Messung und statistische Analyse von Kundenzufriedenheit

1. Messung und statistische Analyse von Kundenzufriedenheit KF Qualitätsmanagement Vertiefungskurs V

2. Outline • Customer satisfaction measurement • The Structural Equation Model (SEM) • Estimation of SEMs • Evaluation of SEMs • Practice of SEM-Analysis Messung & Analyse von Kundenzufriedenheit

3. The ACSI Model Ref.:http://www.theacsi.org/model.htm Messung & Analyse von Kundenzufriedenheit

4. ACSI-Model: Latent Variables • Customer Expectations: combine customers’ experiences and information about it via media, advertising, salespersons, and word-of-mouth from other customers • Perceived Quality: overall quality, reliability, the extent to which a product/service meets the customer’s needs • Customer Satisfaction: overall satisfaction, fulfillment of expectations, comparison with ideal • Perceived Value: overall price given quality and overall quality given price • Customer Complaints: percentage of respondents who reported a problem • Customer Loyalty: likelihood to purchase at various price points Messung & Analyse von Kundenzufriedenheit

5. Messung & Analyse von Kundenzufriedenheit

6. The European Customer Satisfaction Index (ECSI) Ref.:http://www.swics.ch/ecsi/index.html Messung & Analyse von Kundenzufriedenheit

7. ACSIe-Model for Food Retail Emotional Factor Hackl et al. (2000) Latent variables and path coefficients Perceived Quality 0,33 0,35 Custo- mer Satis- faction 0,37 0,36 0,73 (-0,01) 0,34 Expec- tations Loyalty 0,53 Value 0,34 (0,06) Messung & Analyse von Kundenzufriedenheit

8. Austrian Food Retail Market • Pilot for an Austrian National CS Index (Zuba, 1997) • Data collection: December 1996 by Dr Fessel & GfK (professional market research agency) • 839 interviews, 327 complete observations • Austria-wide active food retail chains (1996: ~50% from the 10.5 B’EUR market) • Billa: well-assorted medium-sized outlets • Hofer: limited range at good prices • Merkur: large-sized supermarkets with comprehensive range • Meinl: top in quality and service Messung & Analyse von Kundenzufriedenheit

9. The Data Messung & Analyse von Kundenzufriedenheit

10. The Emotional Factor Principal component analysis of satisfaction drivers • staff (availability, politeness) • outlet (make-up, presentation of merchandise, cleanliness) • range (freshness and quality, richness) • price-value ratio (value for price, price for value) • customer orientation (access to outlet, shopping hours, queuing time for checkout, paying modes, price information, sales, availability of sales) identifies (Zuba, 1997) • staff, outlet, range: “Emotional factor” • price-value ratio: “Value” • customer orientation: “Cognitive factor” Messung & Analyse von Kundenzufriedenheit

11. Structural Equation Models Combine three concepts • Latent variables • Pearson (1904), psychometrics • Factor analysis model • Path analysis • Wright (1934), biometrics • Technique to analyze systems of relations • Simultaneous regression models • Econometrics Messung & Analyse von Kundenzufriedenheit

12. Customer Satisfaction Is the result of the customer‘s comparison of • his/her expectations with • his/her experiences has consequences on • loyalty • future profits of the supplier Messung & Analyse von Kundenzufriedenheit

13. Expectation vs. Experience • Expectation reflects • customers‘ needs • offer on the market • image of the supplier • etc. • Experiences include • perceived performance/quality • subjective assessment • etc. Messung & Analyse von Kundenzufriedenheit

14. CS-Model: Path Diagram Expecta- tions Custo- mer Satis- faction Perceived Quality Loyalty Messung & Analyse von Kundenzufriedenheit

15. A General CS-Model Voice Expecta- tions Custo- mer Satis- faction Perceived Quality Loyalty Profits Messung & Analyse von Kundenzufriedenheit

16. CS-Model: Structure EX: expectation PQ: perceived quality CS: customer satisfaction LY: loyalty Recursive structure: triangular form of relations Messung & Analyse von Kundenzufriedenheit

17. CS-Model: Equations PQ = a1 + g11EX + z1 CS = a2 + b21PQ + g21EX + z2 LY = a3 + b32CS + z3 Simultaneous equations model in latent variables Exogenous: EX Endogenous: PQ, CS, LY Error terms (noises): z1, z2, z3 Messung & Analyse von Kundenzufriedenheit

