Monitoring Changes in Covariance Structure

2012 ◽  
pp. 293-354
Keyword(s):  
Covariance Structure

OPTIMAL QUADRATIC UNBIASED ESTIMATION FOR MODELS WITH LINEAR TOEPLITZ COVARIANCE STRUCTURE

Statistics ◽  
2003 ◽  
Vol 37 (1) ◽  
pp. 1-15
Author(s):  
JEAN-MICHEL MARIN ◽  
THIERRY DHORNE
Keyword(s):  
Covariance Structure ◽  
Unbiased Estimation

Power of Modified Brown-Forsythe and Mixed-Model Approaches in Split-Plot Designs

Methodology ◽  
2017 ◽  
Vol 13 (1) ◽  
pp. 9-22 ◽  
Author(s):  
Pablo Livacic-Rojas ◽  
Guillermo Vallejo ◽  
Paula Fernández ◽  
Ellián Tuero-Herrero
Keyword(s):  
Repeated Measures ◽  
Statistical Power ◽  
Mixed Model ◽  
Covariance Structure ◽  
Simulation Method ◽  
Future Research ◽  
Repeated Measures Design ◽  
Fixed And Random Effects ◽  
Split Plot ◽  
High Level

Abstract. Low precision of the inferences of data analyzed with univariate or multivariate models of the Analysis of Variance (ANOVA) in repeated-measures design is associated to the absence of normality distribution of data, nonspherical covariance structures and free variation of the variance and covariance, the lack of knowledge of the error structure underlying the data, and the wrong choice of covariance structure from different selectors. In this study, levels of statistical power presented the Modified Brown Forsythe (MBF) and two procedures with the Mixed-Model Approaches (the Akaike’s Criterion, the Correctly Identified Model [CIM]) are compared. The data were analyzed using Monte Carlo simulation method with the statistical package SAS 9.2, a split-plot design, and considering six manipulated variables. The results show that the procedures exhibit high statistical power levels for within and interactional effects, and moderate and low levels for the between-groups effects under the different conditions analyzed. For the latter, only the Modified Brown Forsythe shows high level of power mainly for groups with 30 cases and Unstructured (UN) and Autoregressive Heterogeneity (ARH) matrices. For this reason, we recommend using this procedure since it exhibits higher levels of power for all effects and does not require a matrix type that underlies the structure of the data. Future research needs to be done in order to compare the power with corrected selectors using single-level and multilevel designs for fixed and random effects.

scholarly journals Evaluation of a novel threonine source for nursery pig diets

2020 ◽  
Vol 4 (4) ◽  
Author(s):  
Dalton Humphrey ◽  
Spenser Becker ◽  
Jason Lee ◽  
Keith Haydon ◽  
Laura Greiner
Keyword(s):  
Repeated Measures ◽  
Fixed Effects ◽  
Average Daily Gain ◽  
Covariance Structure ◽  
Treatment Phase ◽  
Positive Control ◽  
Negative Control ◽  
Feed Ratio ◽  
Experimental Unit ◽  
Nursery Pigs

Abstract Four hundred and eighty (PIC 337 X 1050, PIC Genus, Hendersonville, TN) pigs were used to evaluate a novel threonine source (ThrPro, CJ America Bio, Fort Dodge, IA) for nursery pigs from approximately 7 to 20 kg body weight (BW). After weaning, pigs were sorted by sex and fed a common diet for 1 wk. Upon completion of the first week, pigs were sorted into randomized complete blocks, equalized by weight, within 16 replications. Pigs were allocated to one of three dietary treatments: positive control (POS)—standard ileal digestible threonine-to-lysine ratio (SID; Thr:Lys) 0.60, negative control (NEG)—SID Thr:Lys ≤0.46, and alternative Thr source (TEST)—SID Thr:Lys 0.60. The alternative Thr source included fermentative biomass and was assumed to contain 75% Thr and a digestibility coefficient of 100% based on the manufacturer’s specifications. All other nutrients met or exceeded the NRC recommendations. Growth and intake data were analyzed as repeated measures with a compound symmetry covariance structure using the MIXED procedure in SAS 9.4 (SAS Institute Inc., Cary, NC) with pen as the experimental unit. Treatment, phase, the interaction between treatment and phase, and block were included as fixed effects in the model. Differences in total removals were tested using Fisher’s Exact Test of PROC FREQ. Results were considered significant at P ≤ 0.05 and considered a trend at P > 0.05 and P ≤ 0.10. During the first 14 d, pigs fed TEST had decreased gain-to-feed ratio (G:F; 0.77 vs. 0.80, P = 0.022) compared to POS and increased G:F (0.77 vs. 0.73, P < 0.001) compared to NEG. Over days 14–28, pigs fed TEST had similar G:F (0.71 vs. 0.70, P = 0.112) compared to POS and increased G:F (0.71 vs. 0.63, P < 0.001) compared to NEG. Overall (days 0–28), pigs fed TEST had similar average daily gain (ADG; 0.47 vs. 0.47 kg/d, P = 0.982) and G:F (0.76 vs. 0.74, P = 0.395) compared to POS and increased ADG (0.47 vs. 0.43 kg/d, P < 0.001) and G:F (0.76 vs. 0.67, P < 0.001) compared to NEG. The average daily feed intake was not significantly different across treatments for the entirety of the study. In conclusion, the replacement of crystalline L-Thr with a novel Thr source resulted in similar growth performance in nursery pigs from approximately 7 to 20 kg.

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