Messung und statistische analyse von kundenzufriedenheit
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Messung und statistische Analyse von Kundenzufriedenheit . KF Qualitätsmanagement Vertiefungskurs V. Outline. Customer satisfaction measurement The Structural Equation Model (SEM) Estimation of SEMs Evaluation of SEMs Practice of SEM-Analysis. The ACSI Model.

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Messung und statistische analyse von kundenzufriedenheit

Messung und statistische Analyse von Kundenzufriedenheit

KF Qualitätsmanagement

Vertiefungskurs V


Outline

Outline

  • Customer satisfaction measurement

  • The Structural Equation Model (SEM)

  • Estimation of SEMs

  • Evaluation of SEMs

  • Practice of SEM-Analysis

Messung & Analyse von Kundenzufriedenheit


The acsi model

The ACSI Model

Ref.:http://www.theacsi.org/model.htm

Messung & Analyse von Kundenzufriedenheit


Acsi model latent variables

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


Messung und statistische analyse von kundenzufriedenheit

Messung & Analyse von Kundenzufriedenheit


The european customer satisfaction index ecsi

The European Customer Satisfaction Index (ECSI)

Ref.:http://www.swics.ch/ecsi/index.html

Messung & Analyse von Kundenzufriedenheit


Acsi e model for food retail

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


Austrian food retail market

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


The data

The Data

Messung & Analyse von Kundenzufriedenheit


The emotional factor

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


Structural equation models

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


Customer satisfaction

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


Expectation vs experience

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


Cs model path diagram

CS-Model: Path Diagram

Expecta-

tions

Custo-

mer Satis-

faction

Perceived

Quality

Loyalty

Messung & Analyse von Kundenzufriedenheit


A general cs model

A General CS-Model

Voice

Expecta-

tions

Custo-

mer Satis-

faction

Perceived

Quality

Loyalty

Profits

Messung & Analyse von Kundenzufriedenheit


Cs model structure

CS-Model: Structure

EX: expectation

PQ: perceived

quality

CS: customer

satisfaction

LY: loyalty

Recursive structure:

triangular form of

relations

Messung & Analyse von Kundenzufriedenheit


Cs model equations

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


Simple linear regression

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


Criteria of model fit

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


Multiple linear regression

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


Simultaneous equations models

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


Simultaneous equations models1

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


Path analytic model

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


Path analysis

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


Example

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


Direct and indirect effects

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


Decomposition of covariance s yx

Decomposition of Covariance syx

: variable on path from X to Y

YI: path coefficient of variable I to Y

Messung & Analyse von Kundenzufriedenheit


First law of path analysis

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


Identification

Identification

PQ = g11EX + z1Y1 = g11X + z1

CS = b21PQ + g21EX + z2Y2 = 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


Identification cont d

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


Condition for identification

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


Latent variables and indicators

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


Indicators for expectation

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


Notation

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


Notation1

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


Cs model path diagram1

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


Sem model path diagram

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


Sem model notation

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


Statistical assumptions

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


Covariance matrix of manifest variables

Covariance Matrix of Manifest Variables

Unrestricted covariance matrix (order: K = kx+ky)

S = Var{(X’,Y’)’}

Model-implied covariance matrix

Messung & Analyse von Kundenzufriedenheit


Estimation of the parameters

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


Discrepancy function

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


Covariance fitting lisrel

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


Pls techniques

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


The pls algorithm

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


Estimation of factor scores

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


Example1

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


Example cont d

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


Choice of inner weights

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


Measurement model examples

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


Measurement models

Measurement Models

Reflective model: each indicator is reflecting the latent variable (example 1)

Yij = lijhi + eij

Yij is called a reflective or effect indicator (of hi)

Formative model: (example 2)

hi = py'Yi + di

py is a vector of ki weights; Yij are called formative or cause indicators

Hybrid or MIMIC model (for “multiple indicators and multiple causes”)

  • Choice between formative and reflective depends on the substantive theory

  • Formative models often used for exogenous, reflective and MIMIC models for endogenous variables

Messung & Analyse von Kundenzufriedenheit


Estimation of outer weights

Estimation of Outer Weights

  • “Mode A” estimation of Yi(o): reflective measurement model

    weight wij is coefficient from simple regression of Yi(i) on Yij: wij = corr(Yij,Yi(i))

  • “Mode B” estimation of Yi(o): formative measurement model

    weight wij is coefficient of Yij from multiple regression of Yi(i) on Yij, j=1,…,Ji

    multicollinearity?!

