Restricted Common Component and Specific Weight Analysis: A Constrained Explorative Approach for the Customer Satisfaction Evaluation

Abstract

Servqual is a service measurement multidimensional model (Parasuraman et al. in J Mark 49(4):41–50, 1985; Parasuraman et al. in J Retail 64:12–40, 1988) which involves a set of five dimensions representing service quality. It is based on a questionnaire to measure the gaps between customers’ expectations and perceptions of service. A re-examination and extension of this model, named Servperf, is instead based only on the perceptions (Taylor in J Mark 56(3):55–68, 1992; Taylor in J Mark 58:125–131, 1994). Common Components and Specific Weights Analysis (Qannari et al. in Food Qual Prefer 11:151–154, 2000) (CCSWA) is a useful tool to analyze customer satisfaction evaluation data. The rationale behind this method is the existence of a common structure to the data tables. Therefore, it determines a common space of representation for all data. Each table, which represents a ServPerf dimension, assesses a specific weight to each dimension of the common space. Customer satisfaction can be then investigated with respect to a common reference system where all the dimensions contribute to forming it. Sometimes we may have additional knowledge about some relationships among the service variables that can be incorporated in the analysis as external information. The aim of this paper is then to provide an extension of CCSWA based on an objective function which takes directly into account the external information (as linear constraints). This extension may lead to a simpler interpretation of the analysis results and to explore new relationships. A student satisfaction evaluation study highlights this hypothesis.

Appendix

A1. The normal equations of (4) for the first solutions are

$$\begin{aligned} \frac{1}{4}&\frac{\partial L}{\partial {\mathbf {q}}_1}= \sum _{k = 1}^K{({\mathbf {q}}_1^{T}{{\mathbf {X}}_k^{(1)}{\mathbf {u}}_k^{(1)})^3}} {\mathbf {X}}_k^{(1)}{\mathbf {u}}_k^{(1)}-\lambda _{1} {\mathbf {q}}_1=0 \\ \frac{1}{4}&\frac{\partial L}{\partial {\mathbf {u}}_k^{(1)}}=({\mathbf {q}}_1^{T}{{\mathbf {X}}_k^{(1)}{\mathbf {u}}_k^{(1)})^3}{{\mathbf {X}}_k^{(1)}}^T{\mathbf {q}}_1-\mu ^{(1)}_{k}{\mathbf {u}}_k^{(1)}-\frac{1}{2}{\mathbf{H}}_k {\varvec{\gamma }}_k=0\qquad (k=1,\ldots ,K) \end{aligned}$$

(14)

$$\begin{aligned} \frac{1}{2}&\frac{\partial L}{\partial \mu ^{(1)}_{k}}=1-{{\mathbf {u}}_k^{(1)}}^T{\mathbf {u}}_k^{(1)} =0 \\ \frac{1}{2}&\frac{\partial L}{\partial \lambda _{1}}=1-{\mathbf {q}}_1^{T}{\mathbf {q}}_1=0 \\ \frac{1}{2}&\frac{\partial L}{\partial {\varvec{\gamma }}_k}={\mathbf{H}}_k^T{\mathbf {u}}_k^{(1)}=0 \end{aligned}$$

(15)

Eigen-system (5) is obtained by left multiplying (14) with ${\mathbf {X}}_k^{(1)}{\mathbf {P}}^{\perp }_{\mathbf{H}_k}$ using (15) and (8) with the identities $\mu ^{(1)}_{k}=\root 4 \of {{\mu ^{{(1)}}_{k}}^3}\root 4 \of {{\mu ^{{(1)}}_{k}}}$ and $\root 4 \of {{\mu ^{{(1)}}_{k}}^3}=\root 4 \of {{\mu ^{{(1)}}_{k}}}\sqrt{{\mu ^{{(1)}}_{k}}}$, and by adding both terms of the identity up to $K$ and finally considering formula (7).