\begin{equation} \newcommand{\func}[2] { \mathrm{#1}\left(#2\right) } \newcommand{\mathcolorbox}[2]{\colorbox{#1}{$\displaystyle #2$}} \end{equation} \begin{equation} \renewcommand{\Pr}[1] { \func{Pr}{#1} } \newcommand{\Supp}[1] { \func{Supp}{#1} } \newcommand{\E}[1] { \func{E}{#1} } \newcommand{\Var}[1] { \func{Var}{#1} } \newcommand{\SD}[1] { \func{SD}{#1} } \newcommand{\SE}[1] { \func{SE}{#1} } \newcommand{\Cov}[1] { \func{Cov}{#1} } \newcommand{\Cor}[1] { \func{Cor}{#1} } \newcommand{\EEst}[1] { \widehat{\mathrm{E}}\left(#1\right) } \newcommand{\VarEst}[1] { \widehat{\mathrm{Var}}\left(#1\right) } \newcommand{\CovEst}[1] { \widehat{\mathrm{Cov}}\left(#1\right) } \newcommand{\CorEst}[1] { \widehat{\mathrm{Cor}}\left(#1\right) } \end{equation} \begin{equation} \renewcommand{\ln}[1] { \func{ln}{#1} } \renewcommand{\log}[1] { \func{log}{#1} } \renewcommand{\exp}[1] { \func{exp}{#1} } \newcommand{\logit}[1] { \func{logit}{#1} } \newcommand{\logis}[1] { \func{logistic}{#1} } \renewcommand{\max}[2] { \mathrm{max}_{#1}\left(#2\right) } \renewcommand{\min}[2] { \mathrm{min}_{#1}\left(#2\right) } \newcommand{\argmax}[2] { \mathrm{argmax}_{#1}\left(#2\right) } \newcommand{\argmin}[2] { \mathrm{argmin}_{#1}\left(#2\right) } \newcommand{\abs}[1] { \left|#1\right| } \newcommand{\Indic}[1] { \mathbb{1}\left\{#1\right\} } \newcommand{\rank}[1] { \func{rank} } \newcommand{\diag}[1] { \func{diag} } \newcommand{\tr}[1] { \func{tr} } \newcommand{\det}[1] { \func{det} } \newcommand{\dim}[1] { \func{dim} } \end{equation} \begin{equation} \newcommand{\Bernoulli}[1] { \func{Bernoulli}{#1} } \newcommand{\Bin}[1] { \func{Binom}{#1} } \newcommand{\Hypergeom}[1] { \func{Hypergeom}{#1} } \newcommand{\Geom}[1] { \func{Geom}{#1} } \newcommand{\NB}[1] { \func{NB}{#1} } \newcommand{\Pois}[1] { \func{Pois}{#1} } \newcommand{\Unif}[1] { \func{Unif}{#1} } \newcommand{\Normal}[1] { \func{N}{#1} } \newcommand{\LogNormal}[1] { \func{Lognormal}{#1} } \newcommand{\MVN}[1] { \func{MVN}{#1} } \renewcommand{\Beta}[1] { \func{Beta}{#1} } \renewcommand{\Gamma}[1] { \func{Γ}{#1} } \newcommand{\Exp}[1] { \func{Exp}{#1} } \newcommand{\Chisq}[1] { χ^{2}_{#1} } \end{equation} \begin{equation} \newcommand{\pfrac}[2] { \left(\frac{#1}{#2}\right) } \newcommand{\bfrac}[2] { \left[\frac{#1}{#2}\right] } \newcommand{\nullsim} { \overset{\small{$H_0$}}{\sim} } \newcommand{\iid} { \overset{\small\mathrm{iid}}{\sim} } \newcommand{\defeq} { \overset{\small\mathrm{def}}{=} } \newcommand{\plim} { \overset{p}{→} } \newcommand{\dlim} { \overset{d}{→} } \newcommand{\aslim} { \overset{\mathrm{a.s.}}{→} } \newcommand{\reals} { \mathbb{R} } \newcommand{\MLE}[1] { \hat{#1}_{\mathrm{MLE}} } \newcommand{\MoM}[1] { \hat{#1}_{\mathrm{MoM}} } \newcommand{\REML}[1] { \hat{#1}_{\mathrm{REML}} } \newcommand{\OLS}[1] { \hat{#1}_{\mathrm{OLS}} } \newcommand{\WLS}[1] { \hat{#1}_{\mathrm{WLS}} } \newcommand{\GLS}[1] { \hat{#1}_{\mathrm{GLS}} } \newcommand{\sbullet} { \mathbin{\vcenter{\hbox{\scalebox{0.5}{$\bullet$}}}} } \newcommand{\T} { \top } \end{equation} \begin{equation} \newcommand{\separator} { \vspace{2mm} \par\noindent\rule{\textwidth}{0.7pt} \vspace{2mm} } \newcommand{\zzz} { \vspace{-8mm} } % \let\bm\mathbf \let\bm\symbfup \newcommand{\Note} { $\boxed{\textbf{Note}}$ } \newenvironment{alignBraced}{ \left\{\begin{aligned} }{ \end{aligned}\right\} } \end{equation}
Miles Moran
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On this page

