l10-16.Rnw

% File: l8.Rnw
% Time-stamp: <>
% $Id$
%
% Author: Martin Corley

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<<setup, include=FALSE>>=
require(knitr)
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knit_hooks$set(source = function(x, options) {
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source('R/preamble.R') # useful functions
### apparent issue with Rscript
require(methods)
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@ 


\title[USMR~10]{Ae fareweel, alas\footnote{\url{https://en.wikipedia.org/wiki/Ae_Fond_Kiss}}}
\subtitle{ANOVA, Analysis, Reporting}
\author{Martin Corley}
\date{}

\begin{document}

\begin{frame}[plain]
\titlepage
\end{frame}

\begin{frame}
\frametitle{Today}
\tableofcontents[part=1]
\tableofcontents[part=2]
\tableofcontents[part=3]
\end{frame}

\part{ANOVA and GLM}
\section{ANOVA and GLM}
\subsection{Concepts}
\begin{frame}[plain]
  \partpage
\end{frame}

\begin{frame}
  \frametitle{ANOVA and GLM}
\begin{AQuote}{Cohen (1968)}
  If you should say to a mathematical statistician that you have
  discovered that linear multiple regression analysis and the analysis
  of variance (and covariance) are identical systems, he would mutter
  something like, ``Of course---general linear model,'' and you might
  have trouble maintaining his attention. If you should say this to a
  typical psychologist, you would be met with incredulity, or
  worse. Yet it is true, and in its truth lie possibilities for more
  relevant and therefore more powerful exploitation of research data.
\end{AQuote}

\end{frame}

\begin{frame}
  \frametitle{History: ANOVA and Multiple Regression}
  \begin{block}{Multiple Regression}
\begin{itemize}    
  \item Introduced c.\@ 1900 in biological and behavioural sciences
  \item aligned to ``natural variation''
 \end{itemize}
  \end{block}
  \spc
  \begin{block}{ANOVA}
  \begin{itemize}
  \item Introduced c.\@ 1920 in agricultural research
  \item aligned to experimentation and manipulation
  \item much simpler to calculate (can easily be done by hand)  
  \end{itemize}
\end{block}
  
\end{frame}


\begin{frame}
  \frametitle{History: ANOVA and Multiple Regression}
  \begin{itemize}
  \item ANOVA tells us that groups $(g_1, g_2, \ldots, g_n)$ have
    different means ($\bar{x}$)
  \item MR tells us that means ($\bar{y}$) are related to groups $(g_1, g_2, \ldots, g_n)$
\item both produce $F$-ratios, discussed using different language, but identical  \end{itemize}
\spc\pause
\begin{block}{Why teach ANOVA separately?}
  \begin{itemize}
  \item you can make students do ANOVA by hand
  \item it can be useful to explain experimental design
  \end{itemize}
\end{block}


\end{frame}

\begin{frame}
  \frametitle{Why prefer GLM/Regression?}
  \begin{itemize}
  \item GLM has less restrictive assumptions
    \begin{itemize}
    \item especially true for unbalanced designs/missing data
    \end{itemize}
\spc  \item GLM is far better at dealing with covariates
    \begin{itemize}
    \item  can arbitrarily mix continuous and discrete predictors
    \end{itemize}
    \pause
\spc \item<alert@2> GLM is the gateway to other powerful tools
  \begin{itemize}
  \item mixed models and factor analysis\atright{\ra{} MSMR}
  \item structural equation models
  \end{itemize}
  \end{itemize}
  
  
\end{frame}

\subsection{Examples}

\begin{frame}[fragile]
  \frametitle{ANOVA in R}
\framesubtitle{Which Apples are Tastiest?}
<<maked>>=
apples <- data.frame(
    colour = gl(2,2,8,labels=c('green','red')),
    taste = runif(8,1,7)
    )
apples
@ 
\pause
\begin{itemize}
\item linear model, and ANOVA
\end{itemize}
<<doit>>=
r.mod <- lm(taste ~ colour, data = apples)

## alternative ANOVA command

a.mod <- aov(taste ~ colour, data = apples)
@ 
\end{frame}

\begin{frame}[fragile]
  \frametitle{lm() vs.\@ aov()}
  \begin{itemize}
  \item linear model:
  \end{itemize}
<<showme.l>>=
anova(r.mod)
@ 

\begin{itemize}
\item ANOVA:
\end{itemize}
<<showme.a>>=
summary(a.mod)
@ 
\begin{itemize}
\item NB: can't inspect coefficients!
\end{itemize}

