Fitting correlated residual error structures in nonlinear mixed-effects models using SAS PROC NLMIXED

Harring, Jeffrey R.; Blozis, Shelley A.

doi:10.3758/s13428-013-0397-z

Cited by 28 publications

(42 citation statements)

References 35 publications

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“…This could possibly lead to some misspecification, especially given that the model-implied covariance similarly requires the researcher to select the appropriate structures of Ψ and Θ, similar to CPMMs. The most general, parsimonious form of the covariance structure is 1/2 1/2  Σ D PD where the variance matrix, D, can have its own structure uncoupled from the correlational (off-diagonal) structure in P (see, Harring & Blozis, 2014). Covariance structures in either CPMMs and GMMs can be seen as restricted versions of this most general structure.…”

Section: Discussionmentioning

confidence: 99%

Covariance pattern mixture models: Eliminating random effects to improve convergence and performance

McNeish

Harring

2019

Behav Res

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Growth mixture models (GMMs) are prevalent for modeling unknown population heterogeneity via distinct latent classes. However, GMMs are riddled with convergence issues, often requiring researchers to atheoretically alter the model with cross-class constraints to obtain convergence. We discuss how within-class random effects in GMMs exacerbate convergence issues even though these random effects rarely help to answer typical research questions. That is, latent classes provide a discretization of continuous random effects, so including additional random effects within latent classes can unnecessarily complicate the model. These random effects are commonly included to properly specify the marginal covariance; however, random effects are inefficient for patterning a covariance matrix, resulting in estimation issues. Such a goal can be achieved more simply covariance pattern models, which we extend to the mixture model context in this paper (covariance pattern mixture models, CPMMs). We provide evidence from theory, simulation, and an empirical example showing that employing CPMMs (even if misspecified) instead of GMMs can circumvent computational difficulties that can plague GMMs without sacrificing the ability to answer the type of questions commonly asked in empirical studies. Results show advantages of CPMMs with respect to improved class enumeration, and less biased class-specific growth trajectories in addition to vastly improved convergence rates. Results also show that constraining covariance parameters across classes to bypass convergence issues with GMMs leads to poor results. An extensive software appendix is included to assist researchers run CPMMs in Mplus.

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Section: Discussionmentioning

confidence: 99%

Covariance pattern mixture models: Eliminating random effects to improve convergence and performance

McNeish

Harring

2019

Behav Res

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“…Again, this is a limitation with SAS PROC NLMIXED that allows random effects but not autocorrelated errors. Recently, Harring and Blozis have shown how autocorrelated errors can be estimated by this procedure, but their approach is limited to complete data across time and not as many within‐subject observations as is obtained in EMA studies. In some cases, dependency is accommodated by using a lagged dependent variable as a predictor.…”

Section: Discussionmentioning

confidence: 99%

Latent trait shared‐parameter mixed models for missing ecological momentary assessment data

Cursio

Mermelstein

Hedeker

2018

Statistics in Medicine

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Latent trait shared-parameter mixed models for ecological momentary assessment (EMA) data containing missing values are developed in which data are collected in an intermittent manner. In such studies, data are often missing due to unanswered prompts. Using item response theory models, a latent trait is used to represent the missing prompts and modeled jointly with a mixed model for bivariate longitudinal outcomes. Both one-and two-parameter latent trait shared-parameter mixed models are presented. These new models offer a unique way to analyze missing EMA data with many response patterns. Here, the proposed models represent missingness via a latent trait that corresponds to the students' "ability" to respond to the prompting device. Data containing more than 10 300 observations from an EMA study involving high school students' positive and negative affects are presented. The latent trait representing missingness was a significant predictor of both positive affect and negative affect outcomes. The models are compared to a missing at random mixed model. A simulation study indicates that the proposed models can provide lower bias and increased efficiency compared to the standard missing at random approach commonly used with intermittent missing longitudinal data. KEYWORDS ecological momentary assessment, intermittent missing data, latent trait, longitudinal data, shared-parameter model 660

