SPSS AMOS For the Structural Equation Modeling
SPSS AMOS For the Structural Equation Modeling SPSS AMOS For the Structural Equation Modeling Thi Le Ha Nguyen* VNU University of Medicine and Pharmacy, Vietnam National University, Vietnam J. Paulo Moreira IHMRDC - International Healt hcare Management Research & Development Centre, China Keisuke Nagase Graduated school of Medical Sciences, Kanazawa University, Kanazawa City, 920864, Japan Nhat Anh Nguyen Faculty of Information and Computer Science, Kanazawa Institute of Technology, Japan Published By BiomedGrid LLC United States August 02, 2023
SPSS AMOS For the Structural Equation Modeling CONTENTS Preface I 1. Introduction 1-2 a. What is Structural Equation Modeling? b. Testing a Structural Equation Model (SEM) c. SEM: Combining Measurement and Structural Relationships i. Measurement Relationship ii. Structural Relationship d. Why use SEM? 2. Exercise 3 a. Questionnaire i. The Impact of the Relationship Marketing on Repurchase Intention b. Research Hypotheses c. Research Method 3. Step by Step 5 4. Introduction to SPSS 5 a. Entering and Modifying Data i. Creating the Data Definitions ii. Enter data b. Data analysis i. Frequencies: Demographic Characteristics of Respondents ii. Recodes and Transformations: c. Descriptive Statistics d. Cronbach Alpha i. Interpretation of output ii. The output view iii. Reliability and Validity 5. Introduction to AMOS 26 a. Sem Stages for Testing Measurement Theory Validation with CFA b. The Measurement Model in SEM: Confirmatory Factor Analysis (CFA) c. The View Text of CFA 6. Interpret 60 a. Confirmatory Factor Analysis (CFA) and Model Goodness-of-Fit b. The Structural Model in SEM 7. Hypotheses Testing 66 a. Hypotheses Testing 8. Biography 68
SPSS AMOS For the Structural Equation Modeling I Preface The present book will appeal to both scholars and students with an interest in social science, healthcare/medical sciences, service industries as well as service/healthcare officials and organizations. Moreover, the book is a research monograph. It is anticipated to be used by undergraduate students on the Healthcare Management subject/service quality management subject. In addition, it aims at postgraduates, researchers, scholars, managers/leadership in the service industry, and academics to the international academic library market. This book shows step-by-step for the Structural Equation Modeling on SPPP Amos. I would like to thanks Publisher for publishing this book.
SPSS AMOS For the Structural Equation Modeling 1 Introduction What is Structural Equation Modeling? Structural Equation Modeling is a statistical approach to testing hypotheses about the relationships among observed and latent variables. Observed variables are also called indicator variables or manifest variables. Latent variables also denoted unobserved variables or factors [1]. Over the past decade, Structural Equation Modeling (SEM) was used in the research of psychology, sociology, education, and economics. It starts the first conceived by Wright, et al., [2] a biometrician who was credited with the development of path analysis to analyze genetic theory in biology [3] and then spread to other disciplines, such as psychology, political science, and education [4]. SEM improved through by attributed to the advancement of software development including the LISREL (Linear Structural Relations) by Joreskog and Sorbom [5] EQS (Equations)[6], AMOS (Analysis of Moment Structures) by Arbuckle [7], and Mplus [8]. The combination of methodological advances and improved interfaces in various SEM Software has contributed to the diverse usage of SEM. Testing a Structural Equation Model (SEM) The process of testing a Structural Equation Model (SEM) is related to the measurement and structural models. The measurement model may be developed based on theory and then tested with Confirmatory Factor Analysis (CFA) tests measurement theory based on the covariance between all measured items [9]. The goal of measurement theory is to create ways of measuring concepts in a reliable and valid manner. Measurement theories are examined by how well the indicator variables of theoretical constructs relate to one another. The relationships between the indicators are captured in a covariance matrix. CFA tests measurement theory by providing Testing Structural Equations Models evidence on the validity of individual measures based on the model’s overall fit and other evidence of construct validity. SPSS is the Statistical Package for the Social Sciences. It was developed as a programming language for conducting statistical analysis. It is a strong program that supported many ways to test data set in scientific research. SPSS not only supported basic descriptive statistics, such as averages and frequencies but also showed advanced tests such as multivariate analysis. Also, it can describe graphs and tables were of high quality. And nowadays, SPSS is used in management, analysis, and present data by both a graphical and a syntactical interface. IBM SPSS Amos (Analysis of Moment Structures) has implemented the general approach to data analysis of Structural Equation Modeling (SEM), also known as analysis of covariance structures, or causal modeling. This approach includes the general linear model and a common factor analysis. This is an easy-to-use program. It has integrated a graphical interface with an advanced computing engine for Structural Equation Modeling (SEM). With Amos, you can quickly specify, view, and modify your model graphically using simple drawing tools. Then you