PLS structural Equation Modeling for Customer Satisfaction -Methodological and Application Issues-

Transcription

1 PLS structural Equation Modeling for Customer Satisfaction -Methodological and Application Issues- Kai Kristensen, J. Eskildsen, H.J. Juhl, P. Østergaard Centre for Corporate Performance The Aarhus School of Business, Denmark

2 Agenda The EPSI Rating Model Latent Structure Manifests A few recent results The Danish car market External validity Practical problems and observations The choice of scale Reliability:The choice of manifests Explanatory power Missing values Multicollinearity Some results from a simulation study 2

3 The EPSI Rating Model: Latent structure Image Expectations Perceived Value Customer Satisfaction Loyalty Perceived Quality Hardware Perceived Quality Software 3

4 EPSI Rating model Generic model with 7 latent constructs 4 latent exogenous constructs (Image, expectation, quality of hardware and software) 3 endogenous constructs (perception of value, satisfaction and loyalty) Each construct is determined by 3-6 manifest measurements. The model is estimated by use of PLS (Partial Least Squares estimation techniques. 4

5 Examples of manifest measurements Image: General perception of company image with regard to: Reliability Being customer focussed Giving value for money Innovation in products and services Overall image Satisfaction: Overall satisfaction Comparison to ideal Disconfirmation Loyalty: The customer's intention to repurchase, Intention of cross buying (buy another product from the same company), Intention to recommend the brand/company to other consumers. 5

6 Example from the Danish car industry IMAGE EXPECTATIONS QUALITY OF "HARDWARE" QUALITY OF "SOFTWARE" VALUE SATISFACTION LOYALTY Index

7 Individual brands SATISFACTION 2001 SATISFACTION Index Peugeot VW Ford Toyota Opel Citroen Mazda Fiat Other 7

8 Inner coefficients for the 2002 model UNSTANDARDISED INNER COEFFICIENTS EXPECTA- TIONS QUALITY OF "HARDWARE" QUALITY OF "HUMAN WARE" SATISFAC- TION IMAGE VALUE IMAGE EXPECTATIONS QUALITY OF "HARDWARE" QUALITY OF "HUMAN WARE" VALUE 0,36-0,06 0,35 0,32 SATISFACTION 0,44-0,03 0,23 LOYALTY 0,29-0,11 0,24 0,27 0,53 T-VALUES FOR INNER COEFFICIENTS EXPECTA- TIONS QUALITY OF "HARDWARE" QUALITY OF "HUMAN WARE" SATISFAC- TION IMAGE VALUE IMAGE EXPECTATIONS QUALITY OF "HARDWARE" QUALITY OF "HUMAN WARE" VALUE 14,72-3,38 11,30 11,21 SATISFACTION 20,93-1,80 9,06 10,82 5,54 LOYALTY 7,10-4,08 5,22 6,10 13,84 LOYALTY LOYALTY 8

9 The impact of drivers on satisfaction and loyalty 2001 & 2002 Satisfaction 2001 Satisfaction 2002 Loyalty 2001 Loyalty 2002 Impact -0,2-0,1 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 Image 0,47 0,53 0,57 0,54 Drivers Expectations Quality of "hardware" -0,13-0,03 0,01 0,01 0,31 0,26 0,33 0,38 Quality of "software" 0,22 0,29 0,33 0,42 9

10 External validity: Relation to actual service performance 84 Index on "Human ware" in Toyota Mazda Opel VW Other Fiat Peugeot Citroen Ford y = -36,036x + 103,99 R 2 = 0, ,0% 65,0% 70,0% 75,0% 80,0% 85,0% 90,0% Percentage cars with defects 10

11 External validity: Relationship between satisfaction and complaints 0,004 Complaints: Proportion of population mentioned on selfreporting homepage 0,0035 Peugeot 0,003 Citroen 0,0025 VW 0,002 Fiat 0,0015 0,001 Other Ford Opel y = 6E+17x -11,008 R 2 = 0,643 Toyota 0,0005 Mazda Average satisfaction 2001 &

12 Practical problems and observations The Choice of Scale

13 The experiment In order to test the effect of scale choice on the results of customer satisfaction studies a controlled experiment was set up. Under totally identical conditions two samples were drawn from the population. The only difference between the samples was that in the first sample a 5-point scale was used and in the second a 10-point scale was used. The questionnaires were the standard customer satisfaction questionnaires used for a given company. The size of the samples was 545 for the 10-point scale and 563 for the 5-point scale. 13