\end{frame}

\begin{frame}[fragile]
\frametitle{lm() vs.\@ aov()}  
\begin{itemize}
\item linear model:
\end{itemize}
<<showme.l2f,eval=FALSE>>=
summary(r.mod)
@ 
<<showme.l2,echo=FALSE>>=
.pp(summary(r.mod),l=list(0,c(10:12),0))
@ 
\begin{itemize}
\item ANOVA:
\end{itemize}
<<showme.a2>>=
model.tables(a.mod)
@ 
\end{frame}

{\usebackgroundtemplate{\includegraphics[width=\paperwidth]{img/elephant}}
\begin{frame}[t,plain]
  \transdissolve
\vspace*{8.2cm}
\begin{center}
{\huge \textbf{\textcolor{white}{The Elephant In The Room}}}
\end{center}

\end{frame}}

\begin{frame}{The Elephant is Repeated Measures}
  \begin{itemize}
  \item so far, \emph{every} model we've looked at has been `one
    observation per participant' (or `one observation per word')
  \item however, most experiments have a \emph{structure}
\spc
    \item some observations are `more related' to each other than others
    \item for example, because they come from the same person
      (repeated measures)
 \end{itemize}
\end{frame}  

\begin{frame}
  \frametitle{Mixed Models (looking ahead)}
  
  \begin{block}{The Regression Equation}
  \[ y_{i\visible<2->{\alert<2>{j}}} = b_{0\visible<2->{\alert<2>{j}}} +
   b_{1\visible<2->{\alert<2>{j}}}x_{1i\visible<2->{\alert<2>{j}}} +
   \epsilon_{i\visible<2->{\alert<2>{j}}}
   \]

   \pause[3]\spc[.5em]
   \[ b_{0j} = \gamma_{00} + \upsilon_{0j} \]
   \[ b_{1j} = \gamma_{01} + \upsilon_{1j} \]
    
  \end{block}
  \pause[4]
  \begin{itemize}
  \item relatedness accounted for by more regression equations
    
  \item all part of the linear model \atright{\alert{\ra{} NEXT TERM}}
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{ANOVA reading}
  \begin{itemize}
  \item brief introduction: Navarro (pp.\@ 523--534, v0.5)
  
  \item Cohen, J.\@ (1968). Multiple Regression as a General
    Data-Analytic System.  \textit{Psychological Bulletin, 70,}
    426--443.
  \item Chapter 16 of Howell, D.~C.\@ (2002). \textit{Statistical Methods for
      Psychology,} 5th Edn. Duxbury, CA: Duxbury Thomson Learning.
    

  \end{itemize}
\end{frame}

\part{Analysis}
\section{Analysis}
\subsection[Logic]{The Logic of Analysis}
\begin{frame}[plain]
  \partpage
\end{frame}



\begin{frame}
  \frametitle{Analytical Steps}

\begin{itemize}
\item steps typically needed for an analysis \textcolor{gray}{(cough: lab~9, exam)}
\end{itemize}
\spc
\begin{enumerate}
\item specify research questions and hypotheses
\item operationalize variables
\item clean and prepare data
\item describe and visualise data
\item select and run statistics
\item check test and data assumptions
\item interpret results
\end{enumerate}

\end{frame}

\subsection[Data]{Questions and Data}
\begin{frame}
  \frametitle{Research Questions and Hypotheses}
  \begin{Quote}
  produce some graphics and statistics to indicate what the
  relationship is between where people live, their politics, and their
  attitudes towards fox-hunting  
  \end{Quote}
  \spc
  \begin{itemize}
  \item relational statement (relationship)
    \begin{itemize}
    \item can be extended to think about prediction (correlation \ra{}
      regression)
    \end{itemize}
  \item variables
    \begin{itemize}
    \item where people live, politics, attitudes to fox-hunting
    \item[\ra] need to be \term{operationalized}
    \end{itemize}

  \end{itemize}
  
  
\end{frame}

\begin{frame}
  \frametitle{Operationalizing Variables}
  \begin{Quote}
    politics, using the Stone-Corley Wingedness Inventory, which
    returns a score along the political spectrum ranging from -100
    (extremely left-wing, socialist) to 100 (extremely right-wing, conservative)
  \end{Quote}
  \begin{itemize}
  \item continuous, self-rated
  \end{itemize}
\spc
\pause
\begin{Quote}
  where participants lived (urban, suburban, country)
\end{Quote}
\begin{itemize}
\item nominal category with 3~levels
\end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Cleaning Data}
  \begin{enumerate}
  \item are there any impossible values?
    \begin{itemize}
    \item recode them as something sensible; usually \R{NA}
    \end{itemize}
\spc
\pause
\item are there any outliers?
  \begin{itemize}
  \item what test/critical values will be use?
  \item are outliers exerting influence?
  \end{itemize}
\spc
\pause
\item are categorical variables appropriately encoded?
  \begin{itemize}
  \item does \R{R} recognise them as \R{factor}s?
  \item are the levels labelled? Remember how \R{R} deals with labels\ldots
  \end{itemize}
  \end{enumerate}
  
