RUBENS A. ZIMBRESPEDRO P.B. DE OLIVEIRA

Dynamics of quality perception in a social network: A cellular automaton based model in aesthetics services

Universidade Presbiteriana MackenzieSão Paulo, SP

Brazil

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I. INTRODUCTION Main goal: simulate interactions between

customers and providers and understand their rationality using cellular automata.

First survey Second survey

Motivation: linear regression models in service quality literature do not offer a good explanation on the phenomenom.

Overall perspective: the process in the service encounter, regarded as a complex system.

rule

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II. COMPLEX SYSTEMS AND ROLE THEORY Commercial system as a complex system

Clients co-participate in service delivery, influencing service quality (e.g., self-service restaurant)

Role theory sees service delivery as a theatrical metaphor, with actors that act following a script (set of rules according to the situation)

Common behaviours = uniform cellular automata

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III. METHODOLOGICAL PROCEDURES: QUESTIONAIRE DEVELOPMENT

Qualitative: 6 interviews (3 providers and 3 clients, in aesthetic services)

Quantitative: Evaluation of each statement: Likert scale with 5

points: totally disagree, disagree, neither agree nor disagree, agree, totally agree

Development of a measurement scale with 74 questions/statements, evaluated by marketing specialists → 54 were taken

Quantitative pre-test (variance, correlations, factor analysis and reliability) → 45 final statements

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IV. QUANTITATIVE RESEARCH First survey: 115 clients and 96 providers Internal consistency of the questionaire (via

Cronbach's Alpha): 0.937 (clients) and 0.772 (providers) (range from 0 to 1)

Statistical overall quality estimate: given by linear regression (R2): 0.760 (clients) and 0.873 (providers), significant at 0.000, with Variance Inflaction Factor < 10, and normal residues

Second survey: 4 months later 36 responses Cronbach's Alpha: 0.892 (clients) and 0.631

(providers)

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V. PROPOSED MODELo Idea: to predict the evolution of clients-providers

interaction between the two subsequent surveys

o Data of the 1st survey = initial parameterso Interactions between clients and providerso Data of the 2nd survey = final condition, for

comparison

o Focus of the analysis between the two surveys: 7 (out of the 45), all related to intangible aspects of service quality, because they are more relevant to obtain sustainable competitive advantage

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DETAILS OF THE MODELo Lattice = 36 subjects and 7 indicators of

service quality (attention, trust, willingness to help, honesty, concern, responsibility, and adaptation to client’s needs)

o Row = indicator, column individualo No multicollinearity = one-dimensional CAo 7 CAs, same rule = uniform CAo Facilitates to unveil the rationale embedded

in the transition table.

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QUESTIONAIRE AND CELULAR AUTOMATA Same respondents Likert 5 points = CA with 5 states CA radius = 1 (nearest left- and right-hand

neighbours) Hence:

→ 125 possible rationales (neighbourhoods)

→ 2.35 1087 possible rules

Search started from the majority rule (herd behaviour)

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RULE SEARCHo Initial condition: lattice was ordered

according to the 7th indicator (adaptation to customer needs), because of its highest variance (higher diversity of opinions)

Sampling of the space in blocks of 1500 rules, picking each one of them with uniformly distributed random steps in the range from 110 to 1084 (with occasional smaller ranges for closer inspection): total of 1.8106 rules were evaluated (200hs of computer time)

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RULE SEARCHo Direction of the search: • Target success rate, measured in terms of the

best possible match between the state values of corresponding cells in the second survey and the rule outcome (within 20 iterations).

• Trend to best results with 16 timesteps (4 months between surveys); thus, 20 iterations

• Success rate at least 70% • Non-cyclic behaviour• Variance of the lattice ±0.5 when compared

with the second survey

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LIKERT SCALE AND THE CA STATES

5 = Totally agree that attention is very important in service delivery4 = Agree3 = Neither agree nor disagree2 = Disagree1 = Totally disagree

PPCPPPCCCCCPPPPPPPPPPPPPPPPPCCCCCCCC

Example: Attention

Time t=0

Time t=n

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RULE RATIONALE If a given customer (C) that perceives actual

quality as good (Likert scale value equal to 5 and cell state equal to 5) evaluates the service quality offered by one provider (P) as bad (cell state equal to 1) and the service quality offered by another provider as good (cell state equal to 5) this could generate a regular assessment of quality (cell state equal to 2), which could interfere with future intentions of the client to remain with the provider, given the inconsistency of the attitudes.

1 5 5 2

P C P

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RATE OF SUCCESS Rule number

2159062512564987644819455219116893945895958528152021228705752563807959237655911950549124 with 73.80 % of success in predicting the system evolution

0 5 10 15 2055

60

65

70

75

Cy cles

Accuracy

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TRANSITION TABLE FOR THE CHOSEN RULE

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EXPLANATORY POWER CA model offers an additional explanatory power of

8.80 percentage points (73.80%−65.00%). Thus, nonlinear effects appear to contribute with the corresponding gain.

Sharing only 38.80% in common (intersection) explains nonlinearity of phenomena, a new perspective of studying causal relations in management research.