can assess your model’s fit, make any modifications, and print out a publication-quality graphic of your final model. Amos quickly has performed the computations and displays the results. The path diagrams of Amos provided a clear representation of models for researchers which solved estimation and hypothesis testing problems [10]. The purpose of this course is to provide an overview introduction and practice guidelines of structural equation modeling using the AMOS software. Structural Equation Modeling (SEM) encompasses such diverse statistical techniques as path analysis, confirmatory factor analysis, causal modeling with latent variables, and even analysis of variance and multiple linear regression. The course features give an exercise including hypotheses and how to perform SEM analyses using AMOS. By the end of the course, you are able to fit structural equation models using AMOS. You will also gain an appreciation for the types of research questions well-suited to SEM and an overview of the assumptions underlying SEM methods. SEM: Combining Measurement and Structural Relationships Measurement Relationship i. Constructs present by ovals or circles and measured variables are represented by squares or rectangles. ii. Measured variables (indicators) for exogenous constructs referred to as X variables, whereas endogenous construct indicators referred to as Y variables. iii. The X and/or Y measured variables related to tsheir respective construct by a straight arrow from the construct to the measured variable. Notice that the indicators were labeled as either X or Y which are based on, they related to an exogenous or endogenous construct, respectively. Structural Relationship: A structural model presents specifying structural relationships between latent constructs. This is a dependence relationship that descriptive by a straight arrow between measured variables and constructs. In a typical SEM, the arrow is drawn
SPSS AMOS For the Structural Equation Modeling 2 from the latent constructs to the variables that are associated with the constructs. Figure 1 presents a simple SEM model that compounds both the measurement and structural relationships of two constructs including four indicators each. There are two types of relationships that are possible among constructs including dependence relationships and correlational (covariance) relationships. In the measurement model (Figure 1a), it is a correlational relationship between the two constructs, indicating by the curved arrow. The indicators are labeled X1 to X8. In the structural model (Figure 1b) presents a dependent relationship between the exogenous and endogenous construct. The two constructs are the same indicators that change distinguish it in the correlational relationship, in which, the indicators of the exogenous constructs are denoted by X1 to X4, whereas the endogenous indicators are Y1 to Y4 (Figure 1). Figure 1: Structural Equations Modeling overview [9]. Why use SEM? SEM has attractive aspects: i. Assumptions underlying the statistical analyses were clear and testable. ii. Graphical interface software boosts creativity and facilitates rapid model debugging. iii. SEM program supported overall tests of model fit and individual parameter estimate tests simultaneously. iv. Regression coefficients mean, and variances compare simultaneously, even across multiple between-subjects groups.
SPSS AMOS For the Structural Equation Modeling 3 v. Measurement and confirmatory factor analysis models are used to purge errors, making estimated relationships among latent variables less contaminated by measurement error. vi. SEM supported numerous linear models may be fit using flexible, powerful software. Exercise Questionnaire The Impact of the Relationship Marketing on Repurchase Intention Your responses will be used solely for research purposes. The information that you provide will help to improve the quality of healthcare services. Please place a cross in the box corresponding to the level of your agreement/disagreement with each of the following statements. 1. Very strongly disagree, 2. Strongly disagree, 3. Agree, 4. Strongly agree, 5. Very strongly agree. (Table 0).
SPSS AMOS For the Structural Equation Modeling 4 Table 0: Statement/Items 1 2 3 4 5 Relationship Marketing (RM) trust RM1 The provider is very concerned about the safety of the customer RM2 Provider delivery quality service RM3 Provider fulfills to customers’ needs RM4 I have confidence in the providers’ services RM5 I will share the current issue with staff Commitment RM6 The provider makes a change to suit customers’ needs RM7 The provider supports personal services to meet customers’ needs RM8 The provider is flexible to service customers’ needs Communication RM9 The provider supports information in time and exactly RM10 The provider always give information when there is a new service RM11 The provider makes information and fulfills promises Service Quality (SQ) Assurance SQ12 Staffs were courtesy at all times SQ13 Staffs were responding quickly SQ14 Staffs were good professional knowledge SQ15 Customer feel trust and safe in their transaction Empathy SQ16 The provider gave first focus to customer SQ17 Provider understands the specific needs of the customer SQ18 Provider supported for the personal attention of the customer SQ19 Times of operating was convenient SQ20 Provider treated for the customer with dignity and respect Word-of-Mouth (WOM) WOM21 I am proud to tell friends that I used the service provider WOM22 I am willing to encourage friends to use the provider WOM23 