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The second model, for the case of a binary response,
is often called a logistic regression model.
Binary responses are common (success/failure,
survive/die, good customer/bad customer, win/lose,
etc.)
The logistic regression model can help us unde
Correspondence between
Experimental Designs and MixedEffect Models
1
Experimental Design Terminology
Experiment An investigation in which the
investigator applies some treatments to
experimental units and then observes the
effect of the treatments on the
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d=read.delim(
"http:/www.public.iastate.edu/~dnett/S511/SeedlingDryWeight2.txt"
)
d
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Genotype Tray Seedling SeedlingWeight
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These slides illustrate a few example R commands
that can be useful for the analysis of repeated
measures data.
We focus on the experiment designed to compare the
effectiveness of three strength training programs.
1
#Read the data
d=read.delim("http:/www.
MISCELLANEOUS TOPICS
RELATED TO LIKELIHOOD
Copyright c 2012 (Iowa State University)
Statistics 511
1 / 30
INFORMATION CRITERIA
Akaikes Information criterion is given by
AIC = 2 ( ) + 2k,
where ( ) is the maximized log likelihood and k is the
dimension of
REPEATED MEASURES
Copyright c 2012 (Iowa State University)
Statistics 511
1 / 29
Repeated Measures Example
In an exercise therapy study, subjects were assigned
to one of three weightlifting programs
i=1: The number of repetitions of weightlifting was
incr
Name:
STAT 544, Background
1. Which of the following is the denition of conditional probability?
(a) p(|y ) = p(, y )/p(y )
(c) p(|y ) = p(|y )p(y )
(b) p(|y ) = p(|y )/p(y )
(d) p(|y ) = p(, y )p(y )
2. Which of the following properly denes the marginal
Smoothing Scatterplots
Using Penalized Splines
1
What do we mean by smoothing?
Fitting a "smooth" curve to the data in a
scatterplot
2
Why would we want to fit a smooth curve
to the data in a scatterplot?
Imagine the model
yi=f(xi)+ei (i=1,n)
e1,en ~ inde
Solutions to some exercises from Bayesian Data Analysis,
second edition, by Gelman, Carlin, Stern, and Rubin
4 Mar 2012
These solutions are in progress. For more information on either the solutions or the book (published by CRC), check the website, http:/
An Introduction to
the Bootstrap
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As an example, let's see how the bootstrap works for
the law school example.
The goal there is to estimate the correlation between
average LSAT and average GPA in the p
A01 - Knowns (discussion)
Dr. Jarad Niemi
Iowa State University
Date created: January 17, 2013
Jarad Niemi (Iowa State)
A01 - Knowns (discussion)
Date created: January 17, 2013
1/7
Bayesian statistics
Bayesian statistics
Bayesian statistics
Bayesian stati
STAT 544 - Bayesian Statistics
Bayes rule
Dr. Jarad Niemi
Iowa State University
Date created: January 17, 2013
Jarad Niemi (Iowa State)
Bayes rule
Date created: January 17, 2013
1/8
Probability
Set theory
Events
Denition
The set, S , of all possible outco
STAT 544
Whats known?
Bayesian statistics uses conditional probability to describe uncertainty in the world about things that are
unknown (A) conditional on things that are known (B). The objective in this activity is for your team to
determine what is kn
Bayesian statistics
Dr. Jarad Niemi
Iowa State University
Date created: January 17, 2013
Jarad Niemi (Iowa State)
Bayesian statistics
Date created: January 17, 2013
1/7
Bayesian statistics
Bayesian statistics
Bayesian statistics
Recall the denition for Ba
Simulation and Analysis of Data
from a Classic Split Plot
Experimental Design
1
Split-Plot Experimental Designs
Plot
Field
Block 1
Genotype C
0
Block 2
100 150 50
Genotype B
150 100
50
0
Genotype A
Genotype A
50 100 150 0
Genotype A
0
Genotype B
150 100
G
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d=read.delim(
"http:/www.public.iastate.edu/~dnett/S511/SeedlingDryWeight2.txt"
)
d
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Genotype Tray Seedling SeedlingWeight
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Equivalence of the Reduced versus Full Model F test
and the F test of C beta = d
Storage Temperature
Storage Time
20oC
30oC
3 months
25
9 12 15
6 months
6677
16
_
_
time=factor(rep(c(3,6),each=5)
temp=factor(rep(c(20,30,20,30),c(2,3,4,1)
y=c(2,5,9,12,15,6
Example Analysis of an Unbalanced Two-Factor Experiment
An experiment was conducted to study the effect of storage time and
storage temperature on the amount of active ingredient present in a drug
at the end of storage. A total of 16 vials of the drug, ea
Introduction to the Gauss-Markov Linear
Model
Copyright c 2012 Dan Nettleton (Iowa State University)
Statistics 511
1 / 36
Random Vectors
y=
y1
y2
.
.
.
is a random vector if and only if each element of y is a
yn
random variable (i.e., yi is a random var
Proof of the Gauss-Markov Theorem
Copyright c 2012 Dan Nettleton (Iowa State University)
Statistics 511
1/8
The Gauss-Markov Theorem
Under the Gauss-Markov Linear Model, the OLS estimator c of
an estimable linear function c is the unique Best Linear
Unbia
Estimation of the Response Mean
Copyright c 2012 Dan Nettleton (Iowa State University)
Statistics 511
1 / 27
The Gauss-Markov Linear Model
y = X +
y is an n 1 random vector of responses.
X is an n p matrix of constants with columns corresponding to
explan
Estimating Estimable Functions of
Copyright c 2012 Dan Nettleton (Iowa State University)
Statistics 511
1 / 17
The Response Depends on Only through X
In the Gauss-Markov or Normal Theory Gauss-Markov Linear
Model, the distribution of y depends on only th
Alternative Parameterizations
Recall that the Gauss-Markov Linear Model simply says that
E(y) C (X) and Var(y) = 2 I for some 2 > 0.
Thus, as long as C (X) = C (W ), the following models are
identical.
y = X +
(0, 2 I)
y = W +
(0, 2 I)
opyright c 2010 D
Estimable Functions of : An Example
customer
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movie
123
41?
?35
?3
31?
Can we guess ratings
for customer/movie
combinations not
in the dataset?
yij
= customer is rating
of movie j
yij
= + ci + mj +
Copyright c 2010 (Iowa State University)
Which mov