  • Glossary
Categories
Autocorrelation
Bayesian
Contrasts
Data Viz
DoE
GLMMs
GLMs
Heteroskedasticity
LMMs
LMs
Multiple Comparisons
Power Analysis
Quick-Read
R
SAS
Simulation
Spatial
Stata
Stata. Multivariate
Survival

Resources

The following is a curated list of resources I often recommend to our consulting clients. Select one or more niches/categories from the sidebar to filter the list.


    resource-icon
    Sims, Christopher,  Clustering, Random Effects, Mixed Models, Sandwiches
    Heteroskedasticity
    Autocorrelation
    LMMs
    resource-icon
    Hall, Dan,  An Intro to LMMs in R and SAS
    Heteroskedasticity
    Autocorrelation
    LMMs
    R
    SAS
    resource-icon
    Hall, Dan,  An Intro to R Graphics, Part I: Base Graphics
    Data Viz
    R
    resource-icon
    Hall, Dan,  An Intro to R Graphics, Part II: ggplot2
    Data Viz
    R
    resource-icon
    Hall, Dan,  Working with Factors in R
    DoE
    Contrasts
    R
    resource-icon
    Hall, Dan,  Multiple Comparisons & Simultaneous Inference
    DoE
    Contrasts
    Multiple Comparisons
    R
    resource-icon
    Hall, Dan,  Power Analysis and Sample Size Determination
    DoE
    Contrasts
    Multiple Comparisons
    Power Analysis
    R
    resource-icon
    Sainani, Kristin,  The Importance of Accounting for Correlated Observations
    Autocorrelation
    Quick-Read
    resource-icon
    Craigmile, Peter,  A Review of Traditional Stationary Geostatistical Models
    Spatial
    Autocorrelation
    resource-icon
    UCLA Statistical Consulting Group,  Intro to GLMMs
    GLMMs
    Autocorrelation
    resource-icon
    UCLA Statistical Consulting Group,  Intro to LMMs
    LMMs
    Autocorrelation
    resource-icon
    Zeileis, Achim,  Econometric Computing with HC and HAC Covariance Matrix Estimators
    LMs
    GLMs
    Heteroskedasticity
    R
    resource-icon
    Scholer, Falk,  ANOVA (and R): Type I, II and III Sums of Squares
    LMs
    DoE
    R
    resource-icon
    Ford, Clay,  Understanding Semivariograms
    LMs
    LMMs
    R
    Autocorrelation
    Spatial
    Simulation
    resource-icon
    Ford, Clay,  Modeling Non-Constant Variance
    LMs
    Heteroskedasticity
    R
    Simulation
    resource-icon
    Ford, Clay,  Understanding Robust Standard Errors
    LMs
    Heteroskedasticity
    R
    Simulation
    resource-icon
    Rodríguez, Germán,  Survival Analysis (POP 509 Course Materials)
    GLMs
    GLMMs
    Survival
    R
    Stata. Multivariate
    resource-icon
    Rodríguez, Germán,  Generalized Linear Models (POP 507 Course Materials)
    GLMs
    GLMMs
    Survival
    R
    Stata
    resource-icon
    Rodríguez, Germán,  Multilevel Models (POP 510 Course Materials)
    LMMs
    GLMMs
    Autocorrelation
    R
    Stata
    Bayesian
    resource-icon
    Hartig, Florian,  DHARMa: Residual Diagnostics for Hierarchical Regression Models
    GLMs
    GLMMs
    Autocorrelation
    R
    Simulation
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Glossary

Models:

LMs (“Linear Models”)

These are models where \(\E{\bm{y}}=\bm{Xβ}\). Normality is often assumed, i.e. \(\bm{y} \sim \Normal{\bm{Xβ}, \bm{Σ}}\).

LMMs (“Linear Mixed Models”)

These are models where \(\E{\bm{y}|\bm{α}}=\bm{Xβ+Zα}\), where \(\bm{α}\) are random-effects. Normality is often assumed, i.e. \((\bm{y}|\bm{α}) \sim \Normal{\bm{Xβ+Zα}, \bm{Σ}}\).

GLMs (“Generalized Linear Models”)

These are models where \(\bm{θ=Xβ}\), where \(\bm{θ}\) is some parameter of the distribution of \(\bm{y}\).

GLMs (“Generalized Linear Mixed Models”)

These are models where \(\bm{θ=Xβ+Zα}\), where \(\bm{θ}\) is some parameter of the distribution of \(\bm{y}\), and where \(\bm{α}\) are random-effects.