Soc 3306 a Lecture 8 Multivariate 1 Using

  • Slides: 20
Download presentation
Soc 3306 a Lecture 8: Multivariate 1 Using Multiple Regression and Path Analysis to

Soc 3306 a Lecture 8: Multivariate 1 Using Multiple Regression and Path Analysis to Model Causality

Causality n Criteria: ¨ Association (correlation) ¨ Non-spuriousness ¨ Time order ¨ Theory (implied)

Causality n Criteria: ¨ Association (correlation) ¨ Non-spuriousness ¨ Time order ¨ Theory (implied)

Causation Evidence for causation cannot be attributed from correlational data n But can be

Causation Evidence for causation cannot be attributed from correlational data n But can be found in: n 1. the strength of the partial relationships (the bivariate relationship does not disappear when controlling for another variable) 2. assumed time order (derived from theory)

Path Analysis n n Can be used to test causality through the use of

Path Analysis n n Can be used to test causality through the use of bivariate and multivariate regression Note that you are only finding evidence for causality, not proving it. Can use the standardized coefficients (the beta weights) to determine the strengths of the direct and indirect relationships in a multivariate model Is variability in DV stochastic (chance) or can it be explained by systematic components (correctly specified IV’s)

STEP 1 Specify a model derived from theory and a set of hypotheses n

STEP 1 Specify a model derived from theory and a set of hypotheses n Example: Model would predict that the variation in the dependent variable SEI can be explained by four independent variables, SEX, EDUC, INCOME, and AGE n In other words, hypothesizes a causal relationship to explain SEI n

Hypothetical Model For SEI SEX EDUC SEI AGE Exogenous Variables INC Endogenous Variables

Hypothetical Model For SEI SEX EDUC SEI AGE Exogenous Variables INC Endogenous Variables

STEP 2 Test the bivariate correlations to determine which relationships are real. n Initial

STEP 2 Test the bivariate correlations to determine which relationships are real. n Initial correlation matrix showed that SEX was not significantly associated with any of the other variables except INCOME, which was a very weak negative relationship, so it was dropped from the model. n

Revised Hypothetical Model For SEI EDUC SEI AGE Exogenous Variables INC Endogenous Variables

Revised Hypothetical Model For SEI EDUC SEI AGE Exogenous Variables INC Endogenous Variables

Figure 1 Bivariate Correlations Examine correlations between SEI and IV’s n Moderately strong, positive

Figure 1 Bivariate Correlations Examine correlations between SEI and IV’s n Moderately strong, positive relationship between SEI and Education, a weakmoderate relationship with INCOME and a very weak, non-significant one with AGE n Look also at correlations between IV’s n Strong correlations between IV’s ( >. 700) can indicate multicollinearity n

STEP 3: Find Path Coefficients The direct and indirect path coefficients are the standardized

STEP 3: Find Path Coefficients The direct and indirect path coefficients are the standardized slopes or Beta Weights n To find them, a series of multiple regression models are tested n

Testing of Models n Model 1 ¨ SEI = AGE + EDUC + INC

Testing of Models n Model 1 ¨ SEI = AGE + EDUC + INC + e ¨ e = error or unexplained variance n Model 2 ¨ INC n = AGE + EDUC + e Model 3 ¨ EDUC = AGE + e

Figure 1: Model 1 n n n This is a full multiple regression model

Figure 1: Model 1 n n n This is a full multiple regression model to regress SEI on all IV’s Examine the scatterplots for linearity and homoscedasticity Interpret the model. Is it significant? Interpret R (multiple correlation coefficient) and Adj. R 2 (coefficient of determination) Interpret slopes, betas and significance. Check partial correlations. Add betas to model diagram

Figure 2: Model 2 Now we need to calculate the other relationships (Betas) in

Figure 2: Model 2 Now we need to calculate the other relationships (Betas) in the model n Regress INC on EDUC and AGE n Add betas to path diagram. n

Figure 3: Model 3 Regress EDUC on AGE n Again, add beta to path

Figure 3: Model 3 Regress EDUC on AGE n Again, add beta to path diagram. n

Causal Model For SEI EDUC -. 071** . 561*** . 226*** SEI. 175*** AGE

Causal Model For SEI EDUC -. 071** . 561*** . 226*** SEI. 175*** AGE . 182*** INC . 049 ns Exogenous Variables Endogenous Variables

STEP 4 Calculate Causal Effects n Causal Effect of Age: ¨ Indirect…. . AGE-INC->SEI=.

