Influence assessment in censored mixed-effects models using the multivariate Student’s-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si125.gif" display="inline" overflow="scroll"><mml:mi>t</mml:mi></mml:math>distribution

Matos, Larissa A.; Bandyopadhyay, Dipankar; Castro, Luis M.; Lachos, Víctor H.

doi:10.1016/j.jmva.2015.06.014

Cited by 11 publications

(12 citation statements)

References 36 publications

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“…The use of censored regression models like censReg allowed for the accounting of censoring at 0 and 40 min and an unbiased estimation of sex differences. Similar methods have been used to assess risk in drug toxicity studies and human immunodeficiency virus studies (Matos et al, 2015;Berges et al, 2018).…”

Section: Mixed and Fixed Model Analysesmentioning

confidence: 99%

Sex-dependent differences for larkspur (Delphinium barbeyi) toxicosis in yearling Angus cattle1

Green

Keele

Gardner

et al. 2019

Journal of Animal Science

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Larkspur (Delphinium spp.) poisoning is a long-term problem for cattle grazing on rangelands of western North America. Results from preliminary experiments have suggested that differences in larkspur toxicity may exist between heifers and bulls. The objective of this study was to compare the physiological responses of yearling Angus heifers, steers, and bulls with a standardized dose of Delphinium barbeyi and to test the hypothesis that the response is sex dependent. Clinical signs of intoxication, including muscle coordination and function, were measured 24 h after oral dosing with larkspur by walking the cattle at a pace of 5 to 6 km h −1 for up to 40 min on an oval dirt track. Due to the experimental methods used, the variation in susceptibility to larkspur was not quantifiable for walking times of 0 or 40 min or more. Larkspur susceptible animals that were not able to walk (0 min; 36% of the animals) or larkspur resistant animals that walked the entire test period of 40 min (9% of the animals) resulted in censored or truncated data. The statistical methods (censReg and lmec) were used to adjust for data truncation or censoring. The heifers were only able to walk −8.9 ± 3.9 min (65.5% censored on the left) compared with 13.2 ± 3.7 min for bulls and 15.9 ± 2.7 min for steers. When heifers were compared with bulls and steers together, heifers walked 23.4 ± 4.5 min less (P < 0.0001). Serum alkaloid concentrations were measured immediately before walking, and deltaline concentrations averaged 266 ± 28, 131 ± 20, and 219 ± 28 ng mL −1 for all heifers, steers, and bulls, respectively, and serum methyllycaconitine concentrations averaged 660 ± 46, 397 ± 32, and 612 ± 34 ng mL −1 for all heifers, steers, and bulls, respectively. The relative risk of a zero walk time for yearling heifers is 330% that of yearling bulls (P = 0.0008). These results suggest that yearling Angus heifers are more susceptible to larkspur intoxication and, when possible, heifers should be kept from grazing larkspur-infested rangelands as a simple management tool to reduce the risk of fatal poisoning.

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Section: Mixed and Fixed Model Analysesmentioning

confidence: 99%

Sex-dependent differences for larkspur (Delphinium barbeyi) toxicosis in yearling Angus cattle1

Green

Keele

Gardner

et al. 2019

Journal of Animal Science

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“…To assess the influence of minor perturbations on the maximum likelihood estimate

\overset{θ}{true}

for incomplete data problems, Zhu & Lee () proposed the use of the Q ‐displacement function

f_{Q} false(bold-italicω false) = 2 [\overset{Q}{true} ()(, \overset{false^}{bold-italicθ}) - \overset{Q}{true} ()(, {\overset{θ}{true}}_{bold-italicω})]

and the associated influence graph

α false(bold-italicω false) = (\begin{matrix} bold-italicω \\ f_{Q} false(bold-italicω false) \end{matrix}) .