\end{frame}

\begin{frame}
  \frametitle{Describing and Visualising Data}
  \begin{itemize}
  \item descriptions depend on variable types
   \spc
   
 \item \R{politics}: continuous \ra{} mean, SD, (skew, kurtosis),
   histogram or density?
    \spc
    
  \item \R{home}: nominal category \ra{} frequencies, mosaic plot?
  \end{itemize}
\end{frame}

\subsection[Stats]{Statistics}

\begin{frame}
  \frametitle{Statistics!}
  \begin{itemize}
  \item \term{$t$-test:} mean difference 
  \item \term{correlation:} association

  \item \term{regression:} `prediction' 
  \end{itemize}
\spc
\pause
\begin{itemize}
\item choice depends on relational statement in question
\item calculation depends on DV~type etc.
\spc
\item how does this method treat missing data? (\R{na.rm=T}?)
\item what is the key output (from \R{summary()}, for example?)
\end{itemize}

\end{frame}

\begin{frame}
  \frametitle{Checking Assumptions}
\begin{block}{For Linear Models: Required}
  \begin{itemize}
  \item \term{linearity} of relationships(!)
  \item for the \emph{residuals}:
    \begin{itemize}
    \item \term{normality}
    \item \term{homogeneity of variance}
    \item \term{independence}
    \end{itemize}
  \end{itemize}
\end{block}  
\spc[.5em]
\pause[2]
\begin{block}{For Linear Models: Desirable}
  \begin{itemize}
  \item uncorrelated predictors (no collinearity)
  \item no `bad' (overly influential) observations
  \end{itemize}
\end{block}
  
\end{frame}

\begin{frame}
  \frametitle{Logit Regression Assumptions}
  
\begin{block}{For Binomial DVs, Assumptions are Different}
\begin{itemize}
\item \term{linearity} of relationships between IVs and log-odds
\item for the \emph{residuals}:
    \begin{itemize}
    \item \sout{normality}
    \item \sout{homogeneity of variance}
    \item \term{independence}
    \end{itemize}
  \end{itemize}
\end{block}
\spc[.5em]
\pause[2]
\begin{block}{Desirable}
  \begin{itemize}
  \item uncorrelated predictors (no collinearity)
  \item no `bad' (overly influential) observations
  \item large samples (due to maximum likelihood fitting)
  \end{itemize}
\end{block}

\end{frame}

{ \definecolor{mycolor}{HTML}{FEF5DA}
  \setbeamercolor{background canvas}{bg=mycolor}
  \begin{frame}{EXAM INFO}
    \begin{itemize}
    \item for the exam, we do not expect a full suite of assumption
      checks for any \R{glm(\ldots{} family=binomial)} regressions you
      do
      \spc
    \item please provide a rationale for using these regressions based
      on the types of variables you are analysing
    \end{itemize}

  
\end{frame}}

\subsection{Interpretation}

\begin{frame}[fragile]
  \frametitle{Interpretation:  Linear Models}
  <<intslop,echo=F>>=
curve(5+2*x,from=-1,to=4,ylim=c(0,14),frame.plot=F,ylab='y=5+2x')
arrows(0,0,0,5,lwd=3,col='red',code=3,length=0.15)
text(0.1,2,pos=4,"intercept",col='red')
lines(x=c(1,2.5),y=c(7,7),lty='dashed',lwd=2,col='blue')
arrows(2,7,2,9,lwd=3,col='blue',code=3,length=0.15)
text(2.1,8,pos=4,"slope",col='blue')
@   
\cimage[.45\linewidth]{img/auto-intslop-1}
\pause
\begin{block}{Linear Model}
\centering{$\hat{y_i}={b_0}\visible<1-2>{\cdot\textcolor<2>{red}{1}} + b_1\cdot\textcolor<2-3>{blue}{x_i}$\\
\visible<2-3>{\texttt{y \textasciitilde{} \visible<2>{\textcolor{red}{1} +} \visible<2-3>{\textcolor{blue}{x}}}}}
\end{block}
\end{frame}