STEP 4 Calculate Causal Effects n Causal Effect of Age: ¨ Indirect…. . AGE-INC->SEI=. 182 x. 175=. 032 AGE-EDUC->SEI= -. 071 x. 561= -. 040 AGE-EDUC-INC->SEI= -. 071 x. 226 x. 175 = -. 003 ¨ Direct…. Age->SEI =. 049 ¨ Total Causal Effect Indirect + Direct= -. 011 +. 049 =. 038

Causal Effect of EDUC and INC n Causal Effect of EDUC: ¨ Indirect…. .

Causal Effect of EDUC and INC n Causal Effect of EDUC: ¨ Indirect…. . EDUC-INC->SEI=. 226 x. 175=. 040 ¨ Direct…. EDUC->SEI =. 561 ¨ Total Causal Effect Indirect + Direct=. 040 +. 561 =. 601 n Causal Effect of INC: ¨ Direct…. INC->SEI =. 175 Total Causal Effect =. 175

Issues Related to Path Analysis n n n Very sensitive to model specification Failure

Issues Related to Path Analysis n n n Very sensitive to model specification Failure to include relevant causal variables or inclusion of irrelevant variables can substantially affect the path coefficients Example: inclusion of AGE in above model Can build model one variable at a time and test for significant change in R 2 value until new additions do not significantly increase explanatory value of model further. But does not solve problem of irrelevant IV’s

SEM Best strategy is to also examine alternative explanatory models n One new technique

SEM Best strategy is to also examine alternative explanatory models n One new technique is structural equation modeling (SEM) using software (i. e. SPSS’s AMOS program) n Can test several models simultaneously n

Comment on SEI Model (above) n n n n Model shown above had adj.

Comment on SEI Model (above) n n n n Model shown above had adj. R 2 =. 396 Overall, INC, EDUC, AGE explained 39. 6% of variation in SEI But, unexplained variance (error) was 1 -. 396 =. 604 (stochastic component) 60. 4% of variation in SEI still unexplained Furthermore, causal effect of AGE only. 038 Drop AGE and consider other important IV’s (i. e. CLASS, OCCUPATIONAL PRESTIGE)? Specification error – model is underidentified

Soc 1 Soc 2 Soc 3 Soc 4Soc 1 Soc 2 Soc 3 Soc 4
Soc 3306 a Lecture 9 Multivariate 2 MoreSoc 3306 a Lecture 9 Multivariate 2 More
Soc 3306 a Lecture 11 Multivariate 4 ANOVASoc 3306 a Lecture 11 Multivariate 4 ANOVA
Soc 3306 a Lecture 10 Multivariate 3 TypesSoc 3306 a Lecture 10 Multivariate 3 Types
IRB 3306 Food and Beverage Management IRB 3306IRB 3306 Food and Beverage Management IRB 3306
Methoden der Psychologie Multivariate Analysemethoden Multivariate Distanz MultivariateMethoden der Psychologie Multivariate Analysemethoden Multivariate Distanz Multivariate
Multivariate Analysis 1 Multivariate Analysis n n MultivariateMultivariate Analysis 1 Multivariate Analysis n n Multivariate
Soc 3306 a Path Analysis Using Multiple RegressionSoc 3306 a Path Analysis Using Multiple Regression
SOC 1 vs SOC 2 vs SOC 3SOC 1 vs SOC 2 vs SOC 3
Soc 3306 a Lecture 12 The Research ReportSoc 3306 a Lecture 12 The Research Report
Soc 3306 a Lecture 5 Data Analysis OverviewSoc 3306 a Lecture 5 Data Analysis Overview
Soc 3306 a Lecture 2 Overview of SocialSoc 3306 a Lecture 2 Overview of Social
Soc 3306 a Lecture 3 Developing the ResearchSoc 3306 a Lecture 3 Developing the Research
Soc 3306 a Lecture 4 The Research ReportSoc 3306 a Lecture 4 The Research Report
Soc 3306 a The Research Report Revisiting theSoc 3306 a The Research Report Revisiting the
Soc 3306 a Individual Assignment 6 Introduction ForSoc 3306 a Individual Assignment 6 Introduction For
Soc 3306 a ANOVA and Regression Models OneWaySoc 3306 a ANOVA and Regression Models OneWay
Soc 3306 a Multiple Regression Testing a ModelSoc 3306 a Multiple Regression Testing a Model
SOC 206 LECTURE 2 Logic of Multivariate AnalysisSOC 206 LECTURE 2 Logic of Multivariate Analysis