#5 & #6 EDRE Regression Hypothetical Data file to use: Slide 18, in the Lecture #8 notes (I did not modify the data from what I used in the lecture!). Please note: I have not changed the data, so your values will be the same as what I have used in the lecture notes. All methods are in my lecture notes....be sure to copy the whole syntax and copy into a syntax window in SPSS. 1. Run the path analysis model on slide 18, in the Lecture #8 notes (hint: you must run this model using the syntax window. Do not try to run this using the regression command window. You will need to modify the regression command in the syntax window in order to run each of the required regression analyses for the path analysis model) a. Report the slope values (unstandardized) for each of the paths in the model. b. State the null and alternative hypotheses for each of the paths in the model. c. Which of the predictors was significant? d. Run a mediation analysis using the Sobel method to determine if there is any statistical evidence that family background influences coursework through the effects of family background on intellectual ability. 1. State the null and alternative hypotheses for the mediation analysis. 2. Report the Sobel test statistic along with its level of significance. 3. Please explain why or why not the mediation hypothesis was or was not supported. 4. If there was a significant mediation effect, was the mediation effect a \"full mediation effect\" or a \"partial mediation effect\". Justify your answer based on the results for the c path (i.e., the path from family background to academic coursework). 2. Please find one research article published in an educational research journal (e.g., American Educational Research Association Journal, Journal of Educational Psychology, etc) that used path analysis. It is likely that there are many analyses in the article that you found. Just pick one path analysis that is reported in the journal for the questions below. a. What is the null and alternative hypotheses. (note: it is unlikely that the authors will state the null/alternative....but you can easily state these two hypotheses). Reminder: state the null and alternative hypotheses for EACH of the paths in the path model. b. Report the regression findings with respect to the relations between the independent variables and the dependent variable. Note that the article may only report R2 or perhaps only the regression coefficients. Just pull from the article the relevant parameter estimates used in the regression analysis which indicate relations between the DV and the IV's. c. Using plain English, please summarize in a couple sentences what the path analysis indicated. Pretend you are explaining the findings to your grandmother - just indicate what was found and do not use any technical \"regression jargon\". EDRE 9000 Regression Analysis Chapter 12: Causal Models, PART II 1 HW's 3 & 4 HW#3 will also count for HW#4 I will count this homework twice - Once for HW #3 - Once for HW #4 2 Today we will...... Cover content included in Chapter 12. - Path Analysis - some assumptions and dangers - Testing a mediation effect 3 Assumptions of Path Analysis Assumptions from multiple regression hold for path analysis as well - Dependent variable is a linear function of the independent variables - Each person is drawn independently from the population. So performance of one person does not depend on performance of any other person in sample. - Errors are normally distributed and relatively constant for all values of the independent variable. 4 Assumptions of Path Analysis More Assumptions for Path Analysis - 1. Error term (aka disturbance) are not correlated with the predictor. That, of course, makes sense. Why? Predictor Outcome Error 5 Assumptions of Path Analysis More Assumptions for Path Analysis Good - 2. There is no reverse causation. That is, the model is recursive. Predictor Outcome Outcome Bad Outcome Predictor Outcome 6 Assumptions of Path Analysis NOTE: ordinary regression procedures can not be used to estimate nonrecursive models! 7 Assumptions of Path Analysis More Assumptions for Path Analysis - 3. The exogenous variables are measures with perfect reliability and validity An assumption that is rarely met!! If measures are reasonably reliable/valid that we assume that any bias in prediction is minimal. - 4. The \"causal process\" has had a chance to work. 8 So, this model would not make sense with 2 year olds that have not had any academic coursework! Academic Coursework Family Background (SES) Achievement Intellectual Ability Motivation 9 Assumptions of Path Analysis More Assumptions for Path Analysis - 5. No common cause of the presumed cause and the presumed effect has been omitted. The model includes all common causes..... Also, rarely met since we never know for sure what all of the common causes could be! Age is common cause Shoe size Reading Achievement 10 Assumptions of Path Analysis More Assumptions for Path Analysis - So, correlation between shoe size and reading achievement is \"spurious\". It is due to the common cause of age. Age is common cause Shoe size Reading Achievement 11 Assumptions of Path Analysis True Experiments and Common Causes - Experiments provide a way to examine cause and effect without the possibility of common causes in the model. common cause IV: Treatment vs control Reading Achievement 12 Assumptions of Path Analysis More Assumptions for Path Analysis - 6. Paths are in the right direction. Parent Involvement Previous Achievement Current GPA Which one is right?? Previous achievement Parent Involvement Current GPA 13 Mediation Analysis Sometimes, theory suggests that one variable influences another variable through another variable - Phonemic awareness training effects help children learn to read by influencing phonemic awareness IV-PA training versus control Phonemic awareness Reading 14 Mediation Analysis Sometimes, theory suggests that one variable influences another variable through another variable - SES influences GPA through parental involvement. SES Parental Involvement GPA 15 Mediation Analysis Let's watch video 16 Example of Mediation Analysis Remember this model from last class....let's look at whether or not SES influences Academic Coursework through SES effects on Intellectual Academic Ability.... Coursework Family Background (SES) Achievement Intellectual Ability Motivation 17 Example of Mediation Analysis Matrix data variables=fam_back ability motivate courses achieve /contents=n corr sd mean /format=lower diagonal. Begin data 1000 1000 1000 1000 1000 1.000 .417 1.000 .190 .205 1.000 .372 .498 .375 1.000 .417 .737 .255 .615 1.000 1.000 15.000 10.000 2.000 10.000 .000 100.000 50.000 4.000 50.000 End Data. Regression /Matrix=in(*) /dependent = achieve /method=enter fam_back ability motivate courses. 18 Example of Mediation Analysis We run the regressions to obtain the regression coefficients along with their standard errors in parentheses. Academic Coursework .398(.059)*** Family Background (SES) .055 (.004)*** 6.255(.432)*** Intellectual Ability ZSobel = 9.97(SE = .034), p < .001 . Link for conducting Sobel test 19 Mediation Analysis The Sobel test for mediation indicated that there was a significant partial mediation of family background on academic coursework through the effects of family background on intellectual ability. There was also a direct effect of family background on academic coursework while controlling for intellectual ability. 20