#### 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 . . . • • • • • 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 • • • • 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).