On the Analysis of Combined Experiments

2011 ◽  
Vol 25 (1) ◽  
pp. 165-169 ◽  
Author(s):  
David C. Blouin ◽  
Eric P. Webster ◽  
Jason A. Bond
Keyword(s):  
Statistical Analysis ◽  
Random Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Field Research ◽  
Multiple Environments ◽  
Replication Of Experiments

The replication of experiments over multiple environments such as locations and years is a common practice in field research. A major reason for the practice is to estimate the effects of treatments over a variety of environments. Environments are frequently classed as random effects in the model for statistical analysis, while treatments are almost always classed as fixed effects. Where environments are random and treatments are fixed, it is not always necessary to include all possible interactions between treatments and environments as random effects in the model. The rationale for decisions about the inclusion or exclusion of fixed by random effects in a mixed model is presented. Where the effects of treatments over broad populations of environments are to be estimated, it is often most appropriate to include only those fixed by random effects that reference experimental units.

scholarly journals The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 48-76
Author(s):  
Freddy Hernández ◽  
Viviana Giampaoli
Keyword(s):  
Weibull Distribution ◽  
Random Effects ◽  
Mixed Models ◽  
Fixed Effects ◽  
Mixed Model ◽  
Random Effect ◽  
Estimation Procedure ◽  
Weibull Regression ◽  
Two Parameters ◽  
The Impact

Mixed models are useful tools for analyzing clustered and longitudinal data. These models assume that random effects are normally distributed. However, this may be unrealistic or restrictive when representing information of the data. Several papers have been published to quantify the impacts of misspecification of the shape of the random effects in mixed models. Notably, these studies primarily concentrated their efforts on models with response variables that have normal, logistic and Poisson distributions, and the results were not conclusive. As such, we investigated the misspecification of the shape of the random effects in a Weibull regression mixed model with random intercepts in the two parameters of the Weibull distribution. Through an extensive simulation study considering six random effect distributions and assuming normality for the random effects in the estimation procedure, we found an impact of misspecification on the estimations of the fixed effects associated with the second parameter σ of the Weibull distribution. Additionally, the variance components of the model were also affected by the misspecification.

The Messages Replication Factor: Methods Tailored to Messages as Objects of Study

1994 ◽  
Vol 71 (4) ◽  
pp. 984-996
Author(s):  
Sally Jackson ◽  
Daniel J. O'Keefe ◽  
Dale E. Brashers
Keyword(s):  
Statistical Analysis ◽  
Random Effects ◽  
Fixed Effects ◽  
Communication Research ◽  
Concrete Material ◽  
Replication Factor ◽  
Treatment Comparisons ◽  
Replication Factors ◽  
The Relationship

In research on effects of message variables, it is generally necessary to examine responses to actual messages that represent, embody, or instantiate the values of the variable of interest. Researchers have lately become attentive to problems of confounding in the use of individual concrete messages to represent abstract theoretical contrasts, and replicated treatment comparisons are increasingly common in communication research. How to treat the replications factor in the statistical analysis remains controversial. Whether to treat replication factors as fixed or as random hinges on what is assumed about the relationship between abstract treatment contrasts and their concrete material implementations. We argue that reflection on this relationship justifies a general policy of treating replications as random. Two circumstances in which fixed-effects analyses might seem attractive (the case of matched-message designs and the case of experimental manipulations occurring outside of messages) are considered, but it is concluded that these situations also require random-effects analyses.

scholarly journals A generalized linear mixed model for understanding determinant factors of student's interest in pursuing bachelor's degree at Universitas Syiah Kuala

2021 ◽  
Vol 21 (2) ◽  
pp. 72-80
Author(s):  
ASEP RUSYANA ◽  
KHAIRIL ANWAR NOTODIPUTRO ◽  
BAGUS SARTONO
Keyword(s):  
High Schools ◽  
Normal Distribution ◽  
Random Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Generalized Linear Mixed Model ◽  
Likelihood Method ◽  
Response Variable ◽  
Banda Aceh

Generalized Linear Mixed Model (GLMM) is a framework that has a response variable, fixed effects, and random effects. The response variable comes from an exponential family, whereas random effects have a normal distribution. Estimating parameters can be calculated using the maximum likelihood method using the Laplace approach or the Gauss-Hermite Quadrature (GHQ) approach. The purpose of this study was to identify factors that trigger student's interest to continue studying at Universitas Syiah Kuala (USK) using both techniques.  The GLMM is suitable for the data because the variable response has a Bernoulli distribution, and the random effects are assumed to be having a normal distribution. Also, the model helps identify the relationship between the dependent variable and the predictors. This study utilizes data from six high schools in Banda Aceh city drawn using a two-stage sampling technique. Stage 1, we randomly chose six out of sixteen public senior high schools in Banda Aceh. Stage 2, we selected students from each school from four different major classes. The GLMM model includes one binary response variable, five numerical fixed-effects, and two random effects. The response variable is the interest of high school students to continue study at USK (yes or no). The five fixed effects in the model including scores of collaboration (C), Action (A), Emotion (E), Purposes (P), and Hope (H).  Finally, the random effects are schools (S) and majors (M). In this study, both Laplace and GHQ techniques produce identical results. The predictors that can explain student interest are A, E, and H. These predictors have a positive effect. The random effects of schools and majors are not significantly different from zero. The model with three significant predictors is better than the complete predictor model.

