Harrell 1
Randy E. Harrell
Professor Cristina De Leon-Menjivar
English 102
September 26, 2017
Reality of Personality
In My mistress eyes are nothing like the sun, poet William Shakespeare tells how
beauty is in the eye of the beholder, and that someone do
ASSIGNMENT (STATISTICS)
I HAVE USED( R PACKAGE) TO DO MY WORK.
1)Remarks; GRAPHS HAVE BEEN PASTED FROM R PROGRAMME INTO THEIR RESPECTIVE QUESTIONS
AND THE OTHER OUTPUT FROM R HAS ALSO BEEN PASTED DOWN FROM THE PAGE LABLED OUTPUT
2)THE PROGRAM CAN BE COPIE
1. A researcher wishes to estimate the average blood alcohol concentration for drivers
involved in fatal accidents who are found to have positive BAC(blood alcohol
concentration) values. He randomly selects records from 1100 such drivers in 2009 and
deter
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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
Smoothing Scatterplots
Using Penalized Splines
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What do we mean by smoothing?
Fitting a "smooth" curve to the data in a
scatterplot
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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
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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
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
Correspondence between
Experimental Designs and MixedEffect Models
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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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A
B
B
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B
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B
A
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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
A
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A
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.
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#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
Simulation and Analysis of Data
from a Classic Split Plot
Experimental Design
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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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A
B
B
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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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REML Estimation of
Variance Components
Copyright c 2012 (Iowa State University)
Statistics 511
1 / 31
Consider the General Linear Model
y = X + , where
N (0, )
and is an n n positive denite variance matrix that
depends on unknown parameters that are orga
COCHRAN-SATTERTHWAITE APPROXIMATION
FOR LINEAR COMBINATIONS OF MEAN SQUARES
Suppose M1 , ., Mk are independent mean squares and that
di Mi
2i
d
E(Mi )
i = 1, . . . , k.
It follows that
E
di M i
di Mi
E(Mi ) 2
di
= di , Var
= 2di , and Mi
E(Mi )
E(Mi )
THE ANOVA APPROACH TO THE ANALYSIS OF
LINEAR MIXED EFFECTS MODELS
We begin with a relatively simple special case. Suppose
yijk = + i + uij + eijk , (i = 1, . . . , t; j = 1, . . . , n; k = 1, . . . , m)
= (, 1 , . . . , t ) , u = (u11 , u12 , . . . , utn
THE AITKEN MODEL
y = X + ,
(0, 2 V )
Identical to the Gauss-Markov linear model except that
Var( ) = 2 V instead of 2 I.
V is assumed to be a known nonsingular variance matrix.
2 is an unknown positive variance parameter.
Copyright c 2012 (Iowa State Un
The F -test for Comparing Full and Reduced Models
Suppose the normal theory Gauss-Markov model holds.
y = X + ,
N (0, 2 I)
Suppose C (X0 ) C (X) and we wish to test
H0 : E(y) C (X0 ) vs. HA : E(y) C (X) \ C (X0 ).
Copyright c 2012 (Iowa State University)