Multiple Regression: II Three Types of Regression PSGE 7211

Goals I am still confused about… (10 minutes) Why are common causes important to include in my regression equation? Simultaneous regression analyses with 3 and 4 IVs How do I run a sequential regression analysis? What does it do? Why is stepwise regression the work of the devil? Prep for HW 4 Sequential regression analysis Checking for multicollinearity

Still confused… Computing scales Interpreting SPSS output (regression equation) Bs vs. Betas (what does standardized mean?)

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Writing up regression analyses Results Overview of purpose of the study Preliminary analyses Descriptives Correlational analyses Main analyses Regression analyses

No Multicollinearity Tolerance = ranges from 0 (no independence from other variables) to 1 (complete independence) Multicollinearity - when Tolerance is low (closer to 0; < .4) and VIF is high (> 2.5, become really concerned around 6, 7)

Multicollinearity Present ?

Parental Ed Grades Time HW

HWin ParEd GPA HWout Three IVs DV: 10th grade GPA (English, Math, Science, Social Studies) IVs: Parental Education (control) Time Spent on HW in School Time Spent on HW outside of School HWin ParEd GPA HWout

*Note the change in scales Frequencies *Note the change in scales

Predictions?

Regression Results

Note: Betas displayed (not Bs) Regression Results HWin ParEd GPA .23*** .26*** HWout Note: Betas displayed (not Bs)

Magnitude of Effects Significance level vs. Effect Size Keith’s rules: Applies to influences on school learning, relevance to other areas? Betas < .05: too small to be considered meaningful Betas > .05: small, but meaningful if statistically significant Betas > .10: moderate Betas > .25: large

HWin GPA HWout Four IVs ParEd PrAchvt DV: 10th grade GPA (English, Math, Science, Social Studies) IVs: Parental Education (control) Prior Achievement (control) Time Spent on HW in School Time Spent on HW outside of School HWin ParEd GPA PrAchvt HWout

Regression Results What changed?

Regression Results HWin ParEd .08* GPA .40*** PrAchvt .19*** HWout

Comparison of Coefficients Regression coefficients will often change depending on the variables including the regression analysis Without prior achievement, parent education has strong to moderate effect

Why do Coefficients Change?

Common Cause Common cause: important common causes must be included to interpret regression coefficients as valid effects

Indirect Effects The regression weight for parental involvement changed because of previous achievement; Parental education affects grades indirectly through prior achievement

Should R2 be low or high? For explanation, a high R2 is less important that proper variable selection; A high R2 is important for prediction R2 should be within expected range; explaining 25% of the variance may be surprisingly high or low A firm grounding in theory and prior research is critical for explanation

Multiple Regression IV1 IV1 IV2*** IV2 IV2 IV4** IV3 IV4 IV3 IV4 Simultaneous Sequential Stepwise Block 1 IV1 IV2 IV1 IV2 IV3 IV4 IV2*** IV4** Block 2 IV3 IV4 Block 3 IV1 x IV3

The Variables DV: 10th grade Social Studies Achievement (Standardized score on History, Civics, and Geography Test) IVs: SES (control) Previous Achievement (control) Self-esteem/Self-concept Locus of Control

All coefficients p<.001 Predictions? All coefficients p<.001

Simultaneous Regression Results

Regression Results

Purpose Simultaneous regression is useful for explanatory research to determine the extent of influence of one or more variables on a DV Can be used for prediction: Useful for determining the relative influence of variables

Strengths Useful for explanation, especially when guided by theory Allows comparison of relative effects/importance of variables Policy/intervention implications Estimates direct effects Order of variables in model unimportant

Weaknesses Results change based on which variables are included in analysis Implies a theoretical model (you should know what that model is) Estimates only direct effects

What to interpret Overall R2 Significance of Model and Regression Coefficients Magnitude of Bs: Useful for intervention; policy when variables are assessed on meaningful metric Magnitude of Betas: Useful for determining relative influence

Sequential Regression Results

Sequential Regression Results is it significant?

Sequential Regression Results

Sequential MR, Different Order

Sequential MR, Different Order

Sequential MR, Another Order

Why Order of Entry is Important The variance symbolized by area 3 is attributed to whichever variable, X1 or X2, is entered first

Sequential v. Simultaneous MR Simultaneous MR estimates direct paths (a), whereas sequential MR also estimates variance due to total effects (direct effect + indirect effect; a + e x d)

Order of Entry Sequential MR implies a model; You should think about what that model is! As you read others’ research, see if you can draw their “model” is it reasonable?

Variations of Sequential MR Interpretation from last step The regression coefficient from each step may be interpreted as the “total” effect of a variable Can enter variables in blocks; enter background/control variables simultaneously, variables of interest sequentially Enter variables simultaneous, enter interactions/curves sequentially (Chapters 7&8)

Total Effects

Unique Variance Some researchers add each variable last in a sequential regression to determine its “unique” effects/variance You can get the same info in simultaneous regression, if you request semipartial (part) correlations and square the part correlations to determine unique variance (see pg. 89 of text)

Purpose Explanation Is a variable (or block of variables) important for an outcome? Does a variable explain variance beyond that explained by other influences? Test for significance of interactions and curves Prediction Does a variable aid in predicting some criterion? Useful for determining the relative influence of variables

Strengths Useful for explanation, especially when guided by theory Useful for testing interactions and curves Estimates total effects in implied model

Weaknesses/Caveats Results change ( ) based on which variables are included in analysis Can over or underestimate effects based on order of entry Order of entry implies a theoretical model

What to interpret Statistical significance of Magnitude of May interpret coefficients... -- From final block (same as simultaneous) -- From each bock (total effects, given a model)

Stepwise MR Variables are entered in steps, one at a time Computer determines order of entry based on contribution of each variable to explained variance Varieties: Forward, Backward, Stepwise (combination)

Stepwise MR

Stepwise MR, continued

Purpose Is there a purpose? Mostly “theoretical garbage” (Wolfie, 1980) and “tool of the devil” (Keith, 2006) Could be used if prediction is your sole goal...however, you can also use simultaneous and sequential MR for that purpose

Strengths (?) Which subset of variables useful for efficient prediction Doesn’t require thought or theory

Weaknesses/Caveats Doesn’t require thought or theory Give up control to computer Cannot use for valid explanation Theoretical garbage

Final Thoughts See summary table on page 100 of textbook Consider purpose of your research, then choose appropriate method Can combine methods

HW 4 Using a dataset of your choice, run a sequential or hierarchical multiple regression analysis with three or more independent (continuous) variables. As always, interpret your regression analysis using APA style (see HW 4 wikipage for more information). As part of your interpretation, discuss how and why you chose the variables in your regression model. What theoretical model is implied by your analysis? How did you decide which variables to include and the order of entry? You must support your decision with references to theory and past research (this need not exceed a couple of paragraphs). Now that you have conducted one sequential analysis, change the order of entry of the variables. In other words, run an alternative sequential regression analysis. Do you note any changes in the significance of your regression coefficients? Why or why not?