# CFA model (in AMOS)

Module 3 – SLP INSTRUCTIONS

CFA – HANDS-ON

Please return to your SLP1 assignment, and use the same dataset for constructing and estimating a CFA model (in AMOS), which mimics the factor structure you identified in the EFA process (with varix rotation).

1. What are the fit indices? Are they good?

2. What are the correlations between latent variables (if any)?

3. Draw a diagram of the model

4. What is the highest modification index? What does it tell us?

· The paper is usually between 1 and 3 pages long.

SLP Assignment Expectations

1. Able to run CFA procedures in AMOS.

2. Able to read CFA results in AMOS.

3. Able to effectively and efficiently describe CFA results in research.

Module 3 – Background for SLP 3 and Case 3

CFA – HANDS-ON

Required Reading

Confirmatory Factor Analysis in SEM: https://www.youtube.com/watch?v=MCYmyzRZnIY&list=UUOMWLcopuV4xj8U3dePhVlQ

Multivariate Assumptions: https://www.youtube.com/watch?v=Gkp1DKbU-es&index=32&list=UUOMWLcopuV4xj8U3dePhVlQ

Validating the CFA: https://www.youtube.com/watch?v=hqV9RUSwwdA&list=UUOMWLcopuV4xj8U3dePhVlQ&index=30

Overview of CFA: https://www.youtube.com/watch?v=EorM5OEyNNY&index=22&list=UUOMWLcopuV4xj8U3dePhVlQ

Optional Reading

AMOS User Guide: ftp://public.dhe.ibm.com/software/analytics/spss/documentation/amos/20.0/en/Manuals/IBM_SPSS_Amos_User_Guide.pdf

Introduction to AMOS: http://vimeo.com/21136244

CFA in AMOS- Part 1: https://www.youtube.com/watch?v=kqLXexjwJP4

CFA in AMOS- Part 2: https://www.youtube.com/watch?v=gGw6cTrdutI

CFA in AMOS- Part 3: https://www.youtube.com/watch?v=FykQMaePLDc [Title Here, up to 12 Words, on One to Two Lines]

SLP 1 (SUBMITTED TO THE PROFESSOR AND NOW WILL BE USED IN THE SLP 3 ASSIGNMENT

This SLP will apply three techniques to the subscale scores for the Weschler Intelligence Scale for Children, using the SPSS. Therefore, in this assignment, I should find out what indicators load on its components that provide a high correlation.

Factor Analysis

The internal structure of a cognitive measure has been investigated using factor analysis. More specifically, exploratory factor analysis (EFA) has been employed in many studies to evaluate the reliability of the factor structure of the Wechsler scales across different groups of children to investigate structural validity. This study also has applied exploratory factor analysis using a principal-component analysis factor extraction to determine the factor structure.

The factorability of 11 items under the Weschler Intelligence Scale for Children was examined. Principal component analysis, under no rotation, varimax orthogonal and Promax methods of rotation for the factorability of a correlation are used.

Correlation Matrix Table

First, we determine if our dataset is suitable for EFA by checking if there is a patterned relationship amongst our variables using the Correlation matrix output table (Conway & Huffcutt, 2003). Since most of the variables have a large number of correlation coefficients, which range from (r = + .20 to r = + .625), we deduce that our dataset is suitable for factor analysis. It can also be observed that there is an absence of multicollinearity because no coefficient correlations above r = -0.9 or +0.9 quantifying a patterned relationship among variables (see Table 1). Looking at Bartlett’s Test of Sphericity which reported a chi-square of 524.488 at df = 55, we confirm that our dataset has a patterned relationship between the variables (p < .001). Finally, we will determine if our data is suitable for EFA by looking at the Kaiser-Meyer- Olkin Measure (KMO) of Sampling Adequacy, whose cut-off is above 0.5. Our KMO value is 0.820 implying that the data is suitable for exploratory factor analysis (see Table 2).