18. Simple Linear Regression Model: Y = a + gX + z Observations: (xi, yi), i=1,…,n Fitted Model: Ŷ = a + cX OLS-estimates a, c: minimize the sum of squared residuals sxy: sample-covariance of X and Y Messung & Analyse von Kundenzufriedenheit

19. Criteria of Model Fit R2: coefficient of determination the squared correlation between Y and Ŷ: R2 = ryŷ2 t-Test: Test of H0: g=0 against H1:g≠0 t=c/s.e.(c) s.e.(c): standard error of c F-Test: Test of H0: R2=0 against H1: R2≠0 follows for large n the F-distribution with n-2 and 2 df Messung & Analyse von Kundenzufriedenheit

20. Multiple Linear Regression Model: Y = a + X1g1+ ... + Xkgk+ z = a + x’g + z Observations: (xi1,…, xik, yi), i=1,…,n In Matrix-Notation: y = a + Xg + z y, z: n-vectors, g:k-vector, X: nxk-matrix Fitted Model: ŷ = a + Xc OLS-estimates a, c: R2 = ryŷ2 F-Test t-Test Messung & Analyse von Kundenzufriedenheit

21. Simultaneous Equations Models A 2-equations model: PQ = a1 + g11EX + z1 CS = a2 + b21PQ + g21EX + z2 In matrix-notation: Y = BY + GX + z with path coefficients Messung & Analyse von Kundenzufriedenheit

22. Simultaneous Equations Models Model: Y = BY + GX + z Y, z: m-vectors, B: (mxm)-matrix G:(mxK)-matrix, X: K-vector Problems: Simultaneous equation bias: OLS-estimates of coefficients are not consistent Identifiability: Can coefficients be consistently estimated? Some assumptions: z: E(z)=0, Cov(z) = S Exogeneity: Cov(X,z) = 0 Messung & Analyse von Kundenzufriedenheit

23. Path Analytic Model • PQ = g11EX + z1 • CS = b21PQ + g21EX + z2 EX d1 z2 g21 CS Var(d1) = sEX2 g11 PQ b21 z1 Messung & Analyse von Kundenzufriedenheit

24. Path Analysis • Wright (1921, 1934) • A multivariate technique • Model: Variables may be • structurally related • structurally unrelated, but correlated • Decomposition of covariances allows to write covariances as functions of structural parameters • Definition of direct and indirect effects Messung & Analyse von Kundenzufriedenheit

25. Example sCS,EX = g21s2EX + b21sPQ,EX =g21s2EX + g11b21s2EX EX d1 z2 g21 CS g11 PQ b21 with standardized variable EX: rCS,EX = g21 + g11b21 z1 Messung & Analyse von Kundenzufriedenheit

26. Direct and Indirect Effects rCS,EX = g21 + g11b21 • Direct effect: coefficient that links independent with dependent variable; e.g., g21 is direct effect of EX on CS • Indirect effect: effect of one variable on another via one or more intervening variable(s), e.g., g11b21 • Total indirect effect: sum of indirect effects between two variables • Total effect: sum of direct and total indirect effects between two variables Messung & Analyse von Kundenzufriedenheit

27. Decomposition of Covariance syx : variable on path from X to Y YI: path coefficient of variable I to Y Messung & Analyse von Kundenzufriedenheit

28. First Law of Path Analysis Decomposition of covariance sxy between Y and X: Assumptions: • Exogenous (X) and endogenous variables (Y) have mean zero • Errors or noises (z) • have mean zero and equal variances across observations • are uncorrelated across observations • are uncorrelated with exogenous variables • are uncorrelated across equations Messung & Analyse von Kundenzufriedenheit

29. Identification PQ = g11EX + z1 Y1 = g11X + z1 CS = b21PQ + g21EX + z2 Y2 = b21Y1 + g21X + z2 In matrix-notation: Y = BY + GX + z Number of parameters: p=6 Model is identified, if all parameters can be expressed as functions of variances/covariances of observed variables Messung & Analyse von Kundenzufriedenheit