I am willing to tell friends about the good aspects of provider WOM24 I will recommend to friends about provider frequently Repurchase Intention (RI) RI25 I will use this provider in my mind when repurchasing on healthcare RI26 I will always use this provider although other firms are more famous RI27 I always use this provider for future Research Hypotheses a) Hypothesis H1: Relationship Marketing has a positive influence on Word-of-mouth. b) Hypothesis H2: Relationship Marketing has positive significant on Repurchase Intention. c) Hypothesis H3: Relationship Marketing has an influence on Service Quality d) Hypothesis H4: Service Quality has a positive effect on Word-of-mouth. e) Hypothesis H5: Service Quality has positive significant on Repurchase Intention f) Hypothesis H6: Word-of-mouth has a positive influence on Repurchase Intention
SPSS AMOS For the Structural Equation Modeling 5 Research Method The sample size required for this study (N = 300) was determined based on the recommendations of Wolf, et al., [11]. The study was conducted using a distributed questionnaire to patients aged 18 years and older who were treated at a tertiary-level hospital in Vietnam during June 2019 and agreed to participate in the study. The subject hospital has been providing medical treatment for about 2,500 inpatients per day in various medical fields encompassing 39 clinical departments. Participants were selected from inpatient lists compiled by each department using a simple random sampling method; approximately 10 patients for every department. Therefore, 390 participants were recruited for this study. The instrument of the survey was a structured questionnaire which consisted of 33 questions into two main parts. Firstly, the socio-demographic factor included 6 questions related to age, sex, marital status, educational level, occupation, and method of paying hospital fees. Secondly, it included 27 questions related to Relationship Marketing (RM), Service Quality (SQ), Word-Of-Mouth (WOM), and Repurchase Intention (RI). In which, eleven questions were referred to the RM factors that included five of Trust(RM1-RM5), three of Commitment(RM6-RM8), and three of Communication (RM9-RM11). These questions are based on the work of Ndubisi [12]. and modified for compatibility with the research hospital context. Following that, the SQ factor was nine questions that consist of four for Assurance (SQ12-SQ15), five for Empathy (SQ16-SQ20). The content of these questions was based on previous research [13-15] followed by four questions were constructed to the WOM factor (WOM21-WOM24). These questions were based on the research of Gu, et al., [16]. and we modified it to suitable for the research hospital. Finally, three questions referred to the RI factor (RI25-RI27). All questions of the study were used to measure a Likert scale ranging from one to five (Figure 2). Figure 2: Step by Step Data analysis was performed to generate descriptive statistics on sociodemographic characteristics (frequencies and percentages) using the Statistical Package for the Social Sciences (SPSS) version 25.0. The analytical process consisted of several steps. First, the reliability of the variables was checked for internal consistency. Second, we performed a CFA to support the issues of dimensinality and convergent and discriminant validity and used SEM to test the validity of the proposed model and the hypotheses using AMOS 25.0 software. Introduction to SPSS Firstly, this step is to enter the data. The work in two windows: “Data view” and “Variable view”. We work in the “Variable View” window to name the variables. The next, you switch to the “data view” window to enter the data and then save the data file. Secondly, this is the step of analyzing the data. We work in the Data View window. It can be seen in the output view, the draft output view, and the script view. Finally, it is used to save or refine the queries.
SPSS AMOS For the Structural Equation Modeling 6 Entering and Modifying Data Creating the Data Definitions: Variable View i. Name: it shows the unique name of each variable that the names should be different. The names do not contain space or other illegal characters and the first character must be a letter. Example: AGE, SEX, MARR, EDU, OCU, FEE, RM1, RM2, RM3, RM4, RM5, RM6, RM7, RM8, RM9, RM10, RM11, SQ12, SQ13, SQ14, SQ15, SQ16, SQ17, SQ18, SQ19, SQ20, WOM21, WOM22, WOM23, WOM24, RI25, RI26, RI27 ii. Type: it refers to the type of data for each variable. The original setting was the most frequently used type, the numeric type, which refers to a variable, whose values are numbers. However, we can change it to Comma, Dot, Scientific Notation, Date. Example: numeric iii. Width: the field width. Example: 8 iv. Decimals: number of decimals in case of Numeric type. Example: 2 v. Label: descriptive name of a variable (up to 256 characters). It can contain space or other characters, which we could not use in Names. Example: Relationship marketing (RM): Trust: RM1, RM2, RM3, RM4, RM5; Commitment: RM6, RM7, RM8; Communication: RM9, RM10, RM11. Service quality (SQ): Assurance: SQ12, SQ13, SQ14, SQ15; Empathy: SQ16, SQ17, SQ18, SQ19, SQ20. Word of Mouth: WOM21, WOM22, WOM23, WOM24. Repurchase Intention (RI): RI 25, RI26, RI27. vi. Values: We can assign descriptive value labels for each value of a variable; thus, the numeric codes represent non-numeric categories. Example SEX: Value: 1, Lable: male >add Value: 2, Label: female > ok We see like this (Figure 3). Figure 3: Similarly, MARR: 1-sing, 2-marr, 3-divo, 4-wido (Figures 4).
