a study on consultant statistical competency, client

A Study on Consultant StatisticalCompetency, Client Acceptance and

Consulting Efficiency Using HierarchicalFactor Analysis

Sang-Moon Kim1, Yen-Yoo You∗2,

Chang-Won Lee3 and Jung-Wan Hong4

1Doctoral Student, Department of KnowledgeService and Consulting, Hansung University,

116, samseonyo 16gil, Seongbuk-gu,Seoul Metropolitan Government, 02876, Korea

[email protected]∗2Professor, Division of Smart Management Engineering

Consulting Track, Hansung University,116, samseonyo 16gil, Seongbuk-gu,

Seoul Metropolitan Government, 02876, [email protected]

3Professor, Department of Public Administration,Hansung University, 116, samseonyo 16gil, Seongbuk-gu,

Seoul Metropolitan Government, 02876, [email protected]

4Professor, Department of Industrial and ManagementEngineering, Hansung University, 116,

samseonyo 16gil, Seongbuk-gu,Seoul Metropolitan Government, 02876, Korea

[email protected]

International Journal of Pure and Applied MathematicsVolume 120 No. 6 2018, 4979-4994ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issue http://www.acadpubl.eu/hub/

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Abstract

Background/Objectives: The purpose of this studyis to analyze the effect of consultant statistical competencyon the client consulting acceptance and consulting efficiencyand mediating effect of between the latent variables throughhierarchical factor analysis.

Methods/Statistical Analysis: The subjects of thisstudy were companies that received management consultingfrom government - funded financial institutions. The sam-ple consists of 130 companies. The questionnaire consistsof 19 observational variables. Each survey item has a 5 -point Likert scale. The study hypothesis was applied to thestructural equation model using AMOS19. In order to clar-ify the relationship between variables, a hierarchical factoranalysis method was used for hypothesis test.

Findings: Client consulting acceptance, which was ex-tracted from the latent variables of client consulting partic-ipation and understanding using in the first factor analysis,was used in the hierarchical factor analysis. In the firstfactor analysis, the consultant statistical competency has apositive (+) effect on the client consulting participation andconsulting efficiency, and the client consulting participationhave a positive (+) influence on the client consulting un-derstanding and consulting efficiency. The client consultingparticipation and understanding has no mediating effect onconsultant statistical competency about the consulting ef-ficiency. However, it is found that mediating effects of theclient consulting participation and understanding variableson the effect of the consultant statistical competency onthe consulting efficiency were confirmed. In the hierarchicalfactor analysis, the consultant statistical competency has apositive effect on the client consulting acceptance and theconsulting efficiency, and the client consulting acceptancehas a significant positive effect on the consulting effect. Inaddition, client consulting acceptance of the consultant sta-tistical competency on consulting efficiency has been con-firmed to have a positive mediating effect.

Improvements/Applications: Through this study, thehigher the consultant statistical competency, the higher theclient consulting acceptance and consulting efficiency. Inaddition, hierarchical factor analysis is a way to clarify the

International Journal of Pure and Applied Mathematics Special Issue

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path between latent variables.

Key Words : Hierarchical Factor Analysis, Consul-tant Statistical Competency, Client Consulting Acceptance,Client Consulting Participation, Client Consulting Under-standing, Consulting Efficiency, Consulting Performance.

1 Introduction

With the proliferation of smart devices, SNS, and the Internet, andthe development of IT technology, the amount of information indaily life has become diverse and enormous. The statistical abilityto analyze and predict information and make reasonable decisionsbased on it has become essential.[1] Statistical theory and analyt-ical methods involve collecting data, analyzing them, expressingthem in tables or graphs, and creating mathematical models topredict and estimate the future.[2] Management consultants needspecialized knowledge of statistical theory and analytical methodsto collect, analyze, summarize and predict data in each field ofconsulting. In other words, statistical competence has become anessential factor for successful consulting performance. Bang & Joopoints out that management consultants should have the abilityto develop and use professional services for business managementand business using expertise and information, analytical skills, andsystematic and scientific consulting models and tools.[3] Kinking,Clark also argues that consultants need to perform a variety ofroles, such as technical experts, alternative discoverers, problemsolvers, and require specialized competencies.[4] On the other hand,Structural Equation Modeling (SEM) is a model for analyzing thecausal relationships among various potential variables through themeasurement model and the structural model. The measurementmodel shows how the latent variables are linked to the measuredvariables and sets the model using exploratory factor analysis. Thestructural model is a model that shows the theoretical causal rela-tionship between potential variables.[5] Confirmatory factor analy-sis shows the relationship between several potential variables. Po-tential variables are used in the research hypothesis testing throughpath analysis. The latent variables extracted from the measuredvariables may have a number of latent variables showing a similar