30. Identification, cont’d Y1 = g11X + z1 Y2 = b21Y1 + g21X + z2 s1X =g11sX2 s2X = b21s1X + g21sX2 s21 = b21s12 + g21s1X sX2 = sX2 sy12 = g11s1X+s12 sy22 = b21s21 + g21s2X+s22 p=6 first 3 equations allow unique solution for path coefficients, last three for variances of d and z Messung & Analyse von Kundenzufriedenheit

31. Condition for Identification • Just-identified: all parameters can be uniquely derived from functions of variances/covariances • Over-identified: at least one parameter is not uniquely determined • Under-identified: insufficient number of variances/covariances Necessary, but not sufficient condition for identification: number of variances/covariances at least as large as number of parameters A general and operational rule for checking identification has not been found Messung & Analyse von Kundenzufriedenheit

32. Latent variables and Indicators Latent variables (LVs) or constructs or factors are unobservable, but We might find indicators or manifest variables (MVs) for the LVs that can be used as measures of the latent variable Indicators are imperfect measures of the latent variable Messung & Analyse von Kundenzufriedenheit

33. Indicators for “Expectation” From: Swedish CSB Questionnaire, Banks: Private Customers d1 E1 EX d2 E2 E1, E2, E3: „block“ of LVs for Expectation d3 E3 E1: When you became a customer of AB-Bank, you probably knew something about them. How would you grade your expectations on a scale of 1 (very low) to 10 (very high)? E2: Now think about the different services they offer, such as bank loans, rates, … Rate your expectations on a scale of 1 to 10? E3: Finally rate your overall expectations on a scale of 1 to 10? Messung & Analyse von Kundenzufriedenheit

34. Notation d1 l1 X1=l1x+d1 X2=l2x+d2 X3=l3x+d3 X1 x l2 d2 X2 l3 d3 X3 “reflective” indicators • x: latent variable, factor • Xi: indicators, manifest • variables • li: factor loadings • i: measurement errors, noise Some properties: LV: unit variance noise di: has mean zero, variance si2, uncorrela- ted with other noises Messung & Analyse von Kundenzufriedenheit

35. Notation d1 l1 X1=l1x+d1 X2=l2x+d2 X3=l3x+d3 X = Lx + d X1 x l2 d2 X2 l3 d3 X3 In matrix-notation: with vectors X, L, and d e.g., X = (X1, X2, X3)‘ • x: latent variable, factor • Xi: indicators, manifest • variables • li: factor loadings • i: measurement error, noise Messung & Analyse von Kundenzufriedenheit

36. CS-Model: Path Diagram d1 E1 EX d2 z2 E2 e4 g21 d3 C1 CS E3 e5 g11 C2 e1 e6 Q1 C3 PQ b21 e2 Q2 e3 Q3 z1 Messung & Analyse von Kundenzufriedenheit

37. SEM-Model: Path Diagram d1 X1 x d2 z2 X2 e4 g21 d3 Y4 h2 X3 e5 g11 Y5 e1 e6 Y1 Y6 h1 b21 e2 Y2 • = Bh + Gx + z X = Lxx+d, Y= Lyh+e e3 Y3 z1 Messung & Analyse von Kundenzufriedenheit

38. SEM-Model: Notation Inner relations, inner model • = Bh + Gx + z Outer relations, measurement model X, d: 3-component vector Y, e: 6-component vector X = Lxx+d, Y= Lyh+e Messung & Analyse von Kundenzufriedenheit

39. Statistical Assumptions • Error terms of inner model (z) have • zero means • constant variances across observations • are uncorrelated across observations • are uncorrelated with exogenous variables • Error terms of measurement models (d, e) have • zero means • constant variances across observations • are uncorrelated across observations • are uncorrelated with latent variables and with each other • Latent variables are standardized Messung & Analyse von Kundenzufriedenheit

40. Covariance Matrix of Manifest Variables Unrestricted covariance matrix (order: K = kx+ky) S = Var{(X’,Y’)’} Model-implied covariance matrix Messung & Analyse von Kundenzufriedenheit

41. Estimation of the Parameters • Covariance fitting methods • search for values of parameters q so that the model-implied covariance matrix fits the observed unrestricted covariance matrix of the MVs • LISREL (LInear Structural RELations): Jöreskog (1973), Keesling (1972), Wiley (1973) • Software LISREL by Jöreskog & Sörbom • PLS techniques • partition of q in estimable subsets of parameters • iterative optimizations provide successive approximations for LV scores and parameters • Wold (1973, 1980) Messung & Analyse von Kundenzufriedenheit

