1. ALISON BOWLING STRUCTURAL EQUATION MODELLING

2. WHAT IS SEM? Structural equation modelling is a collection of statistical techniques that allow a set of relationships between one of more IVs, either continuous or discrete, to be examined. DVs and IVs can be factors or measured variables CFA and path (mediation) analyses are special cases of SEM When exploratory factor analysis is combined with multiple regression analyses, you have SEM.

3. KINDS OF RESEARCH QUESTIONS Adequacy of the model How close is the estimated population covariance matrix to the sample covariance matrix Testing theory Which theory generates an estimated population covariance matrix that is most consistent with the sample? Variance How much variance in the DVs is accounted for by the Ivs? Reliability of the indicators Parameter estimates What are the path coefficients for a specific path?

4. ILLUSTRATION Markham, A, Thompson, T and Bowling, A. (2005) Determinants of Body Image Shame. Personality and individual differences, 38, 1529 – 1541. DV: Body image shame IVs : parental care, Parental Protection, Body-Image esteem, Global Self-Worth, Teasing History, Appearance Comparison, Internalisation of a Thin-Ideal.

5. FINAL MODEL

6. PRACTICAL ISSUES Sample size SEM is a large-sample technique How many participants per estimated parameter? Multivariate normality and absence of outliers Screen for skewness an kurtosis, and for univariate and multivariate outliers (Mahalanobis distance) Linearity: inspect scatterplots Absence of Multicollinearity and Singularity Residuals Residuals should be small and centered around zero. The frequency distribution should be symmetric. Residuals are residual covariances.

7. EXAMPLE: HEALTH DATA Hypothesis Perceived Illhealth and Poor Sense of self -> Health care utilisation (in women) Perceived illhealth: indicator variables Attitudes towards women’s roles (ATTROLE) Self-esteem (ESTEEM) Marital satisfaction ((ATTMAR) Locus of control (CONTROL) Perceived illhealth : indicator variables Number of mental health problems (MENHEAL) Number of physical health problems (PHYHEAL) Health care utilisation: indicator variables Visits to health professionals (TIMEDRS) Frequency of drug use (DRUGUSE)

8. Initial run. HYPOTHESISED MODEL

9. GOODNESS OF FIT Result (Default model) Minimum was achieved Chi-square = 176.770 Degrees of freedom = 32 Probability level =.000 Model NFI Delta1 RFI rho1 IFI Delta2 TLI rho2CFI Default model.782.693.814.734.811 Saturated model 1.000 Independence model.000

10. GOODNESS OF FIT (2) Model is not a good fit: CFI =.811 RMSEA =.101 ModelRMSEALO 90HI 90PCLOSE Default model.101.087.116.000 Independence model.196.184.208.000

11. IMPROVING MODEL FIT MODIFICATION INDICES M.I.Par Change F1<---age10.129.187 F2<---F317.106-1.132 attrole<---age23.761.690 attrole<---stress23.225-.012 esteem<---druguse13.284-.067 esteem<---timedrs10.075-.079 control<---age10.780-.082 control<---menheal13.284.049 druguse<---esteem10.394-.310 menheal<---F325.5411.030 menheal<---esteem18.216.178 menheal<---attmar17.592.079 menheal<---control22.403.613

12. IMPROVING FIT Step 1: Add a path from F3 (Poor sense of self) to MENHEAL will improve the fit  = 25.5 This improves model fit (  2 = 140.76) BUT The variance of e11 is negative (-.054) Step 2: Add a path from from Age to ATTROLE The model is further improved, but e11 is still negative. Step 3: Correlate the error terms e8 and e9 (cautiously considered as a final step - this covaries parts of the variables th)at are not common to Poor Sense of Self. Try e7 and e8; e2 and e3) Model fit is improved further, and negative correlation disappears.

13. FINAL MODEL

14. CAVEAT (TABACHNICK AND FIDELL) Adding post hoc paths is a little like eating salted peanuts – one is never enough. Extreme caution should be used when adding paths as they are generally post hoc and therefore capitalising on chance. Conservative p levels (p<0.001) may be used as a criterion for adding post hoc parameters to the model.

15. REGRESSION WEIGHTS EstimateS.E.C.R.PLabel stress<---age-15.7272.621-6.000***par_8 F1<---stress.011.0018.668***par_9 F1<---F3.448.2092.139.032par_10 F2<---F11.145.1597.202***par_11 menheal<---F11.000 phyheal<---F1.574.0599.765***par_1 timedrs<---F21.000 druguse<---F21.657.2227.461***par_2 control<---F3.697.0779.026***par_3 attmar<---F33.739.5177.240***par_4 esteem<---F32.388.2479.657***par_5 attrole<---F3.107.445.241.810par_6 menheal<---F31.333.2325.750***par_12 attrole<---age.630.1384.573***par_13