SPSS AMOS For the Structural Equation Modeling Figure 4: EDU: 1-no, 2-pri, 3-seco, 4-high, 5-bach, 6-post (Figure 5). OCU: 1- gov, 2-nogov, 3-unem, 4-argi, 5-labor, 6-retir (Figure 6). FEE: 1-insu, 2-pay (Figure 7). Questions of factors from RM1 to RI27: 1-vestrdis, 2-strdis, 3-agree, 4-stragr, 5-vestragr It see like this (Figure 8). After the variables were created names, the screen looks like (Figure 9). i. Missing: if we do not have data, because for example, a respondent refused to answer. User missing values were flagged for special treatment and were rejected from most calculations. It is this (Figure 10). 7
SPSS AMOS For the Structural Equation Modeling ii. Missing: if we do not have data, because for example, a respondent refused to answer. User missing values were flagged for special treatment and were rejected from most calculations. It is this iii. Column: it refers to a number of characters for the column width. iv. Align: It is an alignment that controls the display of data. It can be right, left or center. v. Measures: it considers the scales of measurement, which can be nominal, ordinal, interval or ratio scale. In the SPSS we will find the nominal, ordinal and ratio measures. Figure 5: 8
SPSS AMOS For the Structural Equation Modeling 9 Figure 6:
SPSS AMOS For the Structural Equation Modeling Figure 7: 10
SPSS AMOS For the Structural Equation Modeling 11 Figure 8:
SPSS AMOS For the Structural Equation Modeling Figure 9: 12
SPSS AMOS For the Structural Equation Modeling 13 Figure 10: a) Nominal scale: refers to numbers are labels or groups or classes. Simple codes were assigned to objects as labels. We use a nominal scale for qualitative data, including professional classification, geographic classification. b) Ordinal scale: Data elements were ordered according to their relative size or quality, the numbers assigned to objects or events represent the rank order (1st, 2nd, 3rd, etc.). c) Interval scale: refers to a meaning of distances between any two observations. The “zero points” are arbitrary. Negative values can be used. Ratios between numbers on the scale are not meaningful, so operations such as multiplication and division cannot be carried out directly such as temperature with the Celsius scale. d) Ratio scale (Scale): It is the strongest scale of measurement. Distances between observations and also the ratios of distances have a
SPSS AMOS For the Structural Equation Modeling meaning. It contains a meaningful zero such as mass, length. The next, we enter data in the window “Data view” Enter data: Work at the window “Data view” We enter data for all questions. This view displays the actual data values or value labels. Then from the menu the File> select Save As, we save the data file. It sees such as (Figure 11). Figure 11: Data analysis We work in the window “Data view”. Frequencies: Demographic Characteristics of Respondents: This part you analyze for Demographic variables: age, sex, education, etc. 14
SPSS AMOS For the Structural Equation Modeling 15 Try it: From the menu, select Analyze> Descriptive Statistics> Frequencies Double-click on AGE move the variable to the Variable pane, we see like this (Figure 12). Try it: Figure 12: Then click ok, we will has the results in the output view following as. Then from the toolbar the select the save icon we save the Frequencies file. It see like this. The output view Frequencies (Tables 0.1, 0.2). In which
SPSS AMOS For the Structural Equation Modeling Table 0.1: Statistics age N Valid 353 Missing 0 Table 0.2: Valid Frequency Age Percent Valid Percent Cumulative Percent 18 2 0.6 0.6 0.6 19 2 0.6 0.6 1.1 20 6 1.7 1.7 2.8 21 2 0.6 0.6 3.4 22 7 2 2 5.4 23 1 0.3 0.3 5.7 24 5 1.4 1.4 7.1 25 4 1.1 1.1 8.2 26 5 1.4 1.4 9.6 27 3 0.8 0.8 10.5 28 5 1.4 1.4 11.9 29 6 1.7 1.7 13.6 30 9 2.5 2.5 16.1 31 9 2.5 2.5 18.7 32 4 1.1 1.1 19.8 33 12 3.4 3.4 23.2 34 9 2.5 2.5 25.8 35 16 4.5 4.5 30.3 36 9 2.5 2.5 32.9 37 7 2 2 34.8 38 9 2.5 2.5 37.4 39 10 2.8 2.8 40.2 40 10 2.8 2.8 43.1 41 12 3.4 3.4 46.5 42 10 2.8 2.8 49.3 43 12 3.4 3.4 52.7 44 11 3.1 3.1 55.8 45 12 3.4 3.4 59.2 46 7 2 2 61.2 47 15 4.2 4.2 65.4 48 10 2.8 2.8 68.3 49 8 2.3 2.3 70.5 50 13 3.7 3.7 74.2 51 7 2 2 76.2 52 5 1.4 1.4 77.6 53 5 1.4 1.4 79 54 6 1.7 1.7 80.7 55 6 1.7 1.7 82.4 56 8 2.3 2.3 84.7 57 1 0.3 0.3 85 58 1 0.3 0.3 85.3 59 8 2.3 2.3 87.5 60 5 1.4 1.4 89 16
SPSS AMOS For the Structural Equation Modeling 17 61 4 1.1 1.1 90.1 62 3 0.8 0.8 90.9 63 7 2 2 92.9 64 3 0.8 0.8 93.8 65 6 1.7 1.7 95.5 66 1 0.3 0.3 95.8 67 3 0.8 0.8 96.6 68 3 0.8 0.8 97.5 69 4 1.1 1.1 98.6 70 1 0.3 0.3 98.9 72 2 0.6 0.6 99.4 82 1 0.3 0.3 99.7 86 1 0.3 0.3 100 Total 353 100 100 i. Frequency: is the frequency of each expression of counting and adding up ii. Percent: is the frequency calculated as a percentage by taking the frequency of each expression divided by the total number of observations iii. Valid percent: A valid percentage calculated on the number of observations with an answer (excluding questionnaire with errors) iv. Cumulative Percent: The cumulative Percentage accumulates the top-down percentages, indicating how many% are surveying to some degree. v. Note: In this AGE variable has too many age types. Therefore, you encode in each age group as long as the number of people collected in the groups is not too small if too little will lead to difficulties for Chi-squared Test or other procedures For example, we can group into the following groups: 18-39, 40-49, 50-59, 60-86. Recodes and Transformations: Try it: From the menu, select Transform> Recode Into Different Variables Double-click on AGE move the Numeric Variable> Output Variable pane At Output Variable pane: Name and label this new variable, for example Name: ageRecode, Label Label: “Age Recode again” It see like this (Figure 13). Then Click the Range: we enter a new value. For example Range: 18 Through: 39 The Old Value window we clicked on Old and new value window that we click on New Value: 1 It will appear the Add. Click on the Add Similarly, we do for another group: 40-49 (New Value is 2), 50-59 (New Value is 3), 60-86 (New Value is 4). It see such as: (Figure 14). Then click> Continue> ok Click Change> ok.