14 Mean value of latent variables Data source Ten points Five points Variable Mean Mean Significance, two sided Expectations 73,3 75,1 0,13 Products 64,2 64,3 0,88 Service 66,9 66,4 0,70 Value 54,4 54,4 0,96 Satisfaction 65,2 65,2 0,97 Loyalty 57,5 58,7 0,36 Image 63,6 64,0 0,74 14

15 Conclusion: Mean values There is no significant difference between the mean values of the aggregate variables. This means that the choice of scale has no influence on the level of the customer satisfaction index or the loyalty index. 15

16 Standard deviation of aggregate variables Data source Ten points Five points Variable Std Deviation Std Deviation Significance Expectations 19,2 20,1 0,476 Products 19,1 20,5 0,274 Service 21,2 23,4 0,014 Value 19,7 22,4 0,005 Satisfaction 19,3 21,5 0,013 Loyalty 21,7 23,6 0,054 Image 18,1 19,5 0,069 16

17 Conclusion: Latent variable standard deviations As expected the standard deviation of the 10- point scale is smaller than the standard deviation of the 5-point scale with Image, Expectations and Products as possible exceptions. The difference is on the average app. 10%. The reason for this difference is, that the underlying distributions are discrete. 17

18 5- and 10-point scales Shape of the distribution 18

19 Satisfaction: Distribution 10 point scale Mean: 65.2 Std. dev.: Satisfaction 19

20 Comparison of observed and theoretical distributions. (10-point scale) 0,5 0,4 0,3 0,2 Observed Normal Beta 10 0,

21 Satisfaction: Distribution 5 point scale Mean: 65.2 Std. dev.: Satisfaction 21

22 Comparison of observed and theoretical distributions. (5-point scale) 0,4 0,3 0,2 Observed Normal Beta 5 0,

23 A comparison of satisfaction distributions % point 5-point 23

24 Satisfaction: A general comparison of the distribution of 5- and 10-point scales Kolmogorov-Smirnov Z Asymp. Sig. (2-tailed) Image 1,08 0,19 Expectations 2,53 0,00 Products 1,41 0,04 Service 1,63 0,01 Value 1,95 0,00 Satisfaction 1,77 0,00 Loyalty 1,53 0,02 24

25 Conclusion In general the standardized distributions are not identical with Image as a possible exception. This is to be expected due to the discrete underlying distributions. The beta distribution or the doubly truncated normal distribution seem to give the closest approximation to the distribution but even here we have a significant difference in both cases. 25

26 5- and 10- point scales Are demographics and scale interacting? 26

27 Variables and factors for the analysis of variance Dependent variables: All aggregate variables Explanatory variables Data Source (5-point, 10-point) Age (-25, 26-35, 36-45, 46-55, ) Education ( 8 groups from high school to university) Gender (Male, Female) Location (Copenhagen, Sealand, Funen, Jutland) 27

28 Analysis of variance (10% significance) Image Expectation Product Service Value Satisfaction Loyalty Main Age Location Location Age NONE Age Location Education Location Education Location Education Location Education Gender Gender Two-way interaction NONE Age x source NONE NONE Age x source NONE NONE 28

29 Conclusion In the case of Image, Product, Service, Satisfaction and Loyalty there is no effect from the data source. Only in the case of Expectation and Value we can trace an effect. In these cases there is a tendency that the age groups are using the scales differently. Based on this our general conclusion is, that the demographic interpretation of customer satisfaction studies will not be seriously affected by the choice of scale. When it comes to satisfaction there seems to be a universal main effect of Age, Location and Education. Satisfaction is increasing with age and decreasing with education. Satisfaction is decreasing with the degree of urbanization. 29

30 Conclusions concerning scales In general terms a 10-point scale is preferable to a five point scale: Smaller variance. Closer approximation to a continuous variable. 10-point scales are used by all the major national customer satisfaction studies. In general it is possible to compare studies using 5 and 10- point scales since the mean values (on a 100-point scale) are not affected. Demographics have a small but not very important effect on the results from the scales. 30

31 Practical problems and observations Reliability and prediction

32 Internal reliability and validity of the results: The car example IMAGE EXPECTA- TIONS QUALITY OF "HARDWA RE" QUALITY OF "HUMAN WARE" VALUE SATISFAC- TION LOYALTY R-SQUARE FOR LATENT VARIABLES 0,56 0,76 0,55 COMPOSITE RELIABILITY 0,92 0,95 0,89 0,86 0,97 0,90 0,91 AVERAGE VARIANCE EXPLAINED BY LATENT VARIABLES 0,69 0,86 0,73 0,68 0,91 0,75 0,84 R-SQUARE FOR LATENT VARIABLES 0,62 0,72 0,56 COMPOSITE RELIABILITY 0,92 0,94 0,91 0,90 0,97 0,90 0,91 AVERAGE VARIANCE EXPLAINED BY LATENT VARIABLES 0,71 0,84 0,77 0,75 0,91 0,74 0,84 AVE = p i= 1 p i= 1 λ 2 i ( 2 λ +Θ) i i i= 1 c p 2 ρ = p λ 2 p λ + Θ i i= 1 i= 1 i i 32