We will look at the total variance explained of the model as shown in the Total Variance Explained table to determine the number of significant factors noting that only extracted and rotated values are meaning for interpretation (Browne, 2001). The factors are arranged in descending order based on the most explained variance. The Initial Eigenvalues shows that the first four factors are meaningful as they have eigenvalues greater than 1. Factors 1, 2, 3 and 4 explain 34.842%, 1.557%, 1.172% and 1.066% of the variance respectively giving a cumulative 58.753% of variance explained by the model. The eigenvalues for each possible solution are graphically shown in the Scree Plot. As we find with the Kaiser-‐Criterion (eigenvalue greater than 1), the optimal solution has four factors. However, in our case, we could also argue in favor of a three-factor solution because this is the point where the explained variance makes the most significant jump, the elbow criterion (see Table 3 & Figure 1).

The component matrix table contains component loadings, which are the correlations between the variable and the component. Since these are correlations, the possible values range from -1 to +1. It contains the principal components that have been extracted. In our case, three components have been extracted (Eigenvalues greater than 1). A value of 0.753 indicates that Comprehension loaded strongly on component 1 while Client loaded strongly on component 2 as indicated by a value of 0.535. Coding loaded strongly on component 3 with a value of 0.819. Lastly, Age mate on component 4 with the loading of 0.621. Now, we leave all the settings the same in the factor analysis and try a rotation method to check if there will be changes in the components (see Table 4).

Varimax Rotation

We now proceed with our analysis by calling the varimax orthogonal rotation, one of the most popular orthogonal approaches applied in factor analysis. By orthogonal, we imply that we assume that the components or factors are uncorrelated. The Rotated Component Matrix table shows a change in the analysis after varimax rotation. Information, with a value of 0.789 loaded strongly for component 1 while Object Assembly loaded strongly for component 2 with a value of .746. Client loaded strongly for component 3 with a value of .666. Lastly, Coding, with the loading of 0.789 on component 4. In general, there are moderate-to-strong correlations between the six subscale scores for intelligence in children and component 1. Similarly, there are moderate-to-strong correlations between the five subscale scores for intelligence in children and component 2 and so forth (see Table 5).

Promax Rotation

We proceed further with our analysis this time using the Promax rotation method, which allows for correlated factors. Here, we look at two tables, that is, Structure Matrix and the Pattern Matrix. The Structure Matrix can be potentially better than pattern matrix in the back interpretation of variables by factors if such a situation comes on board. The table shows a change in the analysis after the Promax rotation. Information, with a value of 0.804, loaded strongly for component 1 while Object Assembly loaded strongly for component 2 with a value of .733. Client loaded strongly for component 3 with a value of .647. Lastly coding on component 4 with the loading of 0.795. However, in other situations Pattern Matrix can for the basis if interpretation since its coefficients are unique loads of a given factor into the variable. Using this matrix, we note that Information, with a value of 0.807 loads strongly for component 1 while Object Assembly loaded strongly for component 2 with a value of .792. Client loaded strongly for component 3 with a value of .696. and lastly, Coding loaded strongly for component 4 with a value of .790 (see Table 6).

References Browne, M. W. (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36(1), 111-150. doi:10.1207/s15327906mbr3601_05 Conway, J. M., & Huffcutt, A. I. (2003). A review and evaluation of exploratory factor analysis practices in organizational research. Organizational Research Methods, 6(2), 147-168. doi:10.1177/1094428103251541