SPSS AMOS For the Structural Equation Modeling Figure 13: Figure 14: 18
SPSS AMOS For the Structural Equation Modeling 19 Then switch to the window of the Variable View, we create these age groups in the Value column of the new variable: age Recode From 18-39 for Value is 1, 40-49 for Value is 2, 50-59 for Value is 3, 60 - 86 for Value is 4 Note: In the output of frequencies of the above age, you had the percentage of the highest age group is 86, so we can leave this group at the highest age of 86 years. Then you return of the window the Data View for data analysis for frequencies of these new-age groups. Try it: From the menu, select Analyze> Frequencies Double-click on the Age Recode again move the Variable pane> ok. We will has the results in the output view following as: The output view Frequencies (Tables 03,0.4) Table 0.3: Statistics Age Recode again N Valid 353 Missing 0 Table 0.4: Valid Age Frequency Recode Percent Again, Valid Percent Cumulative Percent 18-39 142 40.2 40.2 40.2 40-49 107 30.3 30.3 70.5 50-59 60 17 17 87.5 60-86 44 12.5 12.5 100 Total 353 100 100 Descriptive Statistics In this part, we will have the mean and the standard deviation, max, and min. Therefore, we only analyze descriptive statistics for the age variable. The variables of RM, SQ, WOM, and RI need not be calculated because the highest respondent is 5 and the lowest is 1. However, if we want to know how the respondent chooses, we can analyze it. Try it: From the menu, select Analyze> Descriptive Statistics> Descriptives Double-click Age to move them to the Variables list Click Options In the Descriptive options window, click Mean, Std. deviation, Variance, Range, Minimum, Maximum, it see like this (Figure 15) Click continue Click ok, results displayed, notice that the variable we selected are listed as rows, while the statistics are listed in columns. From the menu, select File> Save As It seem like this The output view (Table 0.5) Table 0.5: Descriptive Statistics N Range Minimum Maximum Mean Std. Deviation Variance age 353 68 18 86 43.2465 12.71112 161.573 Valid N (listwise) 353
SPSS AMOS For the Structural Equation Modeling Figure 15: This section referred to age, sex, marital status, educational level, occupation, and method of paying hospital fees. Total of 353 documents used for all the analysis steps. The data set entered and the analysis of the frequencies and descriptive were used by SPSS 25.0. The results show in Table 1. Table 1 shows that the average age of the respondents was 43.25±12.71 of which 69% were female and 31% were male. The largest of them were married, accounting for 82%, followed by single, widowed, and divorced was 18%. Most of the respondents were high school and bachelor’s degrees, accounting for 77%, and their occupation was agriculture, general labor, accounting 56%, following employees accounted for 26%, while students, unemployed, and retired accounted for 18%. The number of people with health insurance cards is equivalent to those who pay for hospital fees on their own, with 58% of respondents having health insurance cards and 42% of them personal payment. It is suitable for the context of this hospital that most of the respondents are farmers and workers, so they do not buy health insurance. This is also consistent with the context that Vietnam has not covered health insurance for these populations. 20
SPSS AMOS For the Structural Equation Modeling 21 Table 1: Frequencies and percentage of respondents classified by Socio-demographic factors. Socio-demographic Frequency Percentage (%) Age 18 - 39 142 40.2 40 - 49 107 30.3 50 - 59 60 17 60 - 86 44 12.5 >86 0 0 Mean=43.25 SD=12.71 Min=18 Max= 86 Sex Male 109 30.9 Female 244 69.1 Marital status Single 50 14.2 Married 288 81.6 Divorced 3 0.8 Widowed 12 3.4 Educational level No school 3 0.8 Primary school 9 2.5 Secondary school 67 19 High school 151 42.8 Bachelor’s degree 120 34 Postgraduate degree 3 0.8 Occupation Student 15 4.2 Employees 92 26.1 Labor 94 26.6 Agriculture 105 29.7 Unemployed 21 5.9 Retired 26 7.4 Method of paying hospital fees Insurance 204 57.8 Personal payment 149 42.2 Total 353 100 Cronbach Alpha A Likert scale ranging from strongly agree (5) to strongly disagree (1) was used to capture the responses to all the study items. Cronbach’s alpha value was used to assess the scales’ reliability, which considers the degree to which the consistency and stability of a set of indicators reflect a given construct. Usually, we compute Cronbach’s alpha for Likert scale type questions. However, we can also compute for yes/no type questions. This book only considers for Likert scale type questions. After that determine the list of variables that measure a particular construct. In this exercise, we analyze for each group of factors including the group of TRUST (RM1- RM5), COMMITMENT (RM6- RM8), COMMUNICATION (RM9- RM11), ASSURANCE (SQ12- SQ15), EMPATHY (SQ16- SQ20), WOM (WOM21- WOM23), and RI (RI25- RI27). Try it: Open dataset Click Options From the top menu, click Analyze> Scale> Reliability Analysis. Double- click variables RM1 through RM5 to move them to the Items box
