In order to estimation genotypic correlation and heritability of some faba bean traits, 26 faba bean genotypes were evaluated in a randomized complete block design with three replications during 2014-16 growing seasons in Agricultural Research Sation of Borujerd located in Lorestan province, Iran. The restricted maximum likelihood (REML) was used to estimate the genotypic and phenotypic correlations, broad sence heritability and genetic gain. Analysis of variance based on least squares and REML indicated significant effect of genotype on days to maturity, plant height, hundred seed weight, pod length and dry seed yield. Genotype×year interactions were significant on all of the traits except of pod length. Borujerd cultivar (G26) and G20 had the highest dry seed yield in both of years. REML results indicated a significant positive genetic correlation between dry seed yield and biological yield and plant height. Also, there were a significant negative phenotypic correlation between dry seed yield and days to maturity, and significant positive phenotypic correlation between dry seed yield and plant height, biological yield and harvest index. So, the selection of early maturing genotypes with a higher yield is achievable and selection can be done to improve the performance of dry seed yield. Cluster analysis indicated variability among genotypes. According to values of broad sence heritability and genetic gain for plant height and high genetic correlation of this trait and dry seed yield; plant height can be used as a suitable trait for improving dry seed yield by selection.

Applying an appropriate statistical analysis is complementary for conducting a robust experimental design in plant and animal breeding. In these experiments 33 Iranian bread wheat genotypes, cultivated in a randomized complete blocks design with three replications in two normal and saline conditions were evaluated at the field of National Salinity Research Center located in Yazd province, Iran. The restricted maximum likelihood (REML) was used to evaluate the different genotypic variance-covariance structures and to estimate the genotypic and phenotypic correlations of some of Iranian wheat traits under two normal and salt-stressed conditions. The Using different estimation by REML method the traits of grain yield, biological yield and harvest index had different and significant values across two conditions, this genetic variability can be used for salinity tolerance of bread wheat in breeding programs.. In addition, genotype by environment interaction for all traits was not significant, especially for grain yield as important trait for evaluation of salinity tolerance in wheat. The means comparisons of genotypes showed that the SALT22, SALT29 and SALT28 had the highest values and line No. 6, Shahpasand and line No.13 had the lowest values for grain yield, respectively. There were significantly positive genetic correlation between yield with biological yield (0.97) and harvest index (0.94) in combined analysis and negative genetic correlation for days to maturity with grain yield (-0.32) in saline condition by REML estimator. So, the selection of early maturing genotypes with higher yield in the saline condition, especially in the location of conducted experiment (Yazd) is achievable and selection can be done to improve the performance of salinity stress.

Accurate estimation of variance components using pedigree and genomic data plays a key role in prediction of breeding values. Since SNP markers in genomic selection are distributed across the genome, they may cover all quantitative traits loci and potentially explain all of genetic variation. In this study, genotype data from Merino sheep, genotyped by 50k Illumina SNP chip were used. Staple length and Fibre diameter traits were studied in this research. To study the association between allele frequency spectrum and captured additive genetic variance, all SNPs were partitioned in five MAF bins with the equal numbers of SNPs. Two statistical models including separate analysis for each category of MAF SNPs or joint analysis of all MAF groups were fitted. The analysis were performed using REML (parametric) and a Bayesian method implemented via Gibbs sampling and RKHS (semi-parametric) model. Using all common SNPs in REML approach, estimates of genomic heritability were 0. 72 and 0. 48 for Staple length and Fibre diameter, respectively. In Bayesian approach, genomic heritability for mentioned traits were 0. 74 and 0. 47 respectively. In the separate analysis, estimates of genomic heritability using REML and Bayesian approaches for each MAF class were similar, but in joint analysis estimates of two approaches were different. Overall, when the model is simple both approaches perform similarly while when model is complicated as joint analysis in present study, two approaches work different. Therefore, to determine which approach is more reliable, further research is required