Tables

Table 1. Correlation Matrix

Item

Information

Comprehension

Arithmetic

Similarities

Vocabulary

Digit Span

Picture Completion

Paragraph Arrangement

Block Design

Object Assembly

Coding

Information

1.000

.467

.494

.513

.625

.345

.230

.202

.229

.185

.007

Comprehension

.467

1.000

.392

.510

.531

.236

.407

.187

.369

.322

.061

Arithmetic

.494

.392

1.000

.369

.387

.269

.155

.227

.272

.043

.090

Similarities

.513

.510

.369

1.000

.538

.260

.369

.298

.261

.269

-.041

Vocabulary

.625

.531

.387

.538

1.000

.294

.285

.132

.297

.185

.100

Digit Span

.345

.236

.269

.260

.294

1.000

.075

.148

.073

.035

.173

Picture Completion

.230

.407

.155

.369

.285

.075

1.000

.249

.382

.363

-.072

Paragraph Arrangement

.202

.187

.227

.298

.132

.148

.249

1.000

.351

.253

.038

Block Design

.229

.369

.272

.261

.297

.073

.382

.351

1.000

.399

.107

Object Assembly

.185

.322

.043

.269

.185

.035

.363

.253

.399

1.000

.053

Coding

.007

.061

.090

-.041

.100

.173

-.072

.038

.107

.053

1.000

Table 2. KMO and Test of Bartlettt

KMO and Bartlett’s Test

Kaiser-Meyer-Olkin Measure of Sampling Adequacy.

.820

Bartlett’s Test of Sphericity

Approx. Chi-Square

524.488

df

78

Sig.

.000

Table 3. Total Variance Explained

Component

Initial Eigenvalues

Extraction Sums of Squared Loadings

Total

% of Variance

Cumulative %

Total

% of Variance

Cumulative %

1

3.842

29.555

29.555

3.842

29.555

29.555

2

1.557

11.979

41.534

1.557

11.979

41.534

3

1.172

9.017

50.551

1.172

9.017

50.551

4

1.066

8.202

58.753

1.066

8.202

58.753

5

.930

7.154

65.906

6

.784

6.032

71.938

7

.748

5.754

77.692

8

.610

4.692

82.384

9

.590

4.538

86.922

10

.512

3.941

90.863

11

.468

3.601

94.464

12

.408

3.141

97.604

13

.311

2.396

100.000

Extraction Method: Principal Component Analysis.

Table 4. Component Matrix

Component Matrixa

Component

1

2

3

4

Comprehension

.753

Similarities

.744

Vocabulary

.740

Information

.734

Arithmetic

.604

Block Design

.577

.425

Picture Completion

.561

.441

Paragraph Arrangement

.454

.412

Digit Span

.421

client

.535

Object Assembly

.462

.530

Coding

.819

agemate

-.441

.621

Extraction Method: Principal Component Analysis.

a. 4 components extracted.

Table 5. Rotated Component Matrix

Rotated Component Matrixa

Component

1

2

3

4

Information

.789

Vocabulary

.750

Arithmetic

.692

Similarities

.648

.401

Digit Span

.612

Comprehension

.584

.514

Object Assembly

.746

Picture Completion

.708

Block Design

.600

client

.666

Paragraph Arrangement

.634

Coding

.789

agemate

-.632

Extraction Method: Principal Component Analysis.

Rotation Method: Varimax with Kaiser Normalization.

a. Rotation converged in 11 iterations.

Table 6. Pattern and Structure Matrix

Pattern Matrixa

Structure Matrix

Component

Component

1

2

3

4

1

2

3

4

Information

.807

Information

.804

Vocabulary

.759

Vocabulary

.772

.422

Arithmetic

.717

Similarities

.707

.506

Digit Span

.668

Arithmetic

.696

Similarities

.617

Comprehension

.661

.602

Comprehension

.533

.422

Digit Span

.580

Object Assembly

.792

Object Assembly

.733

Picture Completion

.706

Picture Completion

.727

Block Design

.607

Block Design

.617

client

.696

client

.647

Paragraph Arrangement

.633

Paragraph Arrangement

.633

Coding

.790

Coding

.795

agemate

-.643

agemate

-.614

Extraction Method: Principal Component Analysis. Rotation Method: Promax with Kaiser Normalization.

Extraction Method: Principal Component Analysis. Rotation Method: Promax with Kaiser Normalization.