  • MIMIC model

Messung & Analyse von Kundenzufriedenheit


Properties of estimators

Properties of Estimators

A general proof for convergence of the PLS-algorithm does not exists; practitioners experience no problems

  • Factor scores are inconsistent but “consistent at large”: consistency is achieved with increasing sample size and block size

  • Loading coefficients are inconsistent and seem to be overestimated

  • Path coefficients are inconsistent and seem to be underestimated

Messung & Analyse von Kundenzufriedenheit


Acsi model results

ACSI Model: Results

Perceived

Quality

Voice

-0,38

-0,29

0,78

0,47

Custo-

mer Satis-

faction

0,90

0,73

0,17

(0,06)

0,95

0,53

0,57

0,35

(-0,15)

0,12

Expec-

tations

Loyalty

Value

0,40

0,35

-0,24

(0,06)

EQS-estimates

PLS-estimates

Messung & Analyse von Kundenzufriedenheit


Evaluation of sem models

Evaluation of SEM-Models

  • Depends on estimation method

    • Covariance-fitting methods: distributional assumptions, optimal parameter estimates, factor indeterminacy

    • PLS path modeling: non-parametric, optimal prediction accuracy, LV scores

  • Step 1: Inspection of estimation results (R2, parameter estimates, standard errors, LV scores, residuals, etc.)

  • Step 2: Assessment of fit

    • Covariance-fitting methods: global measures

    • PLS path modeling: partial fitting measures

Messung & Analyse von Kundenzufriedenheit


Inspection of results

Inspection of Results

  • Covariance-fitting methods: global optimization

    • Model parameters and their standard errors; do they confirm theory?

    • Correlation residuals: sij-sij(q)

    • Graphical methods

  • PLS techniques: iterative optimization of outer models and inner model

    • Model parameters

    • Resampling procedures like blindfolding or jackknifing give standard errors of model parameters

    • LV scores

    • Graphical methods

Messung & Analyse von Kundenzufriedenheit


Fit indices

Fit Indices

  • Covariance-fitting methods: covariance fit measures such as

    • Chi-square statistics

    • Goodness of Fit Index (GFI), AGFI

    • Normed Fit Index (NFI), NNFI, CFI

    • Etc.

    • Basis is the discrepancy function

  • PLS path modeling: prediction-based measures

    • Communality

    • Redundancy

    • Stone-Geisser’s Q2

Messung & Analyse von Kundenzufriedenheit


Chi square statistic

Chi-square Statistic

  • Test of H0: S = S(q) against non-specified alternative

  • Test-statistic X2=(N-1)F(S;S( ))

  • If model is just identified (c=p): X2=0 [c=K(K+1)/2, p: number of parameters in q]

  • Under usual regularity conditions (normal distribution, ML-estimation), X2 is asymptotically 2(c-p)-distributed

  • Non-significant X2 indicate: the over-identified model does not differ from a just-identified version

  • Problem: X2 increases with increasing N

  • Some prefer X2/(c-p) to X2 (has reduced sensitivity to sample size); rule of thumb: X2/(c-p) < 3 is acceptable

Messung & Analyse von Kundenzufriedenheit


Goodness of fit indices

Goodness of Fit Indices

Goodness of Fit Index (Jöreskog & Sörbom):

  • Portion of observed covariances explained by the model-implied covariances

  • “How much better fits the model as compared to no model at all”

  • Ranges from 0 (poor fit) to 1 (perfect fit)

  • Rule of thumb: GFI > 0.9

  • AGFI penalizes model complexity:

Messung & Analyse von Kundenzufriedenheit


Other fit indices

Other Fit Indices

  • Normed Fit Index, NFI (Bentler & Bonett)

    • Similar to GFI, but compares with a baseline model, typically the independence model (indicators are uncorrelated)

    • Ranges from 0 (poor fit) to 1 (perfect fit)

    • Rule of thumb: NFI > 0.9

  • Comparative Fit Index, CFI (Bentler)

    • Less depending of sample size than NFI

  • Non-Normed Fit Index, NNFI (Bentler & Bonett)

    • Also known as Tucker-Lewis Index

    • Adjusted for model complexity

  • Root mean squared error of approximation, RMSEA (Steiger):

Messung & Analyse von Kundenzufriedenheit


Assessment of pls results

Assessment of PLS Results

  • Not a single but many optimization steps; not a global measure but many measures of various aspects of results

  • Indices for assessing the predictive relevance

    • Portions of explained variance (R2)

    • Communality, redundancy, etc.