\begin{frame}
  \frametitle{Interpretation: Linear Models}
  \cimage[.8\linewidth]{img/extrapolating.png}
\end{frame}

\begin{frame}
  \frametitle{Interpretation: Decisions}
  \begin{enumerate}
  \item is the intercept meaningful?
    \begin{itemize}
    \item can I make it meaningful using \term{scaling}?\ars{\ra{} lec.6}
    \end{itemize}
    \spc\pause
  \item do the units of $y$ and $b$ aid interpretation?
    \begin{itemize}
    \item can I help interpretability using
      \term{standardisation}?\ars{\ra{} lec.8}
    \item often useful to report $b$s and $\beta$s
    \end{itemize}
\spc\pause
\item is the coding of nominal variables sensible?
  \begin{itemize}
  \item right intercept? \ars{\ra{} \R{relevel()} lec.8}
  \item \textcolor{gray}{could I use a better coding?}
  \end{itemize}

  \end{enumerate}
  
  
\end{frame}

\begin{frame}[fragile]
  \frametitle{Interpretation: Interactions}
\begin{columns}
  \column{.49\linewidth}
  \begin{itemize}
  \item \emph{really} useful to have worked through lab~8 (``One Direction'')
  \item<2-> although coffee is more interesting\ldots{}

\end{itemize}
\column{.5\linewidth}
\begin{overprint}
\onslide<1| handout:0>\cimage{img/1d}
\onslide<2-| handout:1>\cimage{img/n_coffee}
\end{overprint}
\end{columns}
\spc\pause[2]

<<coffee,include=F>>=
load('R/l8.Rdata')
coffee <- soup
rm(soup)
@ 
<<cof2>>=
summary(coffee)
@ 

\end{frame}


\begin{frame}[fragile]
  \frametitle{Two Models}
  \begin{itemize}
  \item without interaction
  \end{itemize}
<<tmod,eval=F>>=
mod.0 <- lm(SAT ~ fl + sc, data=coffee)
summary(mod.0)
@ 
<<tmod.1,echo=F>>=
mod.0 <- lm(SAT ~ fl + sc, data=coffee)
.pp(summary(mod.0),l=list(c(10:13)))
@ 
\begin{itemize}
\item with interaction
\end{itemize}
<<tmod.2,eval=F>>=
mod.1 <- lm(SAT ~ fl * sc, data=coffee)
summary(mod.1)
@ 
<<tmod.3,echo=F>>=
mod.1 <- lm(SAT ~ fl * sc, data=coffee)
.pp(summary(mod.1),l=list(c(10:14)))
@ 

\end{frame}

\begin{frame}[fragile]
  \frametitle{What Do the Models Say?}
<<doplot3,include=F,message=F>>=
require(rsm)
persp(mod.0, fl~sc,main='Coffee Satisfaction',col='red',zlim=c(-15,100))
persp(mod.1, fl~sc,main='Coffee Satisfaction',col='red',zlim=c(-15,100))
@ 
\begin{columns}
  \column{.49\linewidth}
 \cimage[.8\linewidth]{img/auto-doplot3-1}
\par
\begin{center}
without interaction  

<<c1a,eval=F>>=
coef(mod.0)
@ 
<<c1,echo=F>>=
t(coef(mod.0))
@ 

\end{center}
\column{.49\linewidth}
\cimage[.8\linewidth]{img/auto-doplot3-2}
\par
\begin{center}
with interaction
<<c2a,eval=F>>=
coef(mod.1)
@ 
<<c2,echo=F>>=
t(coef(mod.1))
@ 

\end{center}
\end{columns}
\atright{\hyperlink{rep}{\beamerskipbutton{skip stuff}}}

\end{frame}

\begin{frame}[fragile]{Some Sample Data}
<<loaddata,cache=F>>=
load(url('https://is.gd/usmrdata'))
# ls()
head(usmr)
@ 

\begin{itemize}
\item \R{lects}: lectures attended
\item \R{prac}: hours spent on lab work
\item \R{likestats}: whether a student likes stats
\item \R{PASS}: did they pass the course?
\end{itemize}

\end{frame}

\part{Reporting}
\section{Reporting}
\subsection[APA]{APA format}
\begin{frame}[plain,label=rep]
  \partpage
\end{frame}

\begin{frame}
  \frametitle{Reporting Results: General Formatting}
  \begin{itemize}
  \item primary source for psychology (and much empirical linguistics)
    is the American Psychology Association Publication Manual, 6th Edn.
    