SPSS AMOS For the Structural Equation Modeling In the dialog box, click Statistics. In the description box, select Item, Scale, and Scale if item deleted. In the inter-item box, select Correlation. We see like this (Figure 16) Click Continue and then OK to generate the output. The output view: Reliability Scale: ALL VARIABLES (Table 0.6, Figure 17, Tables 0.7,0.8, Figure 18 & Table 0.9) Table 0.6: Case Processing Summary Cases N % Valid 353 100 Excludeda 0 0 Total 353 100 Note: a. Listwise deletion based on all variables in the procedure. Table 0.7: Item Statistics Mean Std. Deviation N RM1 3.4023 0.87723 353 RM2 3.4533 0.87821 353 RM3 3.5297 0.93532 353 RM4 3.6261 0.90554 353 RM5 3.5156 0.99168 353 Table 0.8: Inter-Item Correlation Matrix RM1 RM2 RM3 RM4 RM5 RM1 1 0.688 0.588 0.673 0.463 RM2 0.688 1 0.765 0.725 0.573 RM3 0.588 0.765 1 0.718 0.559 RM4 0.673 0.725 0.718 1 0.595 RM5 0.463 0.573 0.559 0.595 1 Table 0.9: Scale Statistics Mean Variance Std. Deviation N of Items 17.5269 14.847 3.85313 5 22
SPSS AMOS For the Structural Equation Modeling 23 Figure 16: Figure 17: Figure 18:
SPSS AMOS For the Structural Equation Modeling Interpretation of output: We can see in table “Reliability Statistics” that the Cronbach’s alpha value for 5 items was 0.895. The cutoff value of 0.7 is usually used in social science research. So, Cronbach’s value of 0.7 or higher is generally considered reliable. The value ranges from 0 to 1. To interpret the output, we can base it on the rule of George and Mallery [17]. Hair Jr, et al., [9]. > 0.9 (Excellent), > 0.8 (Good), > 0.7 (Acceptable), > 0.6 (Questionable), > 0.5(Poor), and < 0.5 (Unacceptable) Notes: i. Cronbach’s alpha reliability coefficient normally ranges between 0 and 1. ii. The closer the coefficient is to 1.0, the greater is the internal consistency of the items (variables) in the scale. iii. Cronbach’s alpha coefficient increases either as the number of items (variables) increases or as the average inter-item correlations increase (i.e., when the number of items is held constant). Also, we can see the table “Item-Total Statistics”. In this table the Cronbach’s Deleted> Cronbach’s Alpha. Thus, it would increase if we would delete one item “Newspaper subscription” from the model. Then, we rerun the overall step by removing that variable “Newspaper subscription”, then there will be a change in the output such as value increased from 0.895 to 0.90. This is because it was re-calculated for 4 items. So, we keep on following the same steps to remove unreliable items and make our tool reliable. However, Cronbach’s alpha shouldn’t be used as a sole criterion for measuring reliability. It is just a statistical guide for quick decisions on reliability measures. In this exercise, we deleted the RM5 item. Thus, the RM5 item was rejected, and only accepted items of RM1, RM2, RM3, RM4. The results show in the output view following as: The output view: (Figure 17 and Table 0.10) Table 0.10: Item-Total Statistics Scale Mean if Item Deleted Scale Variance if Item Deleted Corrected Item-Total Correlation Squared Multiple Correlation Cronbach’s Alpha if Item Deleted RM1 10.6091 6.091 0.715 0.537 0.893 RM2 10.5581 5.713 0.827 0.691 0.853 RM3 10.4816 5.642 0.774 0.642 0.872 RM4 10.3853 5.698 0.795 0.633 0.864 Similarly, we are computing for other variable groups. The results of Cronbach’s Alpha following as: (Table 0.11-0.22) Table 0.11: Reliability Statistics Cronbach’s Alpha N of Items 0.889 3 Table 0.12: Item-Total Statistics Scale Mean if Item Deleted Scale Variance if Item Deleted Corrected Item-Total Correlation Cronbach’s Alpha if Item Deleted RM6 6.8385 2.869 0.797 0.832 RM7 6.7252 2.7 0.822 0.809 RM8 6.7592 2.905 0.735 0.885 Table 0.13: Reliability Statistics Cronbach’s Alpha N of Items 0.843 3 Table 0.14: Item-Total Statistics Scale Mean if Item Deleted Scale Variance if Item Deleted Corrected Item-Total Correlation Cronbach’s Alpha if Item Deleted RM9 6.8244 2.628 0.67 0.818 24
SPSS AMOS For the Structural Equation Modeling 25 RM10 6.8215 2.471 0.754 0.738 RM11 6.9773 2.465 0.704 0.787 Table 0.15: Reliability Statistics Cronbach’s Alpha N of Items 0.891 4 Table 0.16: Item-Total Statistics Scale Mean if Item Deleted Scale Variance if Item Deleted Corrected Item-Total Correlation Cronbach’s Alpha if Item Deleted SQ12 11.0538 6.727 0.702 0.881 SQ13 10.7564 6.338 0.786 0.849 SQ14 10.5184 6.517 0.794 0.847 SQ15 10.5722 6.586 0.758 0.86 Table 0.17: Reliability Statistics Cronbach’s Alpha N of Items 0.874 5 Table 0.18: Item-Total Statistics Scale Mean if Item Deleted Scale Variance if Item Deleted Corrected Item-Total Correlation Cronbach’s Alpha if Item Deleted SQ16 13.6232 9.048 0.68 0.853 SQ17 13.1983 8.841 0.789 0.828 SQ18 13.2011 8.746 0.7 0.849 SQ19 13.1756 8.958 0.705 0.847 SQ20 13.3966 9.456 0.645 0.861 Table 0.19: Reliability Statistics Cronbach’s Alpha N of Items 0.926 4 Table 0.20: Item-Total Statistics Scale Mean if Item Deleted Scale Variance if Item Deleted Corrected Item-Total Correlation Cronbach’s Alpha if Item Deleted WOM21 10.4051 5.793 0.82 0.906 WOM22 10.2493 5.744 0.853 0.895 WOM23 10.221 5.843 0.812 0.909 WOM24 10.2748 5.581 0.827 0.905 Table 0.21: Reliability Statistics Cronbach’s Alpha N of Items 0.831 3