    • Stone-Geisser’s Q2

  • Reliability indices

    • NFI, assuming normality of indicators

    • Allows comparisons with covariance-fitting results

Messung & Analyse von Kundenzufriedenheit


Some indices

Some Indices

Assessment of diagonal fit (proportion of explained variances)

  • SMC (squared multiple correlation coefficient) R2: (average) proportion of the variance of LVs that is explained by other LVs; concerns the inner model

  • CommunalityH2: (average) proportion of the variance of indicators that is explained by the LVs directly connected to it; concerns the outer model

  • Redundancy F2: (average) proportion of the variance of indicators that is explained by predictor LVs of its own LV

  • r2: proportion of explained variance of indicators

Messung & Analyse von Kundenzufriedenheit


Some indices cont d

Some Indices, cont’d

Assessment of non-diagonal fit

  • Explained indicator covariances

    rs = 1-c/s

    with c = rms(C), s = rms(S); C: estimate of Cov(e)

  • Explained latent variable correlation

    rr = 1-q/r

    with q = rms(Q), r = rms(Cov(Y)); Q: estimate of Cov(z)

  • reY = rms (Cov(e,Y)), e: outer residuals

  • reu = rms (Cov(e,u)), u: inner residuals

    rms(A) = (SiSjaij2)1/2: root mean squared covariances (diagonal elements of symmetric A excluded from summation)

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Stone geisser s q 2

Stone-Geisser’s Q2

  • Similar to R2

    E: sum of squared prediction errors; O: sum of squared deviations from mean

  • Prediction errors from resampling (blindfolding, jackknifing)

  • E.g., communality of Yij, an indicator ofhi

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Lohm ller s advice

Lohmöller’s Advice

  • Check fit of outer model

    • Low unexplained portion of indicator variances and covariances

    • High communalities in reflective blocks, low residual covariances

    • Residual covariances between blocks close to zero

    • Covariances between outer residuals and latent variables close to zero

  • Check fit of inner model

    • Low unexplained portion of latent variable indicator variances and covariances

  • Check fit of total model

    • High redundancy coefficient

    • Low covariances of inner and outer residuals

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Acsi model results1

ACSI Model: Results

Perceived

Quality

Voice

-0,38

-0,29

0,78

0,47

Custo-

mer Satis-

faction

0,90

0,73

0,17

(0,06)

0,95

0,53

0,57

0,35

(-0,15)

0,12

Expec-

tations

Loyalty

Value

0,40

0,35

-0,24

(0,06)

EQS-estimates

PLS-estimates

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Diagnostics eqs

Diagnostics:EQS

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Diagnostics pls centroid weighting

Diagnostics:PLS (centroid weighting)

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Practice of sem analysis

Practice of SEM Analysis

  • Theoretical basis

  • Data

    • Scaling: metric or nominal (in LISREL not standard)

    • Sample-size: a good choice is 10p (p: number of parameters); <5p cases might result in unstable estimates; large number of cases will result in large values of X2

    • Reflective indicators are assumed to be uni-dimensional; it is recommended to use principal axis extraction, Cronbach’s alpha and similar to confirm the suitability of data

  • Model

    • Identification must be checked for covariance fitting methods

    • Indicators for LV can be formative or reflective; formative indicators not supported in LISREL

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Practice of sem analalysis cont d

Practice of SEM Analalysis cont’d

  • Model

    • LISREL allows for more general covariance structures e.g., correlation of measurement errors

  • Estimation

    • Repeat estimation with varying starting values

  • Diagnostic checks

    • Use graphical tools like plots of residuals etc.

    • Check each measurement model

    • Check each structural equation

    • Lohmöller’s advice

    • Model trimming

    • Stepwise model building (Hui, 1982; Schenk, 2001)

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Lisrel vs pls

LISREL vs PLS

  • Models

    • PLS assumes recursive inner structure

    • PLS allows for higher complexity w.r.t. B, G, and L; LISREL w.r.t. Y and Q

  • Estimation method

    • Distributional assumptions in PLS not needed

    • Formative measurement model in PLS

    • Factor scores in PLS

    • PLS: biased estimates, consistency at large

    • LISREL: ML-theory

    • In PLS: diagnostics much richer

  • Empirical facts

    • LISREL needs in general larger samples

    • LISREL needs more computation

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The extended model

The Extended Model

Emotional

Factor

(0,20)

