Transcript LISREL: The short course - Victoria University of Wellington

LISREL:
The short course
Paul Jose
Nov. 8, 15, 22, 29
Victoria University
Okay, what are we going to do
here today?
• Overview of SEM
• Basic background on key statistical concepts (covariance)
• Introduction to confirmatory factor analysis—how does
CFA fit into a systematic research plan?
• Detailed example of a CFA
------------------------------------------------------------------------• Warning: I will at times be too technical, and at times I’ll
be too obvious and simple, but hopefully it will all work
out.
• Ask questions as I go. There are no stupid questions!
• What do you want me to cover in the last session?
• Homework? A prize for the best performance!
What is LISREL?
• LISREL stands for “Linear structural relations”,
written by Karl Joreskog and Dag Sorbom. Now at
version 8.51 (over 25 yrs.). Matrix-based.
• AMOS (Analysis of Moment Structures) is written
by Arbuckle at Temple Univ., linked to SPSS.
Diagrams.
• EQS (Equations) is written by Peter Bentler at
UCLA. Equation-based.
• There are others: CALIS, RAMONA, LISCOMP,
SEPATH.
• Which is the best? Tough question.
Okay, fine, but what do they do?
• They all can do SEM (structural equation
modeling).
• That’s not all they can do, but that’s their main
strength.
• What is SEM? There are a number of terms used
somewhat interchangeably. They are:
–
–
–
–
Covariance structure analysis;
Causal modeling;
Analysis of covariance structures;
Model fitting
LISREL specifically can do for
you . . .
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Confirmatory factor analysis
Observed variable path modeling
Latent variable path modeling
Longitudinal path modeling
Group comparisons on any parameter estimated in
any model (achieved through multi-group runs)
• Whiter teeth, smarter kids, and the envy of your
neighbors
Confirmatory Factor Analysis
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Why does one perform a CFA?
When does one perform a CFA?
How do I know if I have a good factor structure?
I hope that you didn’t answer “because they’re neat to run”;
“as often as possible”; and “if it looks good to me”; if you
did, then you need to listen for the next hour or so.
• You should perform a CFA to make sure that you have a
clear and reliable instrument.
• You should perform it before doing your main analyses.
• There are a number of indicators from LISREL that indicate
that you have a “good-fitting model”
Suggested method for using a
CFA
• Need to conduct a CFA after work has shown that
a measure has a reliable factor structure.
• Do it first in measure development? I don’t
recommend this.
• Two ways to do CFA:
– Use author(s)’ factor structure from previous work;
and/or
– Do the exploratory factor analysis yourself (if you have
sufficient sample size to divide into two equal subsamples)
Overview of LISREL model
• It’s all Greek to me!!!
• Yes, it’s true, all parameters in the model are
signified by a particular Greek letter.
• One does have to learn (re-learn) the names for
each peculiar squiggle because so much of the
input and output of LISREL depends on knowing
these associations.
• This model contains all possible parameters.
Almost all models that you actually run are
truncated versions of this one. (Observed variable
models lack multiple indicators.)
Computations are performed on
covariances
• What is a covariance? Definition please . . . .
• If I told you that the covariance between stress and
social support coping in a sample of 1115
adolescents was –91.018, what would you think?
• If I told you that the correlation was -.33, what
would you think?
• Covariancexy = (rxy) x (SDx) x (SDy)
• Correlationxy = (rxy) x (1) x (1)
Example of a covariance matrix
Correlation s
EM UCH
SOCSS
Pearson Correlation
Sig . (1-tai led)
Sum of Sq uares and
Cross-products
Covariance
N
Pearson Correlation
Sig . (1-tai led)
Sum of Sq uares and
Cross-products
Covariance
N
EM UCH
1.000
.
SOCSS
-.333**
.000
385660.3
-101394
346.194
1115
-.333**
.000
-91.018
1115
1.000
.
-101394
240697.8
-91.018
1115
216.066
1115
**. Correlation i s sig nificant at the 0.01 level
(1-tail ed).
Descriptive Statistics
EM UCH
SOCSS
Mean
21.7822
83.9944
Std. Deviation
18.6063
14.6992
N
1115
1115
Measurement model (CFA)
• Four key ingredients in a measurement model:
– Number of latent variables (NK = number of ksi)
– Pattern of factor loadings (PA LX gives the info of
whether a particular indicator loads on one ksi or
another; stands for “pattern of lambda xs”
– Info about how latent variables relate to each other (PH
matrix; phi matrix)
– Info about unique error in measured variables (TD or
theta delta)
LISREL command language
• Many options:
– Prelis: a preliminary data structuring program
– Interactive mode (new, I’m not familiar with it)
– Old style line commands (like old SPSS, etc.).