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tendency, which may complicate the study or make interpretationof the research results difficult. Hierarchical factor analysis can rep-resent two or more potential variables as a new potential variableand can be expressed more clearly and concretely by examining itthrough path analysis.[6]

The purpose of this paper is to investigate the relationship be-tween the statistical capacity of consultants and the consultingefficiency of consultants and the efficiency of consulting by usinghierarchical factor analysis. Also, the validity of the hierarchicalfactor analysis is examined by comparing the test results using thefirst factor analysis and the test results using the hierarchical factoranalysis.

2 Theoretical Basis

2.1 Consultant Competency

Chang-juk Seo et al. concluded that the consultants job compe-tency consists of strategic thinking ability, analysis and alternativepresentation, and expertise. The consultant should have a varietyof job performance capabilities, but it is especially important tohave a knowledge competency to diagnose, analyze, predict, andinfer the statistical aspects of the client’s problems.[7] Young-sukChoi has proved that the competence of the consultant has a posi-tive effect on the trust of consulting service and positively influencesthe acceptance of consulting by the client. In other words, we con-firmed that the higher the consultant’s competency, the higher theacceptance of clients firm.[8]

2.2 Client Consulting Acceptance

Consulting client is expected to actively participate in consultingand try to understand the contents of consulting in order to max-imize the effect of consulting. Appelbaum & Steed found that theexpertise of consultants, and the relationships between consultantsand client firms, have a positive impact on management consultingperformance.[9] Ho-ran Park proved that consulting performance ismore improved as the degree of understanding and involvement of


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clients company is higher in satisfaction and performance of con-sulting firm.[10]

2.3 Consulting Efficiency

Hyo-sung Moon revealed that the willingness to participate in con-sulting to recognize the problems faced by SMEs and to resolvethem has a positive effect on the utilization of consulting. Toachieve the smooth progress and performance of consulting, theclient firm emphasizes the need for a general understanding ofconsulting understanding, process, and consulting goals.[11] Nam-hyeong Kim said that Consulting achievements are due to the resultof that consultation and whether the results gained more valuablethan the degree of satisfaction of consulting fees Consulting per-formed a result, the issue was resolved to be associated with in-creased corporate value or not.[12]

2.4 Hierarchical Factor Analysis

Hierarchical factor analysis takes into account the latent variableof the first factor analysis as a measurement variable and calculatesthe factor structure that decomposes the correlation coefficient ma-trix calculated in the first factor analysis. In general, the orthogonalcommon factor model is expressed as next formula.

X − µX = LFX + ε (1)

Here, X is the observed value, µX is the expected value of X, Lis the matrix of factor loadings, FX is a common factor, and ε is aspecific factor. Hierarchical factor analysis decomposes the matrixLL

′+ ϕ (L

′denotes the transpose matrix of L and ϕ denotes the

variance of the special factor, Var(ε).) obtained by equation (1)and performs a second factor analysis. Y is the potential variableobtained from the first factor analysis. The factor model is as fol-lows.

Y −µY = MFY + ζ (2)


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Where Y is the expected value of Y, M is the matrix of factorloadings, FY is a common factor, and ζ is a specific factor. M isa hierarchical structure derived from LL

′+ ϕ and the first factor

matrix FX . Assume F and ε are independent of each other.[13]

3 Study Model and Hypothesis

3.1 Study Model

The study model of this paper consists of study model 1 and studymodel 2. The study model 1 uses the first factor analysis to ex-amine the relationship between consultant statistical competency(CSC), client consulting participation (CCP), client consulting un-derstanding (CCU), and consulting efficiency (CE). Latent vari-ables and study hypotheses related to Study Model 1 are shown inFigure 1.

Figure 1: Study Model 1

The study model 1 also tests the indirect effects of consultingparticipation and understanding on the direct effect of each latentvariable and the effect of consultant statistical competency on con-sulting efficiency.

The study model 2 is based on the hierarchical factor analysis,in which it is intended to study the relationship between the con-sultant statistical competency, client consulting efficiency and thenew latent variable the client consulting acceptance (CCA) that isextracted from the client consulting participation and understand-ing. Latent variables and study hypotheses related to study model2 are shown in Figure 2.