SPSS AMOS For the Structural Equation Modeling Table 0.22: Item-Total Statistics Scale Mean if Item Deleted Scale Variance if Item Deleted Corrected Item-Total Correlation Cronbach’s Alpha if Item Deleted RI25 7.2266 3.466 0.667 0.799 RI26 6.8612 2.671 0.661 0.813 RI27 7.0567 2.804 0.773 0.682 Reliability and Validity: The Cronbach’s alpha value of the RM factor was between 0.84 and 0.90, that of SQ was from 0.87 to 0.89, that of WOM was 0.93, and that for the RI factor was 0.83 (Table 2). The alpha coefficients for all latent variables exceeded the cut-off reliability value of 0.70, showing the reliability and adequate internal consistency of the questionnaire. Of the 27 original items, 26 were retained, with 1 omitted to ensure sufficient reliability of the research instrument (Table 2). Table 2: Reliability statistics Constructs Items Cronbach’s Alpha Relationship Marketing (RM) Trust 4 0.9 Commitment 3 0.89 Communication 3 0.84 Service Quality (SQ) Assurance 4 0.89 Empathy 5 0.87 Word of Mouth (WOM) 4 0.93 Repurchase Intention (RI) 3 0.83 Introduction to AMOS The data were analyzed via a two-step approach involving a measurement model (CFA) and a structural model. The measurement model shows the underlying structure of the latent variables in a theoretical model. The structural model shows the causal and correlational links among latent variables in a theoretical model. Confirmatory Factor Analysis (CFA) was performed along with Structural Equation Modeling (SEM) to test the validity of the model using the AMOS 25.0 program (SPSS Inc.) [9]. Sem Stages for Testing Measurement Theory Validation with CFA We have 4 latent variables follow as: Factor 1: Relationship Marketing (RM) Trust: RM1- RM5 Commitment: RM6- RM8 Communication: RM9- RM11 Factor 2: Service Quality (SQ) Assurance: SQ12- SQ15 Empathy: SQ16- SQ20 Factor 3: Word-of-Mouth (WOM): WOM21- WOM24 Factor 4: Repurchase Intention (RI): RI25- RI27 The Measurement Model in SEM: Confirmatory Factor Analysis (CFA) All items were accepted from Cronbach’s Alpha used to compute CFA. Open AMOS 25.0 Graphics. We will now see a blank AMOS Graphics diagram page that looks like this (Figure 20) Try it: Open data files From the toolbar, select File> Data files or from the Tools menu in the AMOS Graphics screen, select Data files icon (Figure 21) We looks like this (Figure 22) 26
SPSS AMOS For the Structural Equation Modeling 27 Figure 19: Figure 20:
SPSS AMOS For the Structural Equation Modeling Figure 21: Figure 22: 28
SPSS AMOS For the Structural Equation Modeling 29 Select Data files we need analyze. Click OK. Operating principles of icons: Tools were used by single-clicking on the icon. A tool that is using will have an icon that appears to be lowered. To delete a tool, single-click on its icon once again. Single-click on the Draw Latent Variables and Indicators icon from the toolbar (Figure 23). Figure 23: Figure 24: Move the mouse pointer to the drawing surface and draw an oval by clicking and holding the mouse button. (Figure 24) Once we have a satisfactory oval drawn, click the mouse on the oval the number of times we need the observed indicators. We will now have a latent variable with ten observed indicators. (Figure 25)
SPSS AMOS For the Structural Equation Modeling Figure 25: Notice that a number of the paths are fixed to a value of 1.00. These are present to ensure proper model identification. If we want to have those paths be consistently on the left side of each variable set. To do that, use the Reflect Indicators tool. (Figure 26) or double-click a single arrow appear a table. We write number 1 into the Regression weight box in the object of the Parameters follow such as: (Figure 27) We can copy the portion of the model we have already built. To do this: • Click on the Select All Objects icon: (Figure 28) At that time the entire diagram should change color from black to blue. Then, we click on the Deselect all objects the entire diagram should change color return black. (Figure 29) • Click on the Duplicate Objects tool icon (it resembles a photocopier), click on the latent variable’s oval, and drag your mouse pointer to the right, left, up, down. We have replicas of the latent variable. (Figure 30) 30
SPSS AMOS For the Structural Equation Modeling Figure 26: Figure 27: Figure 28: 31
SPSS AMOS For the Structural Equation Modeling Figure 29: Figure 30: We use the Move objects icon to move the particular shape Use the Erase objects icon to cut the shape Use the Move objects icon combine with the Preserve Symmetries to move all the shape (Figures 31,32) Use the Duplicate Objects icon to copy a particular shape To create a residual for the latent variable, use the Add Unique Variable icon. (Figure 33) Select the Rotate the indicators of the latent variable icon. Click once on the latent variable’s oval. They rotate 90 degrees clockwise. Click the oval once more. The indicators rotate another 90 degrees. Click on the Rotate Indicators tool button to deactivate it. (Figure 34) Select the Draw Covariances tool, represented by a double-headed arrow to relate between two latent variables. 32
