importance in natural history, distribution, response to environmental changes, management and conservation of bird species (Cody 1985, Guisan & Thuiller 2005, Engler et al. 2017). Despite the long tradition of the study of habitat use and selection in birds, however, almost 20 years ago, Jones (2001) had noticed ornithologists usually tended to be inconsistent of what habitat use and selection represent, with major implications on their hypothesis and conclusions about bird ecology (Jones 2001). Currently, some confusion between these terms still persists as a general issue in animal ecology (Lele et al. 2013, Boyce et al. 2016, McGarigal et al. 2016). Here, "habitat" is defined as a distinctive set of physical environmental factors that a species uses for survival and reproduction (Jones 2001, Lele et al. 2013). "Habitat use" refers to the way in which an individual or species uses habitats to meet its life history needs (Jones 2001).

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“…When the data for all subjects are collected at the same time points, we have Z i = Z ∗ so that V = Z ∗ G Z ∗⊤ may be estimated by

\hat{V} = n^{- 1} \sum_{i = 1}^{n} (y_{i} - \overset{true¯}{y}) {(y_{i} - \overset{true¯}{y})}^{⊤} - {\hat{σ}}^{2} I_{m}

where m is the common number of observations per unit,

\overset{boldy}{false} = n^{- 1} \sum_{i = 1}^{n} {boldy}_{i}

and

{\overset{σ}{false}}^{2}

is an estimate of σ 2 . Rochar and Singer () suggest fitting standard linear regression models to the rows of

\overset{boldV}{false}

and using Bonferroni‐corrected reference intervals for the coefficients to decide what random effects should be considered in the model. Based on a simulation study, they show that the procedure is reasonably efficient even for moderate sample sizes, for example, 25 units with five repeated measures each, and for non‐Gaussian random effects or error terms.…”

Section: Some Remedial Measuresmentioning

confidence: 99%

Graphical Tools for Detecting Departures from Linear Mixed Model Assumptions and Some Remedial Measures

Singer

Rocha

Nobre

2016

Int Statistical Rev

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Summary We review some results on the analysis of longitudinal data or, more generally, of repeated measures via linear mixed models starting with some exploratory statistical tools that may be employed to specify a tentative model. We follow with a summary of inferential procedures under a Gaussian set‐up and then discuss different diagnostic methods focusing on residual analysis but also addressing global and local influence. Based on the interpretation of diagnostic plots related to three types of residuals (marginal, conditional and predicted random effects) as well as on other tools, we proceed to identify remedial measures for possible violations of the proposed model assumptions, ranging from fine‐tuning of the model to the use of elliptically symmetric or skew‐elliptical linear mixed models as well as of robust estimation methods. We specify many results available in the literature in a unified notation and highlight those with greater practical appeal. In each case, we discuss the availability of model diagnostics as well as of software and give general guidelines for model selection. We conclude with analyses of three practical examples and suggest further directions for research.

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Selection of terms in random coefficient regression models

Cited by 10 publications

References 15 publications

An F-Type Multiple Testing Approach for Assessing Randomness of Linear Mixed Models

An F-Type Multiple Testing Approach for Assessing Randomness of Linear Mixed Models

Advocating better habitat use and selection models in bird ecology

Graphical Tools for Detecting Departures from Linear Mixed Model Assumptions and Some Remedial Measures

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