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Figure 2: Study Model 2

The study model 2 tests the direct effect of consultant statisti-cal competency on client consulting acceptance and consulting effi-ciency and the indirect effect of client consulting acceptance on theeffect of consultant statistical competency on consulting efficiency.

3.2 Study Hypothesis

The study hypothesis related to the direct effect between variablesin the study model 1 is as follows.

H1: The consultant statistical competency will have a positiveeffect on client consulting participation

H2: The consultant statistical competency will have a positiveeffect on the client consulting understanding.

H3: The consultant statistical competency will have a positiveeffect on consulting efficiency.

H4: The client consulting participation will have a positive effecton client consulting understanding.

H5: The client consulting participation will have a positive effecton consulting efficiency.

H6: The client consulting understanding will have a positiveeffect on consulting efficiency.

The study hypothesis related to the mediating effect of the de-mand level of the firm on the influence of the consultant statisticalcompetency on the consulting efficiency is as follows.

H7: The influence of consultant statistical competency on theconsulting efficiency will be mediated by the client consulting par-ticipation.

H8: The influence of consultant statistical competency on theconsulting efficiency will be mediated by the client consulting un-


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derstanding.H9: The influence of consultant statistical competency on the

consulting efficiency will be mediated by the client consulting par-ticipation and understanding.

The study hypothesis for the direct effect related to the studymodel 2 is as follows.

H10: The consultant statistical competency will have a positiveeffect on the client consulting acceptance.

H11: The consultant statistical competency will have a positiveeffect on consulting efficiency.

H12: The client consulting acceptance will have a positive effecton consulting efficiency.

Finally, the study hypothesis related to the indirect effect ofconsultant statistical competency and consulting efficiency relatedto study model 2 is as follows.

H13: The influence of consultant statistical competency on con-sulting efficiency will be mediated by client consulting acceptance.

4 Data composition and Model Fit Test

4.1 Study Subjects and Questionnaire Compo-sition

The subjects of this study were small and medium enterprises fi-nanced by government financial institutions. The survey was con-ducted from April 2014 to June 2014, and the sampling methodwas Simple Random Sampling. The sample consisted of 130 com-panies. The questionnaire consists of 19 observational variables,and each item has a 5-point Likert scale. SPSS 23 and AMOS 19were used for the questionnaire analysis. Questionnaires consistedof five categories: consultant competency, client consulting par-ticipation, client consulting understanding, consulting performanceand consulting utilization. However, in the exploratory factor anal-ysis, consulting performance and consulting utilization under theeigenvalue 1.0 standard were tied as one latent variable and thiswas used as a consulting efficiency variable. The composition ofdetailed variables is shown in Table 1.


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In hierarchical factor analysis, client consulting participationand understanding were tied to a new latent variable, the clientconsulting acceptance.

4.2 Validity and Reliability Test and StructuralModel Fit Analysis

The validity of the sample was verified using exploratory factoranalysis. In the exploratory factor analysis, four factors with aneigenvalue of 1.0 or higher were selected. The total variance ex-plained by these four factors is 72.1%. The reliability test usedCronbach’s α value and it is composed of 0.83 ∼ 0.93 as shown inTable 2, it is a reliable level.

As a result of confirmatory factor analysis, seven observationalvariables were removed according to the SMC standard in the first19 measurement variables and 12 variables were used in the finalmodel. The results of the fitness test for the initial and final modelsare shown in Table 3.

Ref1. RV: Reference Value, FM: First Model, LM: Last ModelRef2. GFI, AGFI, RMR, and RMSEA represent the absolute fitindex, and IFI, TLI, and CFI represent the incremental fit index.


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GFI, AGFI, IFI, TLI and CFI are considered to be acceptable if >0.8.

In the final model, the null hypothesis is not rejected because theP-value is not significant for the null hypothesis of the test “Theproposed model is appropriate”. Therefore, it can be concludedthat the final selected model is appropriate. In addition, the ex-ponents representing the fitness of the other models have valueswithin the reference value, which shows that the proposed model isvalid.

5 The Study Result

5.1 Study Model 1 Hypothesis Test Result

In order to test the study model 1, a structural equation modeltest was conducted as an item of the final model. The results ofthe study hypothesis are shown in Table 4.

The higher the consultant statistical competency, the higherthe client consulting participation (β = 0.68, p <0.01) and theconsulting efficiency (β = 0.35, p = 0.01). In addition, the higherthe client consulting participation, the higher the client consultingunderstanding (β = 0.63, p <.01) and consulting efficiency (β =0.39 p = .02). However, the consultant statistical competency didnot significantly affect the client consulting understanding (β =0.06, p = 0.69), and the client consulting understanding did nothave a significant effect on the consulting efficiency (β = 0.03, p =0.82). The details of the path analysis result are shown in Figure3.