The paper was to reduce biased estimation using new approach (Penalized Maximum Likelihood Estimation (PMLE) Method) in Logistic Regression. For this aim, unreal four small data sets were randomly generated. Maximum Likelihood Estimation (MLE) and PMLE Methods were applied and compared for separation case including biased estimation in Logistic Regression when one of the cells in 2 x 2 tables becomes equal to zero (separation problem). Parameters1 and their standard error obtained by using MLE for four data sets were 12.56±257.8, 13.46±264.3, 13.42±210.3, and 13.41±180.4, respectively, meaning that MLE’s are biased estimates. Corresponding values for PMLE method were found 2.28 ± 1.81, 3.05 ± 1.59, 3.45 ± 1.53, and 3.45 ± 1.53, respectively, meaning that PMLE’s was unbiased estimates. It is clear that standard error value for data set 1 reduced from 257.8 to 1.81 when using PMLE method for separation problem. According to PMLE Method, the odds of being coronary heart disease risk for smokers were increased 21.08 times than that for non-smokers smoking in data set 2, which is significant at 1% level. The odds of being coronary heart disease risk for smokers were increased 31.63 times than that for non-smokers in data set 3 (P < 0.001). The odds of being coronary heart disease risk for smokers were increased 41.93 times than that for non-smokers in data set 4. When one of the cells in 2 x 2 contingency tables becomes equal to zero, PMLE was more superior to MLE Method because PMLE Method may be performed unbiased (reliable) estimation.

The present work focuses on the second order Markov chain model which arises in a variety of settings and is well-suited to be modeled in many applications. The efficiency of the maximum quasi-likelihood estimators with the full maximum likelihood estimators for second order Markov chain models are given, besides the limiting normality results on the asymptotic properties of the associated estimates. Some efficiency calculations are also given to discuss the feasibility and computational complexity of the QL approach relative to the full likelihood approach.

To conduct any breeding program, understanding of the genetic structure of traits and effect of environment and genetic by environment interaction as well as effects of random or fixed in the analysis of results is essential. Subsequently, analysis of variances and variance components are important in plant and animal breeding. The ANOVA is one of the best estimators for variance components. But this estimator is not preferred to maximum likelihood (ML) and Restricted Maximum Likelihood (REML) methods when variance components are negatively estimated and unbalanced datasets arise. Therefore, the objective of this research is a review of comparison of estimates of variance components using ANOVA, ML and REML method in linear mixed models using experimental data.

In the present research, performance records of Fars native chicken from years 1988 to 2002 were used. Studied traits were body weight at 12 weeks (BW12), age at sexual maturity (ASM) egg weight (EW) and egg number (EN). Variance Components and genetic, phenotype and environmental correlations were estimated using restriction maximum likelihood (REML) and Bayesian analysis method based on Gibbs sampling technique under univariate and multivariate animal model. Univariate estimation of heritabilities with REML for ASM, EW, EN and BW12 were 0.53, 0.63, 0.33 and 0.53, while, with multivariate model these values were 0.51, 0.64, 0.33 and 0.53, respectively.Heritabilities estimates with Bayesian analysis in univariate model for ASM, EW, EN and BW12 were 0.53, 0.63, 0.34 and 0.55, respectively, while with multivariate model were these values 0.56, 0.58, 0.33 and 0.55, respectively. Genetic and environmental correlations between BW12 and ASM using both methods were negative but phenotypic correlation was positive. Genetic, environmental and phenotypic correlations between BW12 and EW and EN with both methods were positive. The estimates between W12 and EW with REML were 0.5, 0.15 and 0.36, whereas with Bayesian were 0.43, 0.26 and 0.28, respectively. Those estimates between BW12 and EN with REML were 0.03, 0.15 and 0.1, respectively, whereas with Bayesian were 0.19, 0.23 and 0.19, respectively. The above mentioned correlations between ASM and EN were high and negative using both methods. It can be concluded that the estimation of the parameters evalvated using with these two methods are close together.