Figure 1. Scatterplot

FILE (DATA) PROVIDED FOR SLP 1 -SPSS STATISTICS DATA

wiscsem.sav

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## CFA model (in AMOS)

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# CFA model (in AMOS)

Module 3 – SLP INSTRUCTIONS

CFA – HANDS-ON

Please return to your SLP1 assignment, and use the same dataset for constructing and estimating a CFA model (in AMOS), which mimics the factor structure you identified in the EFA process (with varix rotation).

1. What are the fit indices? Are they good?

2. What are the correlations between latent variables (if any)?

3. Draw a diagram of the model

4. What is the highest modification index? What does it tell us?

· The paper is usually between 1 and 3 pages long.

SLP Assignment Expectations

1. Able to run CFA procedures in AMOS.

2. Able to read CFA results in AMOS.

3. Able to effectively and efficiently describe CFA results in research.

Module 3 – Background for SLP 3 and Case 3

CFA – HANDS-ON

Required Reading

Confirmatory Factor Analysis in SEM: https://www.youtube.com/watch?v=MCYmyzRZnIY&list=UUOMWLcopuV4xj8U3dePhVlQ

Multivariate Assumptions: https://www.youtube.com/watch?v=Gkp1DKbU-es&index=32&list=UUOMWLcopuV4xj8U3dePhVlQ

Validating the CFA: https://www.youtube.com/watch?v=hqV9RUSwwdA&list=UUOMWLcopuV4xj8U3dePhVlQ&index=30

Overview of CFA: https://www.youtube.com/watch?v=EorM5OEyNNY&index=22&list=UUOMWLcopuV4xj8U3dePhVlQ

Optional Reading

AMOS User Guide: ftp://public.dhe.ibm.com/software/analytics/spss/documentation/amos/20.0/en/Manuals/IBM_SPSS_Amos_User_Guide.pdf

Introduction to AMOS: http://vimeo.com/21136244

CFA in AMOS- Part 1: https://www.youtube.com/watch?v=kqLXexjwJP4

CFA in AMOS- Part 2: https://www.youtube.com/watch?v=gGw6cTrdutI

CFA in AMOS- Part 3: https://www.youtube.com/watch?v=FykQMaePLDc [Title Here, up to 12 Words, on One to Two Lines]

SLP 1 (SUBMITTED TO THE PROFESSOR AND NOW WILL BE USED IN THE SLP 3 ASSIGNMENT

This SLP will apply three techniques to the subscale scores for the Weschler Intelligence Scale for Children, using the SPSS. Therefore, in this assignment, I should find out what indicators load on its components that provide a high correlation.

Factor Analysis

The internal structure of a cognitive measure has been investigated using factor analysis. More specifically, exploratory factor analysis (EFA) has been employed in many studies to evaluate the reliability of the factor structure of the Wechsler scales across different groups of children to investigate structural validity. This study also has applied exploratory factor analysis using a principal-component analysis factor extraction to determine the factor structure.

The factorability of 11 items under the Weschler Intelligence Scale for Children was examined. Principal component analysis, under no rotation, varimax orthogonal and Promax methods of rotation for the factorability of a correlation are used.

Correlation Matrix Table

First, we determine if our dataset is suitable for EFA by checking if there is a patterned relationship amongst our variables using the Correlation matrix output table (Conway & Huffcutt, 2003). Since most of the variables have a large number of correlation coefficients, which range from (r = + .20 to r = + .625), we deduce that our dataset is suitable for factor analysis. It can also be observed that there is an absence of multicollinearity because no coefficient correlations above r = -0.9 or +0.9 quantifying a patterned relationship among variables (see Table 1). Looking at Bartlett’s Test of Sphericity which reported a chi-square of 524.488 at df = 55, we confirm that our dataset has a patterned relationship between the variables (p < .001). Finally, we will determine if our data is suitable for EFA by looking at the Kaiser-Meyer- Olkin Measure (KMO) of Sampling Adequacy, whose cut-off is above 0.5. Our KMO value is 0.820 implying that the data is suitable for exploratory factor analysis (see Table 2).