  \item plenty of material on the website: \url{http://www.apastyle.org/}
  \end{itemize}
  \spc
  \pause
  \begin{itemize}
  \item there are formal ways to present statistical results
  \item plenty of good resources, e.g., \url{http://my.ilstu.edu/~jhkahn/apastats.html}
  \end{itemize}
\end{frame}

\subsection{Tables}
\begin{frame}
  \frametitle{Reporting Results: Tables}
  \begin{itemize}
  \item basic pointers
  \end{itemize}
  \spc
  \begin{enumerate}
  \item if you have fewer than 2 rows/columns, you don't need a table
  \item number tables sequentially and refer to them in text
    \begin{itemize}
    \item \smex{table~1 contains descriptive statistics\ldots}
    \end{itemize}
  \item be consistent in your formatting
    \begin{itemize}
    \item consistency is more important than exactly meeting APA standards
    \end{itemize}
  \item include a brief informative title/caption above the table

  \end{enumerate}
\end{frame}

\begin{frame}
  \frametitle{Example Table}
\begin{table}[h]
	\centering
	\caption{Proportions of trials in which participants referred
          disfluently to disfluency images for Experiments 1 and 2. Standard errors are given in parentheses.}\label{tab:disf}
 \begin{tabular}{llrr}\hline
\multicolumn{1}{l}{}&
\multicolumn{1}{l}{}&
\multicolumn{1}{c}{Confederate Absent}&
\multicolumn{1}{c}{Confederate Present}
\tabularnewline \hline
Exp.~1&Easy Images&$0.06~(0.06)$&$0.06~(0.06)$\tabularnewline
&Hard Images&$0.12~(0.12)$&$0.12~(0.12)$\tabularnewline
\hline
Exp.~2&Easy Images&$0.10~(0.06)$&$0.11~(0.07)$\tabularnewline
&Hard Images&$0.33~(0.10)$&$0.35~(0.10)$\tabularnewline
\hline
\end{tabular}
\end{table}
\end{frame}

\subsection{Figures}

\begin{frame}{Reporting Results: Figures}
  
  \cimage{img/axes.png}
  
\end{frame}


\begin{frame}
  \frametitle{Reporting Results: Figures}
  \begin{itemize}
  \item we spent a lot of time in early labs making graphs\ldots
  \end{itemize}
\spc
\begin{enumerate}
\item figures include all illustrations that aren't tables (chart,
  graph, photograph, drawing\ldots)
\item number figures sequentially and refer to them in text
  \begin{itemize}
  \item tables and figures have different numbering
  \end{itemize}
\item for graphs, make sure
  \begin{itemize}
  \item axes are labelled appropriately
  \item legends are included where necessary
  \end{itemize}
\item include a brief informative title/caption \emph{below} the figure
  
\end{enumerate}
  
\end{frame}


\begin{frame}
  \frametitle{Example Figure}
\begin{figure}[h]
\cimage{img/stutter_fig}  
\caption{Scatterplots showing, for each PWS, total number of onset
  errors (x axis) plotted against self ratings of difficulty speaking
  fluently in 10 commonly occurring speaking situation (y axis). From
  left to right, the three plots show raw numbers of onset errors in
  (1) inner speech; (2) overt speech (self-reports); and (3) overt
  speech (experimenter ratings). The unbroken regression line depicts
  the relationship between the two variables when two outliers (marked
  with $\circ$) are excluded.}
\end{figure}
\end{frame}

\begin{frame}
  \frametitle{Reporting Results: Do's and Don'ts}
  \begin{enumerate}
  \item don't repeat information (\emph{summarise} figures or tables
    in the text)
  \item be concise
  \item provide rationales for the decisions you make, and be
    consistent
  \item describe all your steps, but only include full diagnostic
    information for key analyses
  \end{enumerate}
  
\end{frame}

\mode<beamer>

{\usebackgroundtemplate{\includegraphics[width=\paperwidth]{img/fin}}
\begin{frame}[plain]
~
\end{frame}}

\mode
<all>


% \begin{frame}
%   \frametitle{The End\ldots}
%   \begin{itemize}
%   \item last lab \emph{3pm today}
%   \end{itemize}
  
%   \spc
%   \begin{block}{Office Hours}
%       \begin{itemize}
% \item  Martin \tabto{3cm} Thu \tabto{5cm} ~~9:30--11:00
% \item Alex \tabto{3cm} Mon \tabto{5cm} 14:30--16:30
% \item James \tabto{3cm} Tue, Wed \tabto{5cm} 11:00--12:00
      
 
%       \end{itemize}
   
 
%   \end{block}


% \end{frame}

\end{document}