Stat/For/Hort 571
Hanlon/Larget
September 9, 2011
Assignment #1 Due Friday, September 16 by 4:00 P.M.
Turn in homework to your TAs mailbox using this sheet as the cover page.
Fill in your name and also circle the lecture section in which you are registere
STAT 992/BMI 826
University of Wisconsin-Madison
Missing Data: Theory & Methods
Chapter 3
MLE in Regression Models with Missing Covariates
Lu Mao
[email protected]
3-1
Contents
3.1
Generalized Linear Models
3.2
EM by the Method of Weights
3.3
A Logist
Solution to Statistics 571 Midterm 2
Hanlon/Larget, Fall 2011
1.
Solution:
(a) According to the normal table, the 30th percentile is about 0.525 standard deviations below the mean, which
is 11.2 (0.525)(2.5) = 9.9.
(b)
10.0 11.2
Y 11.2
12.4 11.2
<
<
2.5
2
STAT 571
Qi Jiang
[email protected]
Discussion 2
I. Review
1. Random Varable:
(a) A random variable is a rule that attaches a numerical value to a chance outcome.
(b) Discrete Variable: Random variables with a countably innite set of possible values (i.
STAT 571
Qi Jiang
[email protected]
Discussion 5
R operations
1. Density Plot
The following examples show examples of density plots for the female sockeye salmon mass data
set. First, read in the data. There is a single variable named mass.
The density
STAT 571
Lilun Du
[email protected]
Discussion 9
Review Power and Sample Size
General formula of the sample size such that a P % condence interval constructed with margin of error
smaller than M .
Sample size for proportion:
z 0.5 2
) 4
n>(
M
where M
STAT 571
Lilun Du
[email protected]
Discussion 3
Practice Probelm
1. Consider a discrete random variable X with E(X) = 2.5. The probability distribution of X is given
by the following table.
k
P(X=k)
0
0.1
?
0.2
2
0.1
3
?
4
0.3
Fill in the missing val
STAT 571
Seho Park
[email protected]
Discussion 4
I. Review
1. General Addition Rule:
P (A B) = P (A) + P (B) P (A B)
2. Additional Rule for Mutually Exclusive Events:
If events A and B are mutually exclusive,
P (A B) = P (A) + P (B)
3. Probability of C
STAT 571
Seho Park
[email protected]
Discussion 10
I. Review Analysis of Variance
1. ANOVA:
(a) Compare means three or more populations H0 : 1 = 2 = = k
(b) Mathematical Model: Yij = i + ij = + i + ij . Yij is the jth observation of ith sample
(group) ,
STAT 571
Qi Jiang
[email protected]
Discussion 11
Practice Problem
Problem 1
A scientist wishes to investigate whehter glucose level in the diabetes patients has changed or not after
the patients have taken a kind of new drug. Previous records shows tha
R for Statistics 571
Bret Larget
August 25, 2011
1
Preliminaries
Before the rst discussion section, you ought to install R onto your computer. If you have laptop,
install R on the laptop and bring it to discussion section.
1.1
Installing R
To install R, c
Stat/For/Hort 571
Summary of Statistical methods
Ane/Keuler, Fall 2009
Tests to compare one sample of continuous values with a claim about the true mean 0 . Null hypothesis
H0 : = 0 . Common assumption: The sample is a random sample, i.e. independence of
Solution to Statistics 571 Midterm 1
Hanlon/Larget, Fall 2011
1.
(a)
Solution: Yes. While the researchers do not use a formal random sampling procedure, the researchers make
eorts to ensure that the redds they sample are representative of the redds in eac
STAT 571
Lilun Du
[email protected]
Discussion 6
Review Inference for One Population Mean
Point estimator: a natural point estimator for population mean is the sample mean X =
standard error = s/ n, where
n
n
Xi , with
i=1
(Xi X)2
i=1
s=
1
n
n1
.
samp
STAT 571
Seho Park
[email protected]
Discussion 7
I. Review- Inference for two sample population mean
1 and 2 are means from two populations. We are interested to test whether 1 = 2 (1 2 = 0).