Correlations of Permeability and Geological Characteristics Based on Mercury Intrusion Data and Hierarchical Statistical Models: A Case Study

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Zihao Li ◽  
Wenyu Gao ◽  
Xiangming Li
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Quantitative Relationship ◽  
Petrophysical Properties ◽  
Petrophysical Parameters ◽  
Mercury Intrusion ◽  
Geological Characteristics ◽  
Hierarchical Statistical Model

Abstract The mercury intrusion technique is a crucial in-lab method to investigate the porous medium properties. The potentiality of mercury intrusion data has not been explored significantly in the traditional interpretation. Thus, a hierarchical statistical model that not only captures the quantitative relationship between petrophysical properties but also accounts for different geological members is developed to interpret mercury intrusion data. This multilevel model is established from almost 800 samples with specific geological characteristics. We distinguish the fixed effects and the random effects in this mixed model. The overall connection between the selected petrophysical parameters is described by the fixed effects at a higher level, while variations due to different geological members are accommodated as the random effects at a lower level. The selected petrophysical parameters are observed through hypothesis testing and model selection. In this case study, five petrophysical parameters are selected into the model. Essential visualizations are also provided to assist the interpretations of the probabilistically model. The final model reveals the quantitative relationship between permeability and other petrophysical properties in each member and the order of relative importance for each property. With this studied relationship and advanced model, the geological reservoir simulation can be greatly detailed and accurate in the future.

Multiple Group Comparisons of the Fixed and Random Effects From the Generalized Linear Mixed Model

2021 ◽  
pp. 004912412098618
Author(s):  
Daniel Kasper ◽  
Katrin Schulz-Heidorf ◽  
Knut Schwippert
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Asymptotic Properties ◽  
Generalized Linear Mixed Model ◽  
Test Statistic ◽  
Multiple Group ◽  
Fixed And Random Effects ◽  
Group Comparisons

In this article, we extend Liao’s test for across-group comparisons of the fixed effects from the generalized linear model to the fixed and random effects of the generalized linear mixed model (GLMM). Using as our basis the Wald statistic, we developed an asymptotic test statistic for across-group comparisons of these effects. The test can be applied when the fixed and random effects are multivariate normally distributed, and it works well for any link function and conditional distribution of the dependent variable of the GLMM. We also derived the asymptotic properties of this test, and because power information does not exist for either our new test statistic or Liao’s test, we implemented a power study to demonstrate the superiority of these tests over the alternatively proposed F test. Using an example, we show the application of the test and then discuss its possible restrictions with respect to the distribution of the random effects.

scholarly journals Selection in several environments by BLP as an alternative to pooled anova in crop breeding

2009 ◽  
Vol 33 (5) ◽  
pp. 1342-1350 ◽  
Author(s):  
Júlio Sílvio de Sousa Bueno Filho ◽  
Roland Vencovsky
Keyword(s):  
Plant Breeding ◽  
Random Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Linear Models ◽  
Minimum Variance ◽  
Pooled Analysis ◽  
Balanced Designs ◽  
Best Linear Unbiased ◽  
Combine Information

Plant breeders often carry out genetic trials in balanced designs. That is not always the case with animal genetic trials. In plant breeding is usual to select progenies tested in several environments by pooled analysis of variance (ANOVA). This procedure is based on the global averages for each family, although genetic values of progenies are better viewed as random effects. Thus, the appropriate form of analysis is more likely to follow the mixed models approach to progeny tests, which became a common practice in animal breeding. Best Linear Unbiased Prediction (BLUP) is not a "method" but a feature of mixed model estimators (predictors) of random effects and may be derived in so many ways that it has the potential of unifying the statistical theory of linear models (Robinson, 1991). When estimates of fixed effects are present is possible to combine information from several different tests by simplifying BLUP, in these situations BLP also has unbiased properties and this lead to BLUP from straightforward heuristics. In this paper some advantages of BLP applied to plant breeding are discussed. Our focus is on how to deal with estimates of progeny means and variances from many environments to work out predictions that have "best" properties (minimum variance linear combinations of progenies' averages). A practical rule for relative weighting is worked out.

scholarly journals Analysis of lactation feed intakes for sows with extended lactation lengths

2017 ◽  
Vol 1 (1) ◽  
pp. 1-25
Author(s):  
F. A. Cabezón ◽  
A. P. Schinckel ◽  
Y. L. León ◽  
B. A. Craig
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Polynomial Function ◽  
Random Effect ◽  
Information Criteria ◽  
Polynomial Functions ◽  
Feeding System ◽  
Lactation Length ◽  
Akaike’S Information Criteria