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Figure 3: The Result of Path Analysis in Study Model 1

This is because consultants have diverse competencies such asknowledge competency, ability competency, and attitude compe-tency. In addition, it can be seen that the consulting performanceand utilization are not high because client firms are helping thelack of consulting and solving the problems faced, and the overallunderstanding of consulting is high.

Next, the results of mediation effect are as follows. The boot-strapping method was used to test the mediation effect. The detailresults of test are shown in Table 5.

As a result of the test, the client consulting participation andunderstanding were found to have no mediating effect on the con-sulting efficiency of the consultant statistical competency. However,it is found that the influence of consultant statistical competencyon consulting efficiency is mediated at a significance level of 10%.In other words, it can be understood that the consultant statis-tical competency influences the consulting efficiency when clientfirm actively participates in consulting and understands consultingbased on it. Consultant statistical competency directly affects theconsulting efficiency through the bootstrap method.


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5.2 Study Model 2 Hypothesis Test Result

Hierarchical factor analysis utilized three latent variables: consul-tant statistical competency, client consulting acceptance, and con-sulting efficiency. The fit of the hierarchical model was confirmedto be more appropriate than the first factor analysis. The resultsof the model fit of hierarchical factor analysis are shown in Table6.

It can be seen that the absolute fit index has the same value,while the incremental fit index has a higher value. Table 7 shows theresults of the study hypotheses using hierarchical factor analysis.

As a result of hypothesis testing, the consultant statistical com-petency was found to have a positive effect on the client consultingacceptancy (β = 0.70 p <0.01) and consulting efficiency (β = 0.32p = 0.03). In addition, the client consulting acceptance was foundto have a significant effect on the consulting efficiency (β = 0.44 p= 0.01). The details of the path analysis result are shown in Figure4.

Figure 4: The Result of Path Analysis in Study Model 2


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If the consultant statistical competency is high, client is highlyreceptive to consulting, and the consulting efficiency is high. Inaddition, it can be concluded that the higher the acceptability ofclient company, the higher the consulting efficiency. In the firstfactor analysis, the consultant statistical competency was found tohave a positive effect on the client consulting participation, but itwas found that client consulting understanding was not significant.However, when these two factors are expressed as one factor ofclient consulting acceptance, it can be confirmed that it shows thesame conclusion as general intuition.

The effect of the consultant statistical competency on the con-sulting efficiency was tested as to whether the client consulting ac-ceptance mediates. As the first factor analysis, the bootstrappingmethod was used. As a result of the mediating effect analysis, thestandardized indirect effect is 0.31 and the P-value is 0.07, indicat-ing that there is a mediating effect (indirect effect) at a significancelevel of 10%. It can be said that the hierarchical structural equa-tion model is more consistent with intuition than the first-orderstructural equation model, where indirect effects are not found tobe significant.

6 Conclusion

This study was conducted to investigate the relationship betweenthe consultant statistical competency, client consultant acceptanceand consulting efficiency. The structural hypothesis was tested bythe first factor analysis and the results were compared using hi-erarchical factor analysis. In the first factor analysis, the clientstatistical competency has a significant effect (+) on the client con-sulting participation and consulting efficiency and the client con-sulting participation has a significant influence (+) on the under-standing and consulting efficiency respectively. However, the con-sultant statistical competency did not significant to the client con-sulting understanding, and the client consulting understanding didnot significant to the consulting efficiency. On the other hand, theinfluence of the consultant statistical competency on the consultingefficiency was not mediated by the client consulting participationand understanding.


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As a result of hierarchical factor analysis, the consultant statis-tical competency has a positive effect on the client consulting accep-tance and consulting efficiency and the client consulting acceptanceis also consulting efficiency on the positive effect (+). In addition,the consultant statistical competency showed that mediating effect(+) of consulting efficiency on client consulting acceptance. It wasdifferent result that of the first factor analysis.

This study suggests that consultant statistical competency is animportant factor in successful consulting because client consultingacceptance, consulting achievement and utilization are significantlyinfluenced by consultant statistical competency. In addition, it canbe concluded from the study that it is possible to draw clearerconclusions by extracting potential factors from similar factors hi-erarchically than by concluding the first factor analysis.

7 Acknowledgment

This research was financially supported by Hansung University.

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a study on consultant statistical competency, client

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