There are mainly two kinds of methods t-test and randomizati
Contents
3.1
Generalized Linear Models
3.2
EM by the Method of Weights
3.3
A Logistic Regression Example with Missing Covariates
3.4
Generalized Linear Mixed Models with Missing Covariates
MLE in Regression Models with Missing Covariates
3-46
A Logistic R
STAT 992/BMI 826
University of Wisconsin-Madison
Missing Data: Theory & Methods
Chapter 6
The Estimating Equation Approach
Lu Mao
[email protected]
6-1
Contents
6.1
Basics of M Estimation
6.2
Inverse Probability Weighting for Missing Data
6.3
Doubly R
STAT 992/BMI 826
University of Wisconsin-Madison
Missing Data: Theory & Methods
Chapter 1
Introduction
Lu Mao
[email protected]
1-1
Introduction
Statistical analysis with missing data is a rich and important field owing to
the following two facts:
1.
STAT 992/BMI 826
University of Wisconsin-Madison
Missing Data: Theory & Methods
Chapter 4
Advanced Topics of the EM
Lu Mao
[email protected]
4-1
Contents
4.1
Nonparametric EM (NPEM)
4.2
Supplemented EM (SEM)
4.3
Expectation/Conditional Maximization (E
STAT 992/BMI 826
University of Wisconsin-Madison
Missing Data: Theory & Methods
Chapter 7
A Review
Lu Mao
[email protected]
7-1
Contents
7.1
Missingness Mechanisms and Identifiability
7.2
The Likelihood-Based Analysis Methods
7.3
The Inverse Weighting
Contents
3.1
Generalized Linear Models
3.2
EM by the Method of Weights
3.3
A Logistic Regression Example with Missing Covariates
3.4
Generalized Linear Mixed Models with Missing Covariates
MLE in Regression Models with Missing Covariates
3-19
EM by the Me
STAT 992/BMI 826
University of Wisconsin-Madison
Missing Data: Theory & Methods
Chapter 3
MLE in Regression Models with Missing Covariates
Lu Mao
[email protected]
3-1
Contents
3.1
Generalized Linear Models
3.2
EM by the Method of Weights
3.3
Examples
STAT 992/BMI 826
University of Wisconsin-Madison
Missing Data: Theory & Methods
Chapter 5
Multiple Imputation & Bayesian Analysis
Lu Mao
[email protected]
5-1
Contents
5.1
The Bayesian Paradigm
5.2
Bayesian Analysis
5.3
Multiple Imputation
Multiple Im
STAT 571
Lilun Du
[email protected]
Discussion 12
Review
0.1
Simple Linear Regression
The simple linear regression model for the data is
Yi = + Xi + i
where
1. i is the random vertical deviation between the line and the i th observed data point.
2. th
Solutions to Statistics 571 Midterm 2
Hanlon/Larget, Fall 2010
1.
Solution:
(a) The hypotheses are H0 : = 6 and HA : = 6 (as the test is two-sided). The test statistic is
T=
6.21 6
= 0.68
1.84/ 36
If the population is normal, the sampling distribution is
Inference for one Population Mean
Bret Hanlon and Bret Larget
Department of Statistics
University of WisconsinMadison
October 1214, 2010
One Population Mean
1 / 48
Body Temperature
Case Study
Body temperature varies within individuals over time (it can be
Stat/For/Hort 571
Hanlon/Larget
October 8, 2011
Assignment #5 Due Friday, October 14 by 4:00 P.M.
Turn in homework to your TAs mailbox using this sheet as the cover page.
Fill in your name and also circle the lecture section in which you are registered an
Stat/For/Hort 571
Hanlon/Larget
September 24, 2011
Assignment #3 Due Friday, September 30 by 4:00 P.M.
Turn in homework to your TAs mailbox using this sheet as the cover page.
Fill in your name and also circle the lecture section in which you are register