Abstract The objectives of this research were to quantify and model daily feed intakes to 28 d of lactation in modern sows. A total of 4,512 daily feed intake (DFI) records were collected for 156 Hypor sows from February 2015 to March 2016. The mean lactation length was 27.9 ± 2.0 d. The data included 9 parity 1, 33 parity 2 and 114 parity 3+ sows. Data were collected using a computerized feeding system (Gestal Solo, JYGA Technologies, Quebec, Canada). The feeding system was used to set an upper limit to DFI for the first 7 d of lactation. Overall, the least-squares means of a model including the random effect of sow indicated that DFI's continued to slowly increase to 28 d of lactation. The DFI data were fitted to Generalized Michaelis-Menten (GMM) and polynomial functions of day of lactation (t). The GMM function [DFIi,t (kg/d) = DFI0 + (DFIA − DFI0)(t/K)C/[1 + (t/K)C]] was fitted with 2 random effects for DFI (dfiAi) and intercept (dfi0i) using the NLMIXED procedure in SAS®. The polynomial function DFIi,t (kg/d) = [B0 + B1 t + B2 t2 + B3 t3 + B4 t4] was fitted with three random effects for B0, B1, and B2 using the MIXED procedure in SAS®. Fixed effects models of the two functions had similar Akaike's Information Criteria (AIC) values and mean predicted DFI's. The polynomial function with 3 random effects provided a better fit to the data based on R2 30 (0.81 versus 0.79), AIC (14,709 versus 15,158) and RSD (1.204 versus 1.321) values than the GMM function with two random effects. The random effect for B2 in the polynomial function allowed for the fitting of the function to lactation records that had decreased DFI after 15 d of lactation. The random effects for the polynomial function were used to sort the lactation records into three groups based on the derivative of the function at 21 d of lactation. Lactation records of the three groups had similar DFI the first two weeks of lactation (P > 0.40). The three groups of sows had substantially different DFI's after 18 d of lactation (P < 0.028). The differences in both actual and predicted DFI's between the three groups increased with each day of lactation to day 28 (P < 0.001). Mixed model polynomial functions can be used to identify sows with different patterns of DFI after 15 d of lactation.

scholarly journals Sporthorse performance testing in eventing by own and progeny performance

2012 ◽  
pp. 49-56
Author(s):  
Anita Mezei ◽  
János Posta ◽  
Sándor Mihók
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Performance Testing ◽  
Population Based ◽  
Descriptive Statistics ◽  
European Countries ◽  
Breeding Values ◽  
Progeny Performance

The aim of the study was to evaluate the Hungarian Sporthorse population based on eventing competition performance. The database contained the results of 792 horses and 449 riders between 2000 and 2006. The eventing results were gathered from Hungary and other European countries. Blom transformed ranks were used to evaluate the sport performance.Three models were fitted to the Blom scores. Evaluating all the competition categories at the same time weighted Blom scores were used according to the difficulty of the category. The linear mixed model included fixed effects for age, sex, breeder, owner, location, year; and random effects for animal and rider. Horses from the database were judged by their own performance, and stallions were investigated by performance of their progenies on the basis of descriptive statistics of Blom scores and weighted Blom scores. Breeding values of eventing performance were predicted. To improve the reliability of breeding values, more progenies should beused in eventing competitions. 

scholarly journals Random effects regression trees for the analysis of INVALSI data

2021 ◽  
pp. 29-34
Author(s):  
Giulia Vannucci ◽  
Anna Gottard ◽  
Leonardo Grilli ◽  
Carla Rampichini
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Random Effect ◽  
Regression Trees ◽  
Linear Component ◽  
Non Linear ◽  
Effect Regression ◽  
Tree Component

Mixed or multilevel models exploit random effects to deal with hierarchical data, where statistical units are clustered in groups and cannot be assumed as independent. Sometimes, the assumption of linear dependence of a response on a set of explanatory variables is not plausible, and model specification becomes a challenging task. Regression trees can be helpful to capture non-linear effects of the predictors. This method was extended to clustered data by modelling the fixed effects with a decision tree while accounting for the random effects with a linear mixed model in a separate step (Hajjem & Larocque, 2011; Sela & Simonoff, 2012). Random effect regression trees are shown to be less sensitive to parametric assumptions and provide improved predictive power compared to linear models with random effects and regression trees without random effects. We propose a new random effect model, called Tree embedded linear mixed model, where the regression function is piecewise-linear, consisting in the sum of a tree component and a linear component. This model can deal with both non-linear and interaction effects and cluster mean dependencies. The proposal is the mixed effect version of the semi-linear regression trees (Vannucci, 2019; Vannucci & Gottard, 2019). Model fitting is obtained by an iterative two-stage estimation procedure, where both the fixed and the random effects are jointly estimated. The proposed model allows a decomposition of the effect of a given predictor within and between clusters. We will show via a simulation study and an application to INVALSI data that these extensions improve the predictive performance of the model in the presence of quasi-linear relationships, avoiding overfitting, and facilitating interpretability.

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