The MLE of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\vec {\beta }_{i}$ \end{document}β→i is used for calculating Cook’s distance. Considering a gene i and sample j, Cook’s distance for GLMs is given by [59]: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ D_{ij} = \frac{R_{ij}^{2}}{\tau p} \frac{h_{jj}}{(1 - h_{jj})^{2}}, $$ \end{document}Dij=Rij2τphjj(1−hjj)2, where Rij is the Pearson residual of sample j, τ is an overdispersion parameter (in the negative binomial GLM, τ is set to 1), p is the number of parameters including the intercept, and hjj is the jth diagonal element of the hat matrix H: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ H = W^{1/2} X (X^{t} W X)^{-1} X^{t} W^{1/2}. $$ \end{document}H=W1/2X(XtWX)−1XtW1/2.