33 Reliability and choice of manifests Automobiles Reasonable reliability: No reason for changes. Petrol stations High reliability: No reason for changes. Banks: In the satisfaction construct the comparison to ideal may cause a problem. Much lower level than the two other questions. Supermarkets In the satisfaction construct the comparison to ideal may cause a problem. Much lower level than the two other questions. The value for money indicator and the assortment indicator may cause a problem since they reflect the type of supermarket. The question about opening hours which is classified as belonging to the service block should possibly be re-classified 33

34 Reliability and choice of manifests: Conclusions For most of the areas covered by the Danish Customer Satisfaction Index the manifest questions are working well. The only area where we have observed a necessity for changes is Supermarkets. Other conclusions may apply when we have discussed the problem of missing values. 34

35 Explanatory power The general observation is, that the explanatory power of the model is rather good. There is no problem in obtaining an R 2 beyond.65 for the satisfaction construct as required by the ECSI Technical Committee. In general R 2 is somewhere between.70 and.80. The degree of explanation for value and loyalty is usually a little lower. 35

36 Practical problems and observations Missing values and multicollinearity

37 Missing values Supermarkets Banks Automobiles Petrol Stations Below 10% for all items Relative comparisons are problematic % missing values 19 out of 22 items have missing values below 5% 13 out of 22 have missing values below 10%. 8 have missing values between 10% and 20% 37

38 Multicollinearity (Latent variables) In general the degree of multicollinearity is rather high. Banks: Correlations between.54 (expectation and service) and.82 (product and service). Petrol stations: Correlations between.42 (expectations and service) and.69 (product and service). Automobiles: Correlations between.48 (expectations and service) and.85 (product and service). Mobile telephones: Correlations between.44 (expectations and service) and.76 (product and service). Supermarkets: Correlations between.52 (expectations and image) and.71 (image and product). 38

39 Simulation study A study of some of the implications of the empirical findings

40 Background To get insight into the consequences of some of the empirical problems based on a true model which is very close to the actual models observed. Our model is reflective for all latent variables. To formulate some simple rules of thumb. To supplement and verify the simulation study conducted by Cassel, Hackl and Westlund (1999, 2000). These authors investigated the effect of the following factors on the estimation of an EPSI like model with formative exogenous and reflective endogenous latent variables: Skewness of manifest variables Multicollinearity between latent variables Misspecification (omission of relevant regressors or regressands, or manifests within a measurement model) Sample size Size of the path coefficients 40

41 Simulation setup STAGE 1(Screening): Orthogonal main effect plan with 7 factors in 27 runs with 25 replications for each run. Each replication has a number of observations varying between 50 and Exogenous distribution (Beta vs. Normal) Multicollinearity between latent exogenous variables Indicator validity (bias) Indicator reliability (standard deviation within a block) Structural model specification error Sample size Number of indicators in each block STAGE 2: Full factorial design with 4 factors in 54 runs with 25 replications for each run Multicollinearity, reliability, sample size and number of indicators 41

42 Stage 2 factor levels and response variables FACTOR LEVELS: Multicollinearity: ρ={0.2;0.8}. Reliability: σ={1; 10; 20}. Sample size: n={50; 250; 1000}. Number of indicators: p={2; 4; 6}. RESPONSE VARIABLES: Absolute bias for indices Standard deviation for indices Bias for path coefficients R 2, AVE and RMSE. 42

43 The simulation model (A simplified customer satisfaction model) x ε 1 x x λ *Beta(4,3) x ε 2 x ε 3 x ε 4 x 2 x 3 x 4 x λ 21 φ 12 x λ 32 x λ 42 G 1 G 2 γ = γ = y λ 32 γ = G 3 y λ 42 y3 y4 y ε 3 y ε 4 β = ζ 2 ζ 1 G 4 y λ 11 y λ 21 y 1 y 2 y ε 1 y ε 2 43

