You can install the development version of fullRankMatrix fromGitHubwith: #install.packages("devtools")devtools::install_github("Pweidemueller/fullRankMatrix") Example When using linear models you should check if any of the columns in your model matrix are linearly dependent. If they are this wi...
The present note shows that balanced uniform repeated measurements designs fulfill this criterion.doi:10.1007/BF02613152J. KunertPhysica-VerlagMetrikaAn Example of Universal Optimality in a Full-Rank Model - Kunert - 1987
(Note that, by condition (iii), the matrix G is assumed to have maximal rank and hence any column of the matrix T is equal to GpT, for some word p.) We will illustrate the concept superduality by an example. Example 3 We consider the couple (G∣T) below: In this case n=15, ...
Ifn < KandDis a full-rank matrix, an infinite number of solutions are available for the above representation problem. Thus, a new constraint is introduced into this problem, and the solution is obtained by solving MathML (1) where ||·||0represents thel0-norm. Furthermore,Tdetermines...
where T∈RN×d is the score matrix, P∈RD×d is the loading matrix, d is the retained latent dimensionality, and E is the residual matrix. Technically, if we consider the covariance as the example, by performing the Eigen-decomposition of the covariance matrix S=(XTX)/(N−1), we ge...
Fixed Effects design matrix X must be of full column rank. I don't understand why this is happening -- and probably this shows that I have a pretty big misunderstanding of what the dummy variables actually are. However, if I runtwofitlme's -- one ...
All p-values are tests of equality of population using Wilcoxon rank sum test and suggest statistically significant difference. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) For example a simple logistic ...
The decomposition of the data matrix into loading vectors and latent variables provide valuable graphical outputs to easily visualize the results. For example, the latent variables can be used to represent the similarities and dissimilarities between the samples: Figure 4 illustrates the difference in ...
(paired Wilcoxon signed rank test for same room > different room: Infant 3:p-value = 1.95 × 10−9, Infant 6: 1.0, Infant 12: 3.05 × 10−5, Infant 18: 3.81 × 10−6) as compared to species-FEAST (Infant 3:p-value = 0.41, Infant 6: 1.0,...
The aggregated matrix data was imported into R using Seurat (v3.2.3) and scater (version 1.10.1) package for further data analysis [82]. Outlier cell with library size and number of expressed genes more than 3 median absolute deviations (MADs) below the median value, unique molecular identif...