SPSS AMOS For the Structural Equation Modeling Figure 31: Figure 32: Figure 33: Figure 34: Figure 35: 33
SPSS AMOS For the Structural Equation Modeling We can draw a latent variable or use the copy icon. Finally, we have a shape to all four variable follow as: (Figure 35) Name the latent variable (oval) by double-clicking on the oval shape. Then, we name the latent variable, we will look like this: (Figure 36) Figure 36: Next, single-click the icon of List variables in the data set from the toolbar. We move the indicator variables of the latent variables to the rectangle, we will look like this: (Figures 37,38) The next, we select the Plugins on the toolbar, click the Name Unobserved Variable like this shape (Figure 39) It will appear the errors on the small circle of observed indicator. It is residual of the observed indicator. Note that, we can write the residual yourself by double-click on the residual of the observed indicator (the small circle), it will appear the Object Properties. Select the Text, we type e into the Variable name box, such as e1, etc. (Figure 40) or select Plugins on the toolbar> the Name Unobserved Variable was set up from software program set up, we have resulted is same. (Figure 41) Use the Move objects icon combine with the Preserve Symmetries to move all the shape. Then, we draw covariances to correlate between the latent variables by the double-headed arrow. (Figures 42-45) To request modification index output. From the toolbar select the View> Analysis properties> Output. Click - Minimization history - Standardized estimates 34
SPSS AMOS For the Structural Equation Modeling - Squared multiple correlations - Residual moments - Modification indices (Figure 46) Figure 37: Figure 38: 35
SPSS AMOS For the Structural Equation Modeling Figure 39: 36
SPSS AMOS For the Structural Equation Modeling Figure 40: 37
SPSS AMOS For the Structural Equation Modeling Figure 41: Figure 42: Figure 43: 38
SPSS AMOS For the Structural Equation Modeling Figure 44: Figure 45: 39
SPSS AMOS For the Structural Equation Modeling Figure 46: Figure 47: In addition, we click on the Title icon appear a table (Figures 47,48) We type in the table several indexes follow as: Chi-square= \cmin; df= \df; P= 0\p Chi-square/df= \cmindf GFI=0\gfi; TLI=0\tli; CFI=0\cfi; NFI=0\nfi RMSEA=0\rmsea; AGFI=0\agfi We see like this (Figure 49) 40
SPSS AMOS For the Structural Equation Modeling The next, to run the model, click on the Calculate Estimates tool icon (Figure 50) We check the output by the view text icon (Figure 51) At the top of this section of the AMOS, the Graphics window is an up-arrow located next to a down arrow. (Figure 52) Clicking on the up-arrow the AMOS will display the parameter estimates. Unstandardized or standardized estimates can be chosen by clicking on the appropriate selection. Clicking on the down-arrow returns we to the AMOS Graphics drawing interface, where we can modify your existing model and then re-run it, or you can open a new model or pre-existing model file. When we click on the up-arrow, the following parameter estimates are displayed as part of the output. (Figure 53) To move a parameter on the output diagram, use the Move Parameter tool. (Figure 54) Select the tool and move your mouse pointer over the offending variable until it is highlighted in red. Then click and pull the mouse in a direction we think would allow the parameter estimate value to be displayed more appropriately. In addition, we can see at the Amos Output likes this shape (Figure 55) Figure 48: 41
SPSS AMOS For the Structural Equation Modeling Figure 49: Figure 50: Figure 51: Figure 52: 42
SPSS AMOS For the Structural Equation Modeling Figure 53: Figure 54: 43
SPSS AMOS For the Structural Equation Modeling Figure 55: At this window, we check three paths: i. The Estimates: The table shows the unstandardized estimate, its standard error (abbreviated S.E.), and the estimate divided by the standard error (abbreviated C.R. for Critical Ratio). The probability value associated with the null hypothesis that the test is zero is displayed under the P column. All of the regression coefficients in this model are significantly different from zero beyond the 0.01 level. Standardized estimates allow you to evaluate the relative contributions of each predictor variable to each outcome variable. The standardized estimates for the fitted model appear below. (Figure 56) The next, we calculate Average Variance Extracted (AVE) and Composite Reliability/Construct Reliability (CR) based on the number of the Standardized Regression Weights in the Estimate path by Excel program (Figure 57) According to Hair Jr, et al., [9] 44
SPSS AMOS For the Structural Equation Modeling Average Variance Extracted (AVE): 2 1 n i i L AVE n = = ∑ Composite Reliability/Construct Reliability (CR) 2 1 2 1 1 n i i n n i i i i L CR L e = = = = + ∑ ∑ ∑ Finally, we will see this table (Figures 58,59) Figure 56: 45
SPSS AMOS For the Structural Equation Modeling Figure 57: 46