0,33

Perceived

Quality

0,31

0,35

0,58

0,37

Custo-

mer Satis-

faction

0,55

0,36

0,85

0,53

0,87

0,73

(-0,14)

(-0,01)

0,48

0,34

Expec-

tations

Loyalty

Value

0,41

0,34

(-0,14)

(0,06)

EQS-estimates

PLS-estimates

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Diagnostics eqs1

Diagnostics:EQS

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Diagnostics pls centroid weighting1

Diagnostics:PLS (centroid weighting)

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Model building hui s approach

Model Building: Hui’s Approach

Emotional

Factor

Perceived

Quality

0,61

0,43

0,31

-0,18

Custo-

mer Satis-

faction

0,10

0,35

0,36

0,42

0,33

Expec-

tations

-0,18

0,17

Value

Loyalty

0,63

0,21

0,12

0,23

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Model building schenk s approach

Model Building: Schenk’s Approach

Emotional

Factor

Perceived

Quality

0,32

0,35

0,31

Custo-

mer Satis-

faction

0,32

0,73

0,34

Expec-

tations

0,60

Value

Messung & Analyse von Kundenzufriedenheit


The end

The end

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Data driven specification

Data-driven Specification

  • No solid a priori knowledge about relations among variables

  • Stepwise regression

    • Search of the “best” model

    • Forward selection

    • Backward elimination

    • Problem: omitted variable bias

  • General to specific modeling

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Stepwise se model building

Stepwise SE Model Building

  • Hui (1982): models with interdependent inner relations

  • Schenk (2001): guaranties causal structure, i.e., triangular matrix B of path coefficients in the inner model

    η = B η + ζ

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Stepwise se model building1

Stepwise SE Model Building

Hui’s algorithm

Stage 1

  • Calculate case values Yij for LVs ηias principal component of corresponding block, calculate R = Corr(Y)

  • Choose for each endogenous LV the one with highest correlation to form a simple regression

  • Repeat until a stable model is reached

    • PLS-estimate the model, calculate case values, and recalculate R

    • Drop from each equation LVs with t-value |t|<1,65

    • Add in each equation the LV with highest partial correlation with dependent LV

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Stepwise se model building2

Stepwise SE Model Building

Hui’s algorithm, cont’d

Stage 2

  • Use rank condition for checking identifiability of each equation

  • Use 2SLS for estimating the path coefficients in each equation

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Hui s vs schenk s algorithm

Hui’s vs. Schenk’s Algorithm

  • Hui’s algorithm is not restricted to a causal structure; allows cycles and an arbitrary structure of matrix B

  • Schenk’s algorithm

    • uses an iterative procedure similar to that used by Hui

    • makes use of a priori information about the structure of the causal chain connecting the latent variables

    • latent variables are to be sorted

Messung & Analyse von Kundenzufriedenheit


Stepwise se model building3

Stepwise SE Model Building

Schenk’s algorithm

  • Calculate case values Yij for LVs ηias principal component of corresponding block, calculate R = Corr(Y)

  • Choose pair of LVs with highest correlation

  • Repeat until a stable model is reached

    • PLS-estimate the model, calculate case values, and recalculate R

    • Drop LVs with non-significant t-value

    • Add LV with highest correlation with already included LVs

Messung & Analyse von Kundenzufriedenheit


Data special cs dimensions

Data, special CS dimensions

1 Dimension of “Emotional Factor”

Messung & Analyse von Kundenzufriedenheit


References

References

C. Fornell (1992), “A National Customer Satisfaction Barometer: The Swedish Experience”. Journal of Marketing, (56), 6-21.

C. Fornell and Jaesung Cha (1994), “Partial Least Squares”, pp. 52-78 in R.P. Bagozzi (ed.), Advanced Methods of Marketing Research. Blackwell.

J.B. Lohmöller (1989), Latent variable path modeling with partial least squares. Physica-Verlag.

H. Wold (1982), “Soft modeling. The basic design and some extensions”, in: Vol.2 of Jöreskog-Wold (eds.), Systems under Indirect Observation. North-Holland.

H. Wold (1985), “Partial Least Squares”, pp. 581-591 in S. Kotz, N.L. Johnson (eds.), Encyclopedia of Statistical Sciences, Vol. 6. Wiley.

Messung & Analyse von Kundenzufriedenheit


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