Variance and the Covariance José M. Merigó,1,2,3,∗ Montserrat Guillén,1 José M. Sarabia4 1Department of Econometrics, Riskcenter–IREA, University of Barcelona, Barcelona 08034, Spain 2Manchester Business School, University of Manchester, Manchester M15 6 PB, United Kingdom 3Department of Management Control and Information Systems, University of Chile, Santiago 8330015, Chile 4Department of Econ...

In long-term follow-up studies, irregular longitudinal data are observed when individuals are assessed repeatedly over time but at uncommon and irregularly spaced time points. Modeling the covariance structure for this type of data is challenging, as it requires specification of a covariance function that is positive definite. Moreover, in certain settings, careful modeling of the covariance st...

Spatial data analysis provides valuable information to the government as well companies. The rapid improvement of modern technology with a geographic system (GIS) can lead collection and storage more spatial data. We developed algorithms choose optimal locations from those permanently in space for an efficient analysis. Distances between neighboring permanent are not necessary be equispaced dis...

Analysis of covariance serves two main purposes in the analysis of clinical trials. It provides for a more powerful statistical test through variance reduction for comparison of treatment groups; and it addresses comparisons between randomized groups with adjustment for random imbalance of covariates. Certain methods of covariance analysis such as logistic regression for ordinal response data a...

Notes on Variance, Covariance, and Summation Operator By Hiro Kasahara Properties of Summation Operator For a sequence of the values {x1, x2, ..., xn}, we write the sum of x1, x2, ..., xn−1, and xn using the summation operator as x1 + x2 + ... + xn = n ∑ i=1 xi. (1) Given a constant c, n ∑ i=1 cxi = cx1 + cx2 + ... + cxn = c× (x1 + x2 + ... + xn) = c n ∑ i=1 xi. (2) • For example, consider the ...

Improved methods for analysis of covariance structures now permit the rigorous testing of multivariate genetic hypotheses. Using Jöreskog's Lisrel IV computer program we have conducted a confirmatory factor analysis of dermal ridge counts on the individual fingers of 509 offspring of 107 monozygotic twin pairs. Prior to the initiation of the model-fitting procedure, the sex-adjusted ridge count...

Most traits of agronomic importance are quantitative in nature, and genetic markers have been used for decades to dissect such traits. Recently, genomic selection has earned attention as next generation sequencing technologies became feasible for major and minor crops. Mixed models have become a key tool for fitting genomic selection models, but most current genomic selection software can only ...