1. Assessing measurement invariance in cross-cultural research Hans Baumgartner Penn State University

2. Measurement invariance Jan-Benedict E.M. Steenkamp and Hans Baumgartner, “Assessing Measurement Invariance in Cross- National Consumer Research,” Journal of Consumer Research, 25 (June), 78-90.

3. Measurement invariance Key points  Types of invariance: □ configural □ metric □ scalar  Degree of invariance □ full □ partial  The type of invariance required depends on the goal of the research: □ comparison of relationships between constructs □ comparison of factor means

4. Measurement invariance x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x7x7 x8x8 11 22 1 x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x7x7 x8x8 11 22 1 Configural invariance Group 1: Group 2:

5. Measurement invariance x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x7x7 x8x8 11 22 1 x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x7x7 x8x8 11 22 1 Metric invariance Group 1: Group 2:

6. Measurement invariance x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x7x7 x8x8 11 22 1 x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x7x7 x8x8 11 22 1 Scalar invariance Group 1: Group 2:

7. Measurement invariance Key points  Types of invariance:  configural  metric  scalar  Degree of invariance  full  partial  The type of invariance required depends on the goal of the research:  comparison of relationships between constructs  comparison of factor means

8. Measurement invariance Partial measurement invariance  for identification purposes, one item per factor has to have invariant loadings and intercepts (marker item); the marker item has to be chosen carefully;  at least one other invariance constraint on the loadings/ intercepts is necessary to ascertain whether the marker item satisfies metric/scalar invariance;

9. Measurement invariance x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x7x7 x8x8 11 22 1 x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 x7x7 x8x8 11 22 1 Metric invariance Group 1: Group 2: 1 1 1 1

10. Measurement invariance Key points  Types of invariance:  configural  metric  scalar  Degree of invariance  full  partial  The type of invariance required depends on the goal of the research:  comparison of relationships between constructs  comparison of factor means

11. Measurement invariance Linking the types of invariance required to the research objective Configural invariance Metric invariance Scalar invariance Exploring the basic structure of the construct cross-nationally Examining structural relationships with other constructs cross- nationally Conducting cross- national comparisons of means

12. Measurement invariance Comparing relationships between constructs xy ξ η x y  1  xx  yy

13. Measurement invariance Comparing means of constructs x =  x + x  y =  y + y  E(x) =  x + x E(  E(y) =  y + y E(  xy ξ η x y  1  xx  yy

14. Measurement invariance He, Merz, and Alden (2008)  content analysis of 243 cross-nationally focused, empirical marketing articles published between 2000 and 2005 in 15 peer-reviewed journals;  67 articles (28%) reported assessing MI (in 82% of cases based on CFA);  for 41 articles (17% of the total) the type of MI assessed was consistent with the goal of the study;  assessment of MI was less likely if more countries were involved in the study and if single-item measures were used;

15. Measurement invariance He, Merz, and Alden (cont’d)  in a follow-up study, 86 authors indicated the following:  self-reported knowledge of MI assessment was relatively low (4.51 on 7-point scale);  MI assessment was not viewed as particularly important (4.12) [although positive correlation with knowledge];  MI assessment was not reported because o the data were not conducive to it o it was not viewed as necessary o familiarity with the method was insufficient

16. Measurement invariance Life satisfaction in Austria and the US  393 Austrian and 1181 U.S. respondents completed the Satisfaction with Life Scale (SWLS; Diener et al. 1985), which is a well-known instrument used to assess the cognitive component of subjective well-being. The scale consists of the following five items:  In most ways my life is close to my ideal.  The conditions of my life are excellent.  I am satisfied with my life.  So far I have gotten the important things I want in life.  If I could live my life over, I would change almost nothing.  Respondents indicated their agreement or disagreement with these statements using the following five-point scale: 1 = strongly disagree, 2 = disagree, 3 = neither agree nor disagree, 4 = agree, and 5 = strongly agree.  Perform an analysis of measurement invariance on the SWLS and test whether Austrian or American respondents are more satisfied with their lives (if possible).

17. Measurement invariance

18. Results: Final partial scalar invariance model Factor loadingsItem intercepts AUTUSAUTUS ls1.92 -.03 ls2.90.12 ls31.00 0.00 ls4.80.72 ls51.10.83.06 Latent meansAUT: 3.91US: 3.26

19. Measurement invariance Indicator means by country GROUP: AUT Means ls1 ls2 ls3 ls4 ls5 -------- -------- -------- -------- -------- 3.57 3.63 3.91 3.81 3.31 GROUP: USA Means ls1 ls2 ls3 ls4 ls5 -------- -------- -------- -------- -------- 2.97 3.04 3.26 3.33 2.75 Mean D.60.58.65.52.56 D/.65.65.65.65 ?

20. Measurement invariance What happens for ls5?  Difference in latent means is: 3.91 - 3.26 =.65  Adjusting for difference in loadings leads to a difference of : (1.1.0)(3.91) – (.83)(3.26) = 1.62  Adjusting for difference is intercepts leads to: (4.31 – 1.00) – (2.69 +.06) =.56

21. Measurement invariance