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“…Data that are collected over time such as this data often have serial correlation in the random error term (Sen and Srivastava 1990). To account for this correlation, an AR (2) autocorrelation error structure was incorporated into the likelihood function using the fitting technique described by Harring and Blozis (2014). The AR (2) model assumes that e ij = ϕ 1 × e ij-1 + ϕ 2 × e ij-2 + a ij where a ij are independently normally distributed errors with a mean of 0 (Seber and Wild 1989).…”

Section: Discussionmentioning

confidence: 99%

“…The likelihood function for an AR (2) process from Seber and Wild (1989, pp. 286-288) was programed in place of the AR (1) structure presented in Harring and Blozis (2014). The variance of a ij (see AR (2) model definition above) is often assumed to be constant across all observations but a preliminary analysis showed that it varies considerably by tree.…”

Section: Discussionmentioning

confidence: 99%

The effect of leader damage on lodgepole pine site tree height growth

NighGord

2017

The Forestry Chronicle

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Site index is an important parameter in forest management. Selecting good site trees is critical for both developing and applying models to estimate site index. Along with other characteristics, site trees must be free of damage so that the growth of the tree reflects the potential productivity of the site. Detecting and avoiding leader damage in site trees is very difficult because radial stem growth eventually hides the damage, even in young trees. This project quantifies the loss in height growth due to hidden leader damage. Thirty-seven lodgepole pine (Pinus contorta var. latifolia) site trees were destructively sampled. Annual height growth was measured and incidents of leader damage noted. Height growth was modelled in a mixed-effects framework and allowed for growth reductions due to leader damage. Height growth was reduced on average by 35% in the year the damage occurred and by 15% in the year after the damage event. Height growth returned to normal in subsequent years. The effect of leader damage on the estimated site index depends on when and how many damage events occur, and when the site index estimate is made. For a tree with a site index of 20 m at base age 50 years at breast height that has leader damage at age 8, a reduction in the estimated site index of 0.59 m and 0.31 m can be expected when site index is estimated at ages 10 and 25, respectively.Keywords: lodgepole pine; leader damage; height growth; site index; stem analysis RÉSUMÉ L'indice de qualité de station est un paramètre important en aménagement forestier. Il importe donc de choisir des arbres adaptés au site (site trees) pour élaborer des modèles d' estimation de l'indice de qualité de station et pour les utiliser. Comme pour les autres variables, les arbres adaptés doivent être exempts de défaut afin que leur croissance reflète bien toute la productivité de la station. Il est très difficile de déceler et d' éviter les dommages à la flèche terminale chez les arbres adaptés parce que la croissance radiale finit par masquer ce dommage, même sur de jeunes arbres. Ce projet avait pour but de quantifier les pertes de croissance en hauteur attribuables aux dommages cachés à la flèche terminale. Trente-sept pins tordus (Pinus contorta var. latifolia) adaptés à la station ont fait l' objet de tests destructifs. On en a mesuré la croissance annuelle en hauteur en plus de noter la présence de dommage à la flèche terminale. On a ensuite utilisé un modèle mixte pour modéliser la croissance en hauteur en tenant compte de la réduction de croissance résultant du dommage relevé sur la flèche terminale. En moyenne, la croissance en hauteur a été réduite de 35 % l'année du dommage et de 15 % l'année suivante. La croissance en hauteur est revenue à la normale dans les années qui suivirent. L' effet du dommage à la flèche terminale sur l' estimation de l'indice de qualité de station dépend du moment où il se produit et du nombre de sites affectés ainsi que du moment où l' on estime l'indice de qualité de station. Pour un arbre dont l'indice de ...

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Fitting correlated residual error structures in nonlinear mixed-effects models using SAS PROC NLMIXED

Cited by 28 publications

References 35 publications

Covariance pattern mixture models: Eliminating random effects to improve convergence and performance

Covariance pattern mixture models: Eliminating random effects to improve convergence and performance

Latent trait shared‐parameter mixed models for missing ecological momentary assessment data

The effect of leader damage on lodgepole pine site tree height growth

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