Mixed Linear Models for Repeated Measures

Among specific genes that may affect economically important traits in sheep, the β-lactoglobulin (LGB) locus has been extensively studied. Polymorphism has been detected in several breeds, but studies of the effect of LGB alleles on milk production traits have given conflicting results. Some found that LGB polymorphism significantly affects milk yield (Bolla et al. 1989; Herget et al. 1995; Fraghì et al. 1996), fat and protein content (Garzon & Martínez 1992; Giaccone et al. 1997; Kukovics et al. 1998), only fat content (Pirisi et al. 1998) and cheese yield and composition (Di Stasio et al. 1997; Rampilli et al. 1997). However, other studies failed to detect any effect of the gene on milk production traits (Barillet et al. 1993; Recio et al. 1997). These inconsistencies, similar to those reported for dairy cattle, can be explained by breed differences, population size, frequency distribution of the genetic variants and a failure to consider relationships among animals (Sabour et al. 1996).Moreover, both the production data considered and the methods used for statistical analysis could be further causes of conflicting results (Ng-Kwai-Hang, 1997). Investigations of the relationships between milk protein polymorphism and milk production usually consider accumulated yields for standardized lactation lengths, assuming that environmental effects average out over a lactation. Such an assumption is not always valid, because there can be marked effects peculiar to individual test day (TD) measures that may not average out (Jamrozik & Schaeffer, 1997). The direct modelling of TD measures offers the advantage of a more accurate removal of environmental variation from phenotypic observations (Stanton et al. 1992). However, particular attention to the temporal dependence of the covariance structure among TD is required. In TD analysis performed by mixed linear models a simple covariance structure, known as compound symmetry, is usually assumed. This structure assumes an equal variance for all TD and an equal correlation between all pairs of TD within each lactation. An initial drawback of this assumption arises because of the heterogeneity of variance throughout lactation. Moreover, since TD values within a lactation are a sequence of repeated measures taken on the same experimental unit (Van der Werf & Schaeffer, 1997), measures close in time are likely to be more highly correlated than measures far apart in time. All these potential patterns of correlation and variation may combine to produce a complicated structure of covariance among TD that, when ignored, may result in inadequate analysis or incorrect conclusions (Littel et al. 1998). In particular, there can be marked differences in the estimates of the fixed factors considered in the analysis; such a bias is enhanced when the data structure is highly unbalanced, as in the case of studies on relationships between milk protein polymorphisms and milk production traits.A possible solution can be found in the property of mixed linear models to assume different (co)variance structures in order to find the one that best fits experimental data. The aim of the present study was to test the possible influence of the statistical model used on the results when the relationships between β-lactoglobulin polymorphism and milk production traits in dairy ewes were analysed. With this aim in view, TD measures were directly modelled with mixed linear models and the effects of alternative (co)variance structures on fixed factors estimates were compared.

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Establishment of Native Grasses with Biosolids on Abandoned Croplands in Chihuahua, Mexico

Applied and Environmental Soil Science ◽

10.1155/2013/573808 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

Pedro Jurado-Guerra ◽

J. Santos Sierra-Tristán ◽

Carlos Lara-Macias ◽

Ruben Saucedo-Teran ◽

Carlos Morales-Nieto

Keyword(s):

Repeated Measures ◽

Linear Models ◽

Waste Water Treatment ◽

Bouteloua Gracilis ◽

Native Grasses ◽

Forage Production ◽

Mixed Linear Models ◽

Blue Grama ◽

Positive Effects ◽

Seedbed Preparation

The objective of the work was to evaluate establishment and forage production of native grasses with application of biosolids, a byproduct of waste-water treatment, at an abandoned field, in Ejido Nuevo Delicias, Chihuahua, Mexico. Four biosolids rates from 0 (control) to 30 dry Mg ha−1and two methods of application, surface applied (BioSur) and soil incorporated (BioInc), were evaluated. Seedbed preparation included plowing and harrowing before rainfall. Field plots of 5 × 5 m were manually sown with a mix of blue grama (Bouteloua gracilis) (50%) and green sprangletop (Leptochloa dubia) (50%) in early August 2005. Experimental design was a randomized block with a split plot arrangement. Grass density, height, and forage production were estimated for three years. Data were analyzed with mixed linear models and repeated measures. Green sprangletop density increased under all biosolids rates regardless of method of application, while blue grama density slightly decreased. Biosolids were more beneficial for green sprangletop height than for blue grama height. Blue grama forage production slightly increased, while green sprangletop forage production increased the most at 10 Mg ha−1biosolids rate under BioSur method. It was concluded that BioSur application at 10 and 20 Mg ha−1rates had positive effects on the establishment and forage production of native grasses, especially green sprangletop.