42. Discrepancy Function The discrepancy or fitting function F(S;S) = F(S; S(q)) is a measure of the “distance” between the model-implied covariance-matrix S(q) and the estimated unrestricted covariance-matrix S Properties of the discrepancy function: • F(S;S) ≥ 0; • F(S;S) = 0 if S=S Messung & Analyse von Kundenzufriedenheit

43. Covariance Fitting (LISREL) • Estimates of the parameters are derived by F(S;S(q)) qmin • Minimization of (K: number of indicators) F(S;S) = log|S| – log|S| + trace (SS-1) – K gives ML-estimates, if the manifest variables are independently, multivariate normally distributed • Iterative Algorithm (Newton-Raphson type) • Identification • Choice of starting values is crucial • Other choices of F result in estimation methods like OLS and GLS; ADF (asymptotically distribution free) Messung & Analyse von Kundenzufriedenheit

44. PLS Techniques • Estimates factor scores for latent variables • Estimates structural parameters (path coefficients, loading coefficients), based on estimated factor scores, using the principle of least squares • Maximizes the predictive accuracy • “Predictor specification”, viz. that E(h|x) equals the systematic part of the model, implies E(z|x)=0: the error term has (conditional) mean zero • No distributional assumptions beyond those on 1st and 2nd order moments Messung & Analyse von Kundenzufriedenheit

45. The PLS-Algorithm Step 1: Estimation of factor scores • Outer approximation • Calculation of inner weights • Inner approximation • Calculation of outer weights Step 2: Estimation of path and loading coefficients by minimizing Var(z) and Var(d) Step 3: Estimation of location parameters (intercepts) • Bo from h = Bo + Bh + Gx + z • Lo from X = Lo + Lxx + d Messung & Analyse von Kundenzufriedenheit

46. Estimation of Factor Scores Factor hi: realizations Yin, n=1,…,N Yin(o): outer approximation of Yin Yin(i): inner approximation of Yin Indicator Yij: observations yijn; j=1,…,Ji; n=1,…,N • Outer approximation: Yin(o)=Sjwijyijn s.t. Var(Yi(o))=1 • Inner weights: vih=sign(rih), if hi and hh adjacent; otherwise vih=0; rih=corr(hi,hh) (“centroid weighting”) • Inner approximation: Yin(i)=ShvihYhn(o) s.t. Var(Yi(i))=1 • Outer weights: wij=corr(Yij,Yi(i)) Start: choose arbitrary values for wij Repeat 1. through 4. until outer weights converge Messung & Analyse von Kundenzufriedenheit

47. Example d1 E1 EX d2 z2 E2 e4 g21(+) d3 C1 CS E3 e5 g11(+) C2 e1 e6 Q1 C3 PQ b21(+) e2 Q2 e3 Q3 z1 Messung & Analyse von Kundenzufriedenheit

48. Example, cont’d Starting values wEX,1,…,wEX,3,wPQ,1,…,wPQ,3,wCS,1,…,wCS,3 Outer approximation: EXn(o) = SjwEX,jEjn; similar PQn(o), CSn(o); standardized Inner approximation: EXn(i) = + PQn(o)+ CSn(o) PQn(i) = + EXn(o)+ CSn(o) CSn(i) = + EXn(o)+ PQn(o) standardized Outer weights: wEX,j = corr(Ej,EX(i)), j=1,…,3; similar wPQ,j, wCS,j Messung & Analyse von Kundenzufriedenheit

49. Choice of Inner Weights Centroid weighting scheme: Yin(i)=ShvihYhn(o) vij=sign(rih), if hi and hh adjacent, vij=0 otherwise with rih=corr(hi,hh); these weights are obtained if vih are chosen to be +1 or -1 and Var(Yi(i)) is maximized Weighting schemes: bih: coefficient in regression of hi on hh Messung & Analyse von Kundenzufriedenheit

50. Measurement Model: Examples Latent variables from Swedish CSB Model • Expectation E1: new customer feelings E2: special products/services expectations E3: overall expectation • Perceived Quality Q1: range of products/services Q2: quality of service Q3: clarity of information on products/services Q4: opening hours and appearance of location Q5: etc. Messung & Analyse von Kundenzufriedenheit