44 Simulation results F1 F2 F3 F4 Multicollinearity Indicator reliability Sample size # indicators F1*F2 F1*F3 F1*F4 F2*F3 F2*F4 F3*F4 g1 ** ** ** ** ** ** g2 ** ** ** ** ** ** g3 ** ** ** ** ** ** g4 ** ** ** ** ** ** stdg1 ** ** ** ** ** stdg2 ** ** ** ** ** stdg3 ** ** ** ** ** ** stdg4 ** ** * ** ** ** gamma21 ** ** ** ** * ** ** gamma22 ** ** ** ** ** gamma11 ** ** ** ** ** ** beta12 ** ** ** ** ** ** stdgam21 ** ** ** ** ** ** ** ** ** stdgam22 ** ** ** ** ** ** ** ** ** stdgam11 ** ** ** ** ** ** ** ** ** stdbet12 ** ** ** ** ** ** ** ** ** rsq1 ** ** ** ** rsq2 ** ** ** ** ** ave1 ** ** ** ave2 ** ** * ave3 ** ** * * ave4 ** ** ** * avetot ** ** * rmse ** ** ** ** ** ** ** ** 44

45 Bias of indices: Multicollinearity and indicator reliability,80,8,60,6 Mean absolute bias,40 G1 Mean absolute bias,4 G1,20 G2,2 G2 G3 G3 0,00 phi=0.2 phi=0.8 G4 0,0 sigma=1 sigma=10 sigma=20 G4 Multicollinearity Indicator reliability 45

46 Bias of indices: Sample size and number of indicators,8,8,6,6 Mean absolute bias,4 G1 Mean absolute bias,4 G1,2 G2,2 G2 G3 G3 0,0 n=50 n=250 n=1000 G4 0, G4 Sample size Number of indicators 46

47 Example of mean relative bias for Gamma 21 8,0 8,0 Mean Relative bias Gamma21 (%) 7,5 7,0 6,5 6,0 5,5 5,0 4,5 Mean Relative bias Gamma21 (%) 7,5 7,0 6,5 6,0 5,5 5,0 4,5 4,0 n=50 n=250 n=1000 4, Sample size Number of indicators 47

48 Example of mean relative bias for Beta 12-4,0-4 -5,0-5 Mean Relative Bias Beta12 (%) -6,0-7,0-8,0-9,0 Mean Relative Bias Beta12 (%) , ,0 n=50 n=250 n= Sample size Number of indicators 48

49 Standard deviation of Gamma 21 as a function of multicollinearity and indicator reliability,060,06 Mean Std. dev. Gamma 21,040,020 Mean Std. dev. Gamma 21,04,02 0,000 phi=0.2 phi=0.8 0,00 sigma=1 sigma=10 sigma=20 Multicollinearity Indicator reliability 49

50 Standard deviation of Gamma 21 as a function of sample size and number of indicators,06,060 Mean Std. dev. Gamma 21,04,02 Mean Std. dev. Gamma 21,040,020 0,00 n=50 n=250 n=1000 0, Sample size Number of indicators 50

51 Degree of explanation. 1,0 1,00,9,90 Mean RSQ,8 Mean RSQ,80,7,70 RSQ1 RSQ1,6 sigma=1 sigma=10 sigma=20 RSQ2, RSQ2 Indicator reliability Number of indicators 51

52 Average variance extracted. 1,00 1,0,90,9 Mean AVETOT,80 Mean AVETOT,8,70,7, ,6 sigma=1 sigma=10 sigma=20 Number of indicators Indicator reliability 52

53 A couple of rough rules of thumb concerning the absolute bias of the indices Let σ be the standard deviation of the manifest variables, n the sample size, and p the number of indicators, then: BIAS(kσ,n,p) = k BIAS(σ,n,p). BIAS(σ,kn,p) = (1/ k) BIAS(σ,n,p). BIAS(σ,n,kp) = (1/k) BIAS(σ,n,p). 53

54 Conclusion to the simulation study Basically our results support The Cassel, Hackl, Westlund results where comparable: Misspecification is in general a serious problem with severe parameter bias. Skewness of distribution is of minor importance to the PLS estimates. Multicollinearity between the latent variables is without importance for the estimated indices. It has a significant but small impact on the bias of the path coefficients. It has a significant effect on all standard deviations. Size of the sample has no influence on the bias of the path coefficients. It has a large effect on all standard deviations. In addition: Indicator reliability has an enormous influence on all measured responses, i.e. bias, standard deviation and fit measures. Furthermore several cases of two-factor interaction with both multicollinearity, sample size, and the number of indicators were found. Likewise the number of indicators has a strong impact on all responses, and also a strong two-factor interaction with sample size and reliability. 54

55 General conclusion PLS provides reasonably robust estimates of a customer satisfaction index in a usual practical setting where the sample size is n=250, the standard deviation around σ=20, and the average multicollinearity around ρ=.60. In a usual practical setting the bias of the indices is low and usually not larger than.50 (on a 100 point scale). The parameter estimates are in general biased. The bias can be both positive and negative depending on the model structure. The relative bias will in a usual practical setting be in the area of 10-20%. 55