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A review of two different approaches for the analysis of growth data using longitudinal mixed linear models: Comparing hierarchical linear regression (ML3, HLM) and repeated measures designs with structured covariance matrices (BMDP5V)

Computational Statistics & Data Analysis ◽

10.1016/0167-9473(96)82296-1 ◽

1996 ◽

Vol 21 (5) ◽

pp. 583-605 ◽

Cited By ~ 10

Author(s):

Rien van der Leeden ◽

Karen Vrijburg ◽

Jan de Leeuw

Keyword(s):

Linear Regression ◽

Repeated Measures ◽

Linear Models ◽

Covariance Matrices ◽

Growth Data ◽

Mixed Linear Models ◽

Repeated Measures Designs

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Inheritance and Correlation Analysis of Main Agronomic Traits in Mungbean (Vigna radiata L.) by Mixed Linear Models

ACTA AGRONOMICA SINICA ◽

10.3724/sp.j.1006.2012.00624 ◽

2013 ◽

Vol 38 (4) ◽

pp. 624-631

Author(s):

Chang-You LIU ◽

Bao-Jie FAN ◽

Zhi-Min CAO ◽

Yan WANG ◽

Zhi-Xiao ZHANG ◽

...

Keyword(s):

Correlation Analysis ◽

Vigna Radiata ◽

Linear Models ◽

Agronomic Traits ◽

Mixed Linear Models

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Effect of Different Dentifrices, Bleaching with 35% Hydrogen Peroxide, and Red Wine on Surface Color and Roughness of Bovine Enamel

Current Dentistry ◽

10.2174/2542579x02999200817112951 ◽

2020 ◽

Vol 02 ◽

Author(s):

RM Garcia ◽

WF Vieira-Junior ◽

JD Theobaldo ◽

NIP Pini ◽

GM Ambrosano ◽

...

Keyword(s):

Hydrogen Peroxide ◽

Generalized Linear Models ◽

Repeated Measures ◽

Red Wine ◽

Linear Models ◽

Artificial Saliva ◽

Surface Color ◽

Dental Bleaching ◽

Surface Alteration ◽

Bovine Enamel

Objective: To evaluate color and roughness of bovine enamel exposed to dentifrices, dental bleaching with 35% hydrogen peroxide (HP), and erosion/staining by red wine. Methods: Bovine enamel blocks were exposed to: artificial saliva (control), Oral-B Pro-Health (stannous fluoride with sodium fluoride, SF), Sensodyne Repair & Protect (bioactive glass, BG), Colgate Pro-Relief (arginine and calcium carbonate, AR), or Chitodent (chitosan, CHI). After toothpaste exposure, half (n=12) of the samples were bleached (35% HP), and the other half were not (n=12). The color (CIE L*a* b*, ΔE), surface roughness (Ra), and scanning electron microscopy were evaluated. Color and roughness were assessed at baseline, post-dentifrice and/or -dental bleaching, and after red wine. The data were subjected to analysis of variance (ANOVA) (ΔE) for repeated measures (Ra), followed by Tukey ́s test. The L*, a*, and b* values were analyzed by generalized linear models (a=0.05). Results: The HP promoted an increase in Ra values; however, the SF, BG, and AR did not enable this alteration. After red wine, all groups apart from SF (unbleached) showed increases in Ra values; SF and AR promoted decreases in L* values; AR demonstrated higher ΔE values, differing from the control; and CHI decreased the L* variation in the unbleached group. Conclusion: Dentifrices did not interfere with bleaching efficacy of 35% HP. However, dentifrices acted as a preventive agent against surface alteration from dental bleaching (BG, SF, and AR) or red wine (SF). Dentifrices can decrease (CHI) or increase (AR and SF) staining by red wine.

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Factors associated to functioning and health in relation to home rehabilitation in Sweden: a non-randomized pre-post intervention study

BMC Geriatrics ◽

10.1186/s12877-021-02360-1 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Anette Johansson ◽

Marie Ernsth Bravell ◽

Eleonor I. Fransson ◽

Sofi Fristedt

Keyword(s):

Repeated Measures ◽

Linear Models ◽

Medical Condition ◽

Rehabilitation Program ◽

Community Dwelling ◽

Rehabilitation Service ◽

Post Intervention ◽

Factors Associated ◽

Rehabilitation Outcomes ◽

Self Rated Health

Abstract Background Home rehabilitation is a growing rehabilitation service in many countries, but scientific knowledge of its components and outcomes is still limited. The aim of this study was to investigate; 1) which changes in functioning and self-rated health could be identified in relation to a home rehabilitation program in a population of community-dwelling citizens, and 2) how socio-demographic factors, health conditions and home rehabilitation interventions were associated to change in functioning and self-rated health after the home rehabilitation program. Method The sample consisted of participants in a municipal home rehabilitation project in Sweden and consisted of 165 community-dwelling citizens. General Linear Models (ANOVA repeated measures) was used for identifying changes in rehabilitation outcomes. Logistic regressions analysis was used to investigate associations between rehabilitation outcomes and potential factors associated to outcome. Result Overall improvements in functioning and self-rated health were found after the home rehabilitation program. Higher frequencies of training sessions with occupational therapists, length of home rehabilitation, and orthopaedic conditions of upper extremities and spine as the main health condition, were associated with rehabilitation outcomes. Conclusion The result indicates that the duration of home rehabilitation interventions and intensity of occupational therapy, as well as the main medical condition may have an impact on the outcomes of home rehabilitation and needs to be considered when planning such programs. However, more research is needed to guide practice and policymaking.

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