65%73.80%

73.80%65%

Linear regression modelCellular automata model

Linear regression modelCellular automata model

0% 100%

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EUCLIDEAN DISTANCE

1st survey 2nd survey model outcome

Consensus (think similarly, intimacy, mutual understanding ): role theory

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EUCLIDEAN DISTANCE FOR THE 7 INDICATORS

Indicator 1 2 3 4 5 6 7Phase 2 - Phase 1 (c) 5,74 3,31 4,24 4,35 5 4,58 6,55Simulation - Phase 1 (d) 5,56 3,46 2 3 4 2,44 21,93Difference c-d 0,18 -0,15 2,24 1,35 1 2,14 -15,38

Euclidean Distances

Highest variance

)

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LATTICE CONFIGURATION ALONG THE RULE ITERATIONS

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EVOLUTION OF THE INDICATORS

Interface C-P

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DISSATISFACTION IN THE NETWORK Extremely problematic customers should not

be in contact with each other, otherwise they would spread the dissatisfaction to everyone they have contact with, customers or providers.

Dynamics of opinions, but also and more importantly, which individuals create dissatisfaction in a social network. This can enable managers to identify problematic customers.

Outbreak of the individuals’ dissatisfaction happens always in the customer-provider interface.

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TOTAL AVERAGE PER INDICATOR If based on averages (as usual in the

traditional literature), and not on a cell-by-cell comparison, the outcome becomes much higher than the model´s success rate!!

Indicator 1 2 3 4 5 6 7Phase 2 - Phase 1 (c) 137 136 140 135 132 138 129Simulation - Phase 1 (d) 130 135 136 134 127 133 126Difference c-d 7 1 4 1 5 5 3Accuracy (%) 94,89% 99,26% 97,14% 99,26% 96,21% 96,38% 97,67%

Total per Indicator

)

VARIANCE explanation in literature (average)Cronin e Taylor (1992) R2 max .47 for SERVPERF and .46 for SERVQUAL.

Elliott (1994) R2 max .65 for SERVPERF and .42 for SERVQUAL. Lee, Lee, Yoo (2000) R2 max .53 for SERVPERF and .35 for SERVQUAL.

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RATE OF SUCCESS (CASE BY CASE)

73.80 %

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EFFECTS OF GROUPING INDIVIDUALS WITH THE SAME OPINION

1 2 3 4

Isolated Group

Rebellion

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ATTEMPTS TO MITIGATE DISSATISFACTION IN A SOCIAL NETWORK

Likert equal to 5

Likert equal to 2

1

1

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SENSITIVITY TO INITIAL CONDITIONS

collide

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DESCRIPTIVE STATISTICS OF THE DATA: THE SURVEYS AND THE MODEL

Initial Final Simulationsurvey survey result

Mean 3.75 3.65 3.67Variance 0.16 0.25 0.97Std deviation 0.25 0.37 0.98Median 4 4 4Kurtosis 8 11.82 10.84Skewness -2.21 -2.72 -3.03Increase inperception

-0.10 -0.08

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LATTICE MEANS (SUM OF INDICATORS) OVER THE 20 TIME STEPS OF THE CA

Cycles

Construct total

cause effect

process

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OSCILLATORY BEHAVIOUR First, inconsistencies in mood of customers and

providers, who may perceive the quality of the relationship differently, according to their emotional state.

Second, inconsistencies in the delivery of service by the provider, who may not always offer the same service quality.

Third, there may be a process of mutual adaptation over the interactions, and the provider cannot always meet the expectations of customers and vice versa.

Intangible aspects of quality and this is probably due to an affective component, involvement.

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STABILITY It might be interesting to increase the

interval between longitudinal surveys to 30 time steps, that is, 30 weeks or 8 months, so as to verify the emergence of consensus and stability.

0 10 20 30 404.0

4.2

4.4

4.6

4.8

5.0

Cy cles

Construtm

ean

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VARIANCES FOUND IN THE FIRST AND THE SECOND QUANTITATIVE

SURVEYS

Indicator

Variance

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EVOLUTION OF MODEL VARIANCE

0 10 20 30 40 0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Cy cles

IndicatorT

otal

consensus

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TRANSITION TABLE OF THE CHOSEN RULECentre Centre

1 2

1 2 3 4 5 1 2 3 4 51 1 5 1 2 5 1 3 1 4 1 22 3 2 5 1 5 2 1 2 2 3 33 3 1 4 2 2 3 3 2 3 5 24 4 1 5 4 5 4 4 2 4 4 35 3 4 3 1 5 5 5 3 4 1 3

Centre Centre3 4

1 2 3 4 5 1 2 3 4 51 3 5 3 5 4 1 5 5 2 4 52 4 4 5 4 5 2 2 1 1 3 33 1 4 5 1 4 3 3 5 2 5 24 1 4 1 5 3 4 5 1 1 1 25 4 1 1 1 5 5 5 4 1 3 5

Centre Centre5 Initial state

1 2 3 4 51 3 1 1 5 52 1 3 3 4 13 1 3 2 4 54 1 5 5 5 15 5 4 5 3 5

RightLe

ft

Neighbour stateN

eigh

bour

sta

te

Final state of the central cellLe

ft

RightLe

ftLe

ft

Left

Right

Left

Right

RightRight

Nonlinear

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CONCLUDING REMARKS A B B C Validation:

Role theory metaphor, Statistical analysis, Careful implementation, and Reliance on real data.

Rationality and behaviours to increase satisfaction. Management of dissatisfied individuals. Linear regression: which indicators and their

magnitudes (cause and effect). CA study nonlinearities in the process.

Cellular automata as a complement to helping management of human behaviour

Limitation: rule-sample, interpretability of observed behaviours (cyclic in honesty), initial condition

rule rule

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THANKS! São Paulo State Foundation for Research

Support: Research grant 2005/04696-3

Mackenzie Research Fund: Research grant from Edital 2007

Wolfram Research: Mathematica Academic Grant No. 1149

National Coordination for the Improvement of University Level Personel