研一上学期研究方法mbmz01lecture

1、MBMZ01 Research MethodologyChapter 18On MulticollinearityMulticollinearityMulticollinearity refers to the correlation among independent variables. MulticollinearityMulticollinearityTypical consequence of multicollinearity are shown in Exhibit 18.1 where multicollinearity between X1 and X2 is shown b

2、y the area d+d. Some variance that each explains is redundant (the area d). Consequently, the total variance explained in Y is less than the simple sum of the variance that each Xi explains.MulticollinearityMulticollinearityAdjusted R2 : Multiple coefficient of determination adjusted for sample size

3、 and number of independent variables. It is a better estimate of the parameter than is the unadjusted sample multiple coefficient of determination.MulticollinearityBeta estimates for all three independent variables have larger standard deviations in samples drawn from the population with multicollin

4、earity (Population 2). This shows that statistical power is reduced by multicollinearity.An examination of the signs of the beta coefficient is also revealing. Although the population betas are all positive, 23 of the sample coefficients are negative in Population 2. Only 4 of the sample betas are n

5、egative in Population 1.MulticollinearityPower is low in statistical tests from both populations (the sample sizes are only 25 in each size), but it is lower in the population with multicollinearity. Thirty of the 75 partial coefficients are statistically significant in samples from Population 1; on

6、ly 6 are statistically significant in samples from Population 2. Addressing Multicollinearity The best way to address multicollinearity is to view it in conceptual terms before data are collected and analyses are performed.Employee age; work experienceTerms to knowBouncing betasAdjusted R2Multicolli

7、nearityIn statistics, the occurrence of several independent variables in a multiple regression model are closely correlated to one another. Multicollinearity can cause strange results when attempting to study how well individual independent variables contribute to an understanding of the dependent v

8、ariable. In general, multicollinearity can cause wide confidence intervals and strange p values for independent variables. ( ) MulticollinearityCollinearity, where two IV are highly correlatedMulticollinearity, where more than two IV are highly correlatedWhen this condition exists, the estimated reg

9、ression coefficients can fluctuate widely from sample to sample, making it risky to interpret the coefficients as an indicator of the relative importance of predictor variables.Correlations at a .80 or greater level should be addressed.High intercorrelations between predictor variables suggest that

10、they are measuring the same construct.The presence of multicollinearity can be dealt in:Retain the variable that best captures the concept/construct you want to measure and delete the otherCreate a new variable that is a composite of the highly intercorrelated variables and use this new variable in

11、place of its componentsVariable Inflation Faction (VIF) index measure the effect of the other IV on a regression coefficient as a result of these correlations.VIF10, suggest collinearity or multicollinearityMulticollinearityMBMZ01 Research MethodologyChapter 19On Causal Models and Statistical Modeli

12、ngCausal ModelsThe empirical research most often is aimed at causal understanding.It focuses on using statistical models to evaluate causal models. A causal model specifies linkages between independent and dependent constructs in a causal chain.Causal model is a conceptual modelStatistical models ar

13、e used to help evaluate the tenability of causal modelsCausal ModelsRecursive models : Causal inference is assumed to go in only one direction, from the independent to the dependent variable.Endogenous variableVariable explained by a causal model. Dependent variables are always endogenous.Exogenous

14、variableIndependent variable in a causal model that is not explained by the model.IV can be endogenous if they depend on some other IVs in the modelExampleSee Exhibit 19.1Yearly salary serves as the dependent variable in all models.Independent variables include the following:Years of experience at t

15、he organizationJob levelPerformance ratingGenderSet of occupationsTwo variables formed by multiplying independent variables together (1) gender times years of experience (2) job level times years of experienceFour Illustrative ModelsDirect Effect ModelsMediated ModelsModerated ModelsHierarchical Mod

16、elsDirect Effect ModelsA direct effect refers to a causal relationship between an IV and a DV that is not mediated by some other variable. It is observed after other independent variables are controlled.When there are two or more IVs in a model, the direct effect of any one IV is represented by its

17、partial coefficient. Mediated ModelsIndirect effectIn a causal model, the influence of an IV that operates through a mediator variable.Total effectThe sum of the direct and indirect effects for any IV in mediated models.Salary and job level are endogenous; Only years of experience is exogenous.Media

18、ted ModelsSee Exhibit 19.3Take the partial regression for years of experience from Model 3 as its direct effect, $324.19.Estimate the influence of years of experience on job level. To do this, regression job level on years of experience. The equation is job level = .20 + .23 *(years of experience) M

19、ediated ModelsEstimate the indirect effect of years of experience on salary by multiplying its direct effect on job level times the direct effect of job level on salary (.23 *$4242.48 = $975.77). A unit change in years of experience in years of experience is expected to increase job level by .23. In

20、 turn, a .23 increase in job level is expected to increase salary by $975.77.The total effect of years of experience on salary is the sum of the direct and indirect effect ($975.77+ $324.19= $1299.96). Except for rounding error, this total effect equals the simple regression coefficient in Model 1 w

21、hen salary is regressed just on years of experience.The difference between the total and direct effects represents the indirect effects of the exogenous variable through the endogenous variables in the modelModerated ModelsGender moderates the relationship between years of experience and salary.Mode

22、rated ModelsSee Exhibit 19.6The direct effect of gender is $2742.80. Given the dummy coding of gender (male=1), the results indicate a $2742.80 advantage for men, controlling for years of experience; this is not statistically significant.Moderated RegressionModerated regressionRegression procedure i

23、n which an IV is created to capture the nonlinear effects of a moderator variable. A moderated regression accounts for the contingent relationship brought about by a moderator variable.A new variable that is the product of the two IVs can help.Moderated ModelsGiven the way the moderator variable was

24、 formed, the partial regression coefficient means males obtain $1248.94 more than females for each additional year of experience. The same result is obtained if you subtract the coefficient on years of experience in the female (Model 2) subgroup from the same coefficient in the male (Model 1) subgro

25、up ($1626.79-$377.84= $1248.95). See Research Highlight 19.4Moderated ModelsThe partial coefficient on years of experience indicates the predicted salary change when gender is equal to zero.The gender coefficient indicates the predicted difference between mens and womens salary at the time of hire (zero years of experience).Moderated ModelsCenteringThe coefficient for years of experience in Model 4 ($375.75) differs fr