We will look at the total variance explained of the model as shown in the Total Variance Explained table to determine the number of significant factors noting that only extracted and rotated values are meaning for interpretation (Browne, 2001). The factors are arranged in descending order based on the most explained variance. The Initial Eigenvalues shows that the first four factors are meaningful as they have eigenvalues greater than 1. Factors 1, 2, 3 and 4 explain 34.842%, 1.557%, 1.172% and 1.066% of the variance respectively giving a cumulative 58.753% of variance explained by the model. The eigenvalues for each possible solution are graphically shown in the Scree Plot. As we find with the Kaiser-‐Criterion (eigenvalue greater than 1), the optimal solution has four factors. However, in our case, we could also argue in favor of a three-factor solution because this is the point where the explained variance makes the most significant jump, the elbow criterion (see Table 3 & Figure 1).

The component matrix table contains component loadings, which are the correlations between the variable and the component. Since these are correlations, the possible values range from -1 to +1. It contains the principal components that have been extracted. In our case, three components have been extracted (Eigenvalues greater than 1). A value of 0.753 indicates that Comprehension loaded strongly on component 1 while Client loaded strongly on component 2 as indicated by a value of 0.535. Coding loaded strongly on component 3 with a value of 0.819. Lastly, Age mate on component 4 with the loading of 0.621. Now, we leave all the settings the same in the factor analysis and try a rotation method to check if there will be changes in the components (see Table 4).

Varimax Rotation

We now proceed with our analysis by calling the varimax orthogonal rotation, one of the most popular orthogonal approaches applied in factor analysis. By orthogonal, we imply that we assume that the components or factors are uncorrelated. The Rotated Component Matrix table shows a change in the analysis after varimax rotation. Information, with a value of 0.789 loaded strongly for component 1 while Object Assembly loaded strongly for component 2 with a value of .746. Client loaded strongly for component 3 with a value of .666. Lastly, Coding, with the loading of 0.789 on component 4. In general, there are moderate-to-strong correlations between the six subscale scores for intelligence in children and component 1. Similarly, there are moderate-to-strong correlations between the five subscale scores for intelligence in children and component 2 and so forth (see Table 5).

Promax Rotation

We proceed further with our analysis this time using the Promax rotation method, which allows for correlated factors. Here, we look at two tables, that is, Structure Matrix and the Pattern Matrix. The Structure Matrix can be potentially better than pattern matrix in the back interpretation of variables by factors if such a situation comes on board. The table shows a change in the analysis after the Promax rotation. Information, with a value of 0.804, loaded strongly for component 1 while Object Assembly loaded strongly for component 2 with a value of .733. Client loaded strongly for component 3 with a value of .647. Lastly coding on component 4 with the loading of 0.795. However, in other situations Pattern Matrix can for the basis if interpretation since its coefficients are unique loads of a given factor into the variable. Using this matrix, we note that Information, with a value of 0.807 loads strongly for component 1 while Object Assembly loaded strongly for component 2 with a value of .792. Client loaded strongly for component 3 with a value of .696. and lastly, Coding loaded strongly for component 4 with a value of .790 (see Table 6).

References Browne, M. W. (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36(1), 111-150. doi:10.1207/s15327906mbr3601_05 Conway, J. M., & Huffcutt, A. I. (2003). A review and evaluation of exploratory factor analysis practices in organizational research. Organizational Research Methods, 6(2), 147-168. doi:10.1177/1094428103251541