Sorry, but that’s the one I will teach
CFA command language
• Title line: anything that doesn’t start with any of
the main command language abbreviations: DA;
RA; SE; LA; MO; etc.
• DA: data line, specifies number of groups-NG;
number of indicators-NI; number of observationsNO; type of matrix analyzed-MA
• RA: raw data, gives address for data file
• LA: labels of all inputted variables
• SE: selects some of the inputted vars, be sure to
finish with a backslash
More LISREL commands
• MO: model line, number of X indicators-NX;
number of ksi’s-NK; lambda X matrix-LX; phi
matrix-PH; theta delta matrix-TD; and other
matrices
• PA LX: pattern of LX loadings
• LK: label of ksi’s
• PD: path diagram
• OU: output
• SS: standardized solutions for ksi’s
• SC: completely standardized
• AD: number of iterations
Values for variables
• Three types of specification of variable values:
– Free (FR): allows the program to estimate this value for
you;
– Fixed (FI): given a specific value, usually 1.0
– Contrained (CO): used in multi-group runs when want
to compare the size of parameters between two samples
on a single model
– Equalized (EQ): used in multi-group runs to equalize
parameters to test one that is not equalized
Two factor model
Confirmatory Factor Analysis of the Buss-Perry Aggression Questionnaire:
Two-factor model
DA NG=1 NI=13 NO=172 MA=CM
RA FI=c:\WPfiles\data\lisrelfiles\bussdemo\buss.dat
la
gender va1 ho1 pa1 ho2 ang1 va2 ang2 pa2 va3 ho3 pa3 ang3
SE
pa1 pa2 pa3 va1 va2 va3/
MO NX=6 NK=2 LX=FU,FR PH=ST TD=DI,FR
PA LX
1 0
1 0
1 0
0 1
0 1
0 1
LK
Physical Verbal
PD
OU SS SC AD=50
Model comparison
• One may wish to compare the fit of two different
models on the same dataset, for example a onefactor and a two-factor solutions to the Buss-Perry
Agg. Questionnaire.
• Does a single factor yield a better fit than two
separate factors?
• Compare them by doing two separate analyses;
one specifying one factor, and the other specifying
two factors.
• Logic of the comparison is that the chi-square
statistic gives one a good sense of how well the
model fits.
Model comparison
chi-square df
Baseline
Model
Two-factor
Model
119.95
9
18.71
8
Difference
101.24
1
--------------------------------------------------------------Look up whether this chi-square value is significant
or not for 1 df. It is!
Model fit
• There are many occasions where one just wants to
know whether a given model fits well for a given
sample.
• Chi-square is typically used. Which direction?
Large chi-sq (small p value) is bad; small chi-sq
(large p value) is good. Can’t use strict p < .05.
Chi-sq is susceptible to distortion due to sample
size also.
• So who are you going to call?
Absolute and relative fit
• Want to avoid overparameterization (too many)
and underpara-meterization (too few) in model.
• Want chi-sq to be as small as possible, but affected
by sample size.
• Want perfect fit AND parsimony—hard to have
both.
• There is no one “magic” fit index, although GFI is
most often used.
• Absolute fit: measures whether the links are
strong; Relative fit: compares model to saturated
model (see handout for specific indices).
• Want GFI > .90, RMSEA < .10, Critical N > 200
Do two samples show the same
factor structure?
• It may occur that you have a large sample that is composed
of two or more sub-samples (e.g., boys and girls), and
you’re curious whether the model fits both groups equally
well.
• Why care? Because it’s in your job description! No, it’s
because you care whether a given measure is
psychometrically reliable for whatever group you use it
for. For example, Buss-Perry for boys and girls: do the four
factors (verbal agg; physical agg; hostility; and anger exist
in the same relationships with each other for both groups?
Multi-group runs
• So, how does one compare two groups? Before,
one would typically do exploratory (or CFAs, if
sophisticated) on both samples and eyeball the
data.
• LISREL can compare the factor structure at
several different levels through the use of multigroup runs. In essence, running two model-fitting
analyses back-to-back in a single run.
3 types of measurement model
comparisons
• Congeneric measurement model: the two
groups should yield the same number and
type of ksi’s.
• Tau-equivalent: the loadings on the ksi’s are
generally equivalent (same # of ksi’s).
• Parallel measures: error variances are
similar (in addition to loadings and ksi’s).