Following the approach of Cook () and Zhu & Lee () (see also Matos et al . ), we use the normal curvature

C_{f_{Q}, boldd}

of α ( ω ) at ω 0 in the direction of some unit vector d to summarise the local behavior of f Q ( ω ). It can be shown that

C_{f_{Q}, d} = - 2 d^{⊤} {\overset{Q}{true}}_{ω_{o}} d and - {\overset{Q}{true}}_{ω_{0}} = {boldΔ}_{{bold-italicω}_{0}}^{⊤} {(}{- \ddot{\overset{Q}{true}} false(\overset{θ}{true} false))}^{- 1} {boldΔ}_{ω_{0}},

where

\ddot{\overset{Q}{true}} false(\overset{θ}{true} false) = \frac{\partial^{2}}{\partial θ \partial {bold-italicθ}^{⊤}} \{...\}

…”

Section: Diagnostic Analysismentioning

confidence: 99%

“…Following the approach of Cook (1986) and Zhu & Lee (2001) (see also Matos et al 2015), we use the normal curvature C f Q ,d of (ω) at ω 0 in the direction of some unit vector d to summarise the local behavior of f Q (ω). It can be shown that…”

Section: Local Influencementioning

confidence: 99%

Influence diagnostics for censored regression models with autoregressive errors

Schumacher

Lachos

Vilca

et al. 2018

Aus NZ J of Statistics

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Summary Observations collected over time are often autocorrelated rather than independent, and sometimes include observations below or above detection limits (i.e. censored values reported as less or more than a level of detection) and/or missing data. Practitioners commonly disregard censored data cases or replace these observations with some function of the limit of detection, which often results in biased estimates. Moreover, parameter estimation can be greatly affected by the presence of influential observations in the data. In this paper we derive local influence diagnostic measures for censored regression models with autoregressive errors of order p (hereafter, AR(p)‐CR models) on the basis of the Q‐function under three useful perturbation schemes. In order to account for censoring in a likelihood‐based estimation procedure for AR(p)‐CR models, we used a stochastic approximation version of the expectation‐maximisation algorithm. The accuracy of the local influence diagnostic measure in detecting influential observations is explored through the analysis of empirical studies. The proposed methods are illustrated using data, from a study of total phosphorus concentration, that contain left‐censored observations. These methods are implemented in the R package ARCensReg.

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“…However, and from a practical standpoint, such an assumption may not be realistic. In fact, some recent works on censored models (see for example, Matos et al 2013Matos et al , 2015Garay et al 2017a, b) have indicated that likelihood-based inference can be seriously affected by the presence of atypical observations and/or misspecification of the parametric distributions for both random effects and errors.…”

Section: Introductionmentioning

confidence: 99%

Heavy-tailed longitudinal regression models for censored data: a robust parametric approach

Matos

Lachos

Lin

et al. 2018

TEST

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Longitudinal HIV-1 RNA viral load measures are often subject to censoring due to upper and lower detection limits depending on the quantification assays. A complication arises when these continuous measures present a heavy-tailed behavior because inference can be seriously affected by the misspecification of their parametric distribution. For such data structures, we propose a robust nonlinear censored regression model based on the scale mixtures of normal distributions. By taking into account the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is considered. A stochastic approximation of the EM algorithm is developed to obtain the maximum likelihood estimates of the model parameters. The main advantage of this new procedure os to allow estimating the parameters of interest and evaluating the log-likelihood function easily and quickly. Furthermore, the standard errors of the fixed effects and predictions of unobservable values of the response can be obtained as a byproduct. The practical utility of the proposed method is exemplified using both simulated and real data.

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Influence assessment in censored mixed-effects models using the multivariate Student’s-tdistribution

Cited by 11 publications

References 36 publications

Sex-dependent differences for larkspur (Delphinium barbeyi) toxicosis in yearling Angus cattle1

Sex-dependent differences for larkspur (Delphinium barbeyi) toxicosis in yearling Angus cattle1

Influence diagnostics for censored regression models with autoregressive errors

Heavy-tailed longitudinal regression models for censored data: a robust parametric approach

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