Tables

Table 1. Correlation Matrix

Item

Information

Comprehension

Arithmetic

Similarities

Vocabulary

Digit Span

Picture Completion

Paragraph Arrangement

Block Design

Object Assembly

Coding

Information

1.000

.467

.494

.513

.625

.345

.230

.202

.229

.185

.007

Comprehension

.467

1.000

.392

.510

.531

.236

.407

.187

.369

.322

.061

Arithmetic

.494

.392

1.000

.369

.387

.269

.155

.227

.272

.043

.090

Similarities

.513

.510

.369

1.000

.538

.260

.369

.298

.261

.269

-.041

Vocabulary

.625

.531

.387

.538

1.000

.294

.285

.132

.297

.185

.100

Digit Span

.345

.236

.269

.260

.294

1.000

.075

.148

.073

.035

.173

Picture Completion

.230

.407

.155

.369

.285

.075

1.000

.249

.382

.363

-.072

Paragraph Arrangement

.202

.187

.227

.298

.132

.148

.249

1.000

.351

.253

.038

Block Design

.229

.369

.272

.261

.297

.073

.382

.351

1.000

.399

.107

Object Assembly

.185

.322

.043

.269

.185

.035

.363

.253

.399

1.000

.053

Coding

.007

.061

.090

-.041

.100

.173

-.072

.038

.107

.053

1.000

Table 2. KMO and Test of Bartlettt

KMO and Bartlett’s Test

Kaiser-Meyer-Olkin Measure of Sampling Adequacy.

.820

Bartlett’s Test of Sphericity

Approx. Chi-Square

524.488

df

78

Sig.

.000

Table 3. Total Variance Explained

Component

Initial Eigenvalues

Extraction Sums of Squared Loadings

Total

% of Variance

Cumulative %

Total

% of Variance

Cumulative %

1

3.842

29.555

29.555

3.842

29.555

29.555

2

1.557

11.979

41.534

1.557

11.979

41.534

3

1.172

9.017

50.551

1.172

9.017

50.551

4

1.066

8.202

58.753

1.066

8.202

58.753

5

.930

7.154

65.906

6

.784

6.032

71.938

7

.748

5.754

77.692

8

.610

4.692

82.384

9

.590

4.538

86.922

10

.512

3.941

90.863

11

.468

3.601

94.464

12

.408

3.141

97.604

13

.311

2.396

100.000

Extraction Method: Principal Component Analysis.

Table 4. Component Matrix

Component Matrixa

Component

1

2

3

4

Comprehension

.753

Similarities

.744

Vocabulary

.740

Information

.734

Arithmetic

.604

Block Design

.577

.425

Picture Completion

.561

.441

Paragraph Arrangement

.454

.412

Digit Span

.421

client

.535

Object Assembly

.462

.530

Coding

.819

agemate

-.441

.621

Extraction Method: Principal Component Analysis.

a. 4 components extracted.

Table 5. Rotated Component Matrix

Rotated Component Matrixa

Component

1

2

3

4

Information

.789

Vocabulary

.750

Arithmetic

.692

Similarities

.648

.401

Digit Span

.612

Comprehension

.584

.514

Object Assembly

.746

Picture Completion

.708

Block Design

.600

client

.666

Paragraph Arrangement

.634

Coding

.789

agemate

-.632

Extraction Method: Principal Component Analysis.

Rotation Method: Varimax with Kaiser Normalization.

a. Rotation converged in 11 iterations.

Table 6. Pattern and Structure Matrix

Pattern Matrixa

Structure Matrix

Component

Component

1

2

3

4

1

2

3

4

Information

.807

Information

.804

Vocabulary

.759

Vocabulary

.772

.422

Arithmetic

.717

Similarities

.707

.506

Digit Span

.668

Arithmetic

.696

Similarities

.617

Comprehension

.661

.602

Comprehension

.533

.422

Digit Span

.580

Object Assembly

.792

Object Assembly

.733

Picture Completion

.706

Picture Completion

.727

Block Design

.607

Block Design

.617

client

.696

client

.647

Paragraph Arrangement

.633

Paragraph Arrangement

.633

Coding

.790

Coding

.795

agemate

-.643

agemate

-.614

Extraction Method: Principal Component Analysis. Rotation Method: Promax with Kaiser Normalization.

Extraction Method: Principal Component Analysis. Rotation Method: Promax with Kaiser Normalization.

Figure 1. Scatterplot

FILE (DATA) PROVIDED FOR SLP 1 -SPSS STATISTICS DATA

wiscsem.sav

The post CFA model (in AMOS) appeared first on Best Custom Essay Writing Services | ourWebsite.

## CFA model (in AMOS)