Conducting Path Analysis Tuba Gezer Doctoral Candidate Outline

Conducting Path Analysis Tuba Gezer Doctoral Candidate

Outline • What is path analysis • Rules for constructing causal diagrams • Key concepts • Running Path Analysis in SPSS • Steps of Structural Equation Modeling (SEM) • Running Path Analysis In AMOS

What is path analysis • “Path analysis allows one to examine the causal processes underlying the observed relationships and to estimate the relative importance of alternative paths of influence. ” (Asher 1983, pp. 36 -37) • Three rules to for establishing the existence of a causal relationship • Covariation • Time order • Non-spuriousness

What is path analysis • Path analysis is superior to regression • The correlation between X 1 and X 2 is. 20; Y and X 1 is. 047 and Y and X 2 is. 49.

What is path analysis • Under the umbrella of Structural Equation Modeling • Specify simultaneous regression equation • The art of path analysis is in specifying models that blend theory and statistical evidence • Graphic display of causal relations.

Rules for constructing causal diagrams • Variables names are represented either by short key words or letters. • Variables placed to the left in a diagram are assumed to be causally prior to those on the right. • Causal relationships between variables are represented by single-headed arrows. • Variables assumed to be correlated but not causally related are linked by a curved double-headed arrow.

Key concepts e • Causal Diagram • Exogenous variable X • Endogenous variable • Direct effect • Indirect effect Y

Key concepts • Activity: Please demonstrate exogenous variable, endogenous variable, direct effect, indirect effect on the following causal diagram

Key concepts • Recursive model • Non-recursive model • Residual Variable • Path analysis • Path coefficient (Hahs-Vaughn, 2017)

Running Path Analysis In SPSS We will run two separate regression analysis Motiv=SES+IQ+e GPA = SES + IQ +Motiv+e

Running Path Analysis in SPSS

GPA Example Amos Results

• Steps of Structural Equation Modeling (SEM)

• Steps of SEM • STEP 1: SPECIFICATION: Statement of theoretical model either as a set of equations or as a diagram. • STEP 2: IDENTIFICATION: The model can in theory and in practice be estimated with observed data • STEP 3: ESTIMATION: The model's parameters are statistically estimated from data. Multiple regression is one such estimation method, but typically more complicated estimated methods are used. Generally, a specialized SEM program (e. g. AMOS or LISREL) is used. • STEP 4: MODEL FIT: The estimated model parameters are used to predict the correlations or covariances between measured variables and the predicted correlations or covariances are compared to the observed correlations or covariances • STEP 5: MODIFY THE MODEL

Identification • Is the model recursive? • The number of variable=n • Total number of covariance terms n*(n+1)/2 • If total number of covariance terms is larger than the number of parameters in the model, the model is over-identified. • If total number of covariance terms is smaller than the number of parameters in the model, the model is under-identified. We cannot run the model. • If total number of covariance terms is equal the number of parameters in the model, the model is just-identified.

Identification Examples n=4 Total number of covariates=4*(4+1)/2=10 4+5+1=10 Df=10 -10=0 Just-identified model n=6 Total number of covariates=6*(6+1)/2=21 6+10+3=19 Df=21 -19=2 Over-identified model

Running Path Analysis in AMOS Carney, J. V. , Liu, Y. , and Hazler, R. J. (2018). A path analysis on school bullying and critical school environment variables: A social capital perspective. Children and Youth Services Review.

Write-Up A path analysis was conducted using Amos 26 to test the overall fit of the hypothetical model (Figure). There were 973 participants. Table 1 presents the correlation between variables. Indices of model-data fit considered were Chi-square test, root mean square error of approximation (RMSEA), standardized root mean squared residual (SRMR), comparative fit index (CFI), and Akaike’s Information Criterion (AIC). Browne and Cudeck (1993) suggested that RMSEA values greater than. 10 might indicate a lack of fit. In this study, the upper 90% confidence interval value lower than. 08 was used to suggest an acceptable fit. CFI values greater than. 90, which indicates that the proposed model is greater than 90% of than that of the baseline model, will serve as an indicator of adequate fit (Kline, 2016). Perfect model fit is indicated by SRMR = 0, and values greater than. 10 may indicate poor fit (Kline, 2016).

Write-Up Table 1 Pearson Correlation among Variables • A path analysis was conducted using Amos 26 to test the overall fit of the hypothetical model (Figure). There were 973 participants. Table 1 presents the correlation between variables. Indices of model-data fit considered were Chisquare test, root mean square error of approximation (RMSEA), standardized root mean squared residual (SRMR), comparative fit index (CFI), and Akaike’s Information Criterion (AIC). Browne and Cudeck (1993) suggested that RMSEA values greater than. 10 might indicate a lack of fit. In this study, the upper 90% confidence interval value lower than. 08 was used to suggest an acceptable fit. CFI values greater than. 90, which indicates that the proposed model is greater than 90% of than that of the baseline model, will serve as an indicator of adequate fit (Kline, 2016). Perfect model fit is indicated by SRMR = 0, and values greater than. 10 may indicate poor fit (Kline, 2016). b_bystan b_victim b_perp support diversity connect 13. 163 4. 204 2. 947 -0. 521 -1. 152 -0. 651 b_victim 11. 616 1. 954 -0. 978 -0. 851 -1. 345 b_perp 5. 706 -1. 457 -1. 518 -2. 314 support 12. 875 3. 989 7. 21 diversity 5. 148 4. 07 connect 12. 875

Write-Up The global fit of the model suggested a reasonable fit (Chi-square = 6. 23 (df=2), p =. 044; CFI=. 996; RMSEA=. 047 [90% CI: . 006 to. 09]; SRMR=. 0160). The regression weight between the between variables are reported in the Table 2. The model indicated several significant effects. Students’ perception of school support decreases 0. 16 unit if bullying perpetrating increase one unit. On the other hand, if school support increases one unit, school connectedness increases 0. 405 unit.

Write-Up Table 2 Unstandardized and Standardized Regression Coefficients the Model Estimate S. E. C. R. P Std Es. support <--- b_perp -0. 24 0. 049 -4. 919 *** -0. 16 support <--- b_victim -0. 044 0. 034 -1. 279 0. 201 -0. 042 diversity <--- b_perp -0. 172 0. 028 -6. 122 *** -0. 18 diversity <--- b_victim -0. 007 0. 019 -0. 374 0. 709 -0. 011 diversity <--- b_bystan -0. 035 0. 019 -1. 882 0. 06 -0. 057 diversity <--- support 0. 288 0. 017 16. 54 *** 0. 456 connect <--- b_perp -0. 209 0. 041 -5. 051 *** -0. 139 connect <--- b_victim -0. 038 0. 028 -1. 359 0. 174 -0. 036 connect <--- diversity 0. 423 0. 046 9. 108 *** 0. 268 connect <--- support 0. 405 0. 029 14. 162 *** 0. 405 connect <--- b_bystan 0. 063 0. 027 2. 291 0. 022 0. 063

Thanks!