Stat209/Ed260 D Rogosa 1/27/19
Assignment 3. Week 3 Path Analysis and Friends
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problem 1. Freedman, Blau-Duncan example in class handout,
Freedman text
Ch6 (revised) or Freedman links "Stat Models for Causation" (pp3-4)
Replicate class handout computations for the path analysis
plus questions from Freedman text
scan of pp.80-81 at (pp86-7 revised ed)
http://web.stanford.edu/~rag/stat209/DAFtextp8081.pdf
includes standardization material (Hookes Law) on week 2 class handout.
Freedman pp80-1 (set A)
prob 1
prob 5
prob 6
prob 8
pdf scan also includes freedman Set E,
p.97 prob 4(a,b) (p.103 revised)
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problem 2
freedman p.101 prob 5 (page 107 in revised version)
Causal Models of Publishing Productivity
This Homework 3 problem considers one of the path
analysis models from "Causal Models of Publishing
Productivity in Psychology", Rogers & Maranto,
J. Applied Psychology, 1989, 74(4), 636-649.
direct link to paper
http://content.apa.org/journals/apl/74/4/636.pdf
The path analysis conducted by the authors
from a sample of 86 men and 76 women is shown
in p.101 of Freedman's text and on page 647
of the publication; that page also exists at
http://www-stat.stanford.edu/~rag/stat209/pathpage647.pdf
You do have the correlation matrix from adding Table 7 fits and residuals.
But here all the problem asks you to do is look at and consider the usefulness
of this analysis. Note they don't display the disturbance paths so we don't
get a look at Rsq values.
What are the predictors of Pubs (direct effects) in this picture?
What are the predictors of Cites (direct effects) in this picture?
think about week1 results for these regression equations
The diagram provides estimates of supposed causal effects ("causal
model of publishing" is the article); it displays regression coeffs
, with coefficient estimates shown on the edges.
Consider a "productive
researcher" to be defined in terms of the number of publications and the
number of cites. The good news is that ability "affects" pubs and cites with
a positive coefficient in each case. Therefore, higher ability leads to a
more "productive researcher", according to the causal path gospel.
Some bad news is that sex is a predictor of pubs with a large coefficient
value. However, it is likely that there are confounding variables between
sex and pubs.
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3. Longitudinal path analysis example (Goldstein ex)
Longitudinal path analysis (based on the Goldstein example)
Apply the path analysis model taken from Goldstein (1979)
(in class handouts week3,also Rogosa eq 2 1988, "casual models...)
to verify results for path coefficients in eq 3 of Rogosa (1988)
(also in handouts).
Data are given in http://www-stat.stanford.edu/~rag/stat209/casualdat
using the top frame of 40 observations for variables (perfectly measured)
Xi(1) Xi(3) Xi(5) and taking the times of observation to
be 1 3 5 respectively.
These data are in wide form--each row is a subject.
you can verify, if you like, that each subject's data lies on a straight-line
(constant rate of change)
try pairs on the three measurements to see the scatter plots over persons.
Obtain values for the path coefficients and the muliple correlations
for the regression fits.
Can you obtain standard errors for the path coefficients for this small sample?
Any interpretations of the results from the path analysis?
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ENRICHMENT ITEM, Structural Equation Models
Problem 4 is an "enrichment" item, and you may want
to look at the solution which is linked.
For latent variable models with multiple indicators
How does structural equation model (latent vars) methods provide a
correction for measurement error?
Method-of-moments for two-variable, two-indicator model
For the Structural Equation Models handout from Joreskog
book, which is linked in the week 3 lecture materials (class handout) but
we did not take up in detail in class, obtain parameter estimates for the
no-correlated error version (9 parameters, top covariance matrix)
in terms of the sample variance and covariances among the four indicators (y_ij).
Brute force substitution will get you a non-optimal estimate,
suffices for instructional purposes.
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solution gives a nicely formatted solution
http://www-stat.stanford.edu/~rag/stat209/hw3p5.pdf
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end HW3 2019