# Confirmatory factor analysis (CFA)

## Validate the hypothesized factor structure of exploratory or theoretical frameworks

**Confirmatory factor analysis (CFA)**is a highly complex statistical technique that is used to confirm or validate the internal structure of the survey that was yielded from

**and**

__reliability__**.**

__Principal Components Analysis (PCA)__**SPSS Amos 23*** is the preferable software package for running this type of analysis. The model yielded from your PCA will serve as the theoretical or conceptual of the construct that confirmatory factor analysis either confirms or rejects. Whereas PCA is focused on reducing data into something that makes "sense," confirmatory factor analysis is used to further

**validate and assess**the "sense" and "structure" yielded from the piloted survey.

### The steps for conducting confirmatory factor analysis (CFA) in SPSS AMOS

1. The data is entered in a within-subjects fashion.

2. Click

3. Click

4. Click on the

5. Click on the database file that has the validation study data for the survey.

6. For every factor yielded from the PCA, researchers should have a composite score for each subscale or factor in the validation study. However many factors that were extracted and interpreted in your PCA, draw that number of rectangles on the right side of the graphics editor. To do this, click on the green rectangle button on the left-hand side of the screen, labeled as

7. Right click the cursor on the rectangle and select

8. Click on the first rectangle and drag the duplicated rectangle about one inch above or below the first rectangle. Have the edges of each rectangle line up vertically.

9. Repeat Steps 7 and 8 until there are as many rectangles as factors yielded from the PCA.

10. Click on the green horizontal oval button, labeled as

11. Right click on the circle and select

12. Click on the first circle and drag the duplicated circle into the same position between the second rectangle and the right side of the graphics editor. Try to have the circles lined up and centered in a similar fashion to the rectangles.

13. Repeat Steps 11 and 12 until all of the rectangles have a circle next to it.

14. Click on the

15. Click on the pointed arrow facing left, labeled as

16. Draw these arrows from each circle on the right hand side of the editor to its corresponding rectangle next to it.

17. Draw an arrow starting from the larger circle to each of the rectangles.

18. In the end, each rectangle should have two arrows pointing at it, one from the small circle on the right side of graphics editor, and one arrow pointing at it from the large circle on the left hand side of the graphics editor.

19. Click

20. Click

21. In the table that appears, click on the first subscale or factor score from the validation study to highlight it.

22. Click and drag the variable into the first rectangle drawn earlier.

23. Click on the second subscale or factor score from the validation study to highlight it.

24. Click and drag the variable into the second rectangle drawn earlier.

25. Repeat these steps until each rectangle has a subscale or factor score in it.

26. Click on the first circle next to the first rectangle to highlight it.

27. Click on the button in the menu on the left-hand side of the screen, denoted as

28. Under the

29. Click on the second circle next to the second rectangle to highlight it.

30. Click on the button in the menu on the left-hand side of the screen, denoted as

31. Under the

32. Repeat these steps until all of the circles have a variable name.

33. Double click on the

34. In the

35. Double-click on the

36. In the

37. Repeat Steps 35 and 36 until all of the arrows from the little circles have a

38. Click

39. Click

40. Under the

41. Click

42. Click

43. Click on

44. Click on

45. Click

46. Click

47. Click on the

48. Click

2. Click

**File**.3. Click

**Data Files**.4. Click on the

**File Name**button.5. Click on the database file that has the validation study data for the survey.

6. For every factor yielded from the PCA, researchers should have a composite score for each subscale or factor in the validation study. However many factors that were extracted and interpreted in your PCA, draw that number of rectangles on the right side of the graphics editor. To do this, click on the green rectangle button on the left-hand side of the screen, labeled as

**Draw observed variables**. Draw the first factor about one inch from the right side of the graphics editor.7. Right click the cursor on the rectangle and select

**Duplicate**. The cursor will change.8. Click on the first rectangle and drag the duplicated rectangle about one inch above or below the first rectangle. Have the edges of each rectangle line up vertically.

9. Repeat Steps 7 and 8 until there are as many rectangles as factors yielded from the PCA.

10. Click on the green horizontal oval button, labeled as

**Draw unobserved variables**. Draw the first unobserved variable in the space between the first rectangle and the right side of the graphics editor.11. Right click on the circle and select

**Duplicate**. The cursor will change.12. Click on the first circle and drag the duplicated circle into the same position between the second rectangle and the right side of the graphics editor. Try to have the circles lined up and centered in a similar fashion to the rectangles.

13. Repeat Steps 11 and 12 until all of the rectangles have a circle next to it.

14. Click on the

**Draw unobserved variables**button again and draw a large circle about one inch away from the left side of the graphics editor. This large circle represents the ONE overall aggregate construct being measured by the survey instrument.15. Click on the pointed arrow facing left, labeled as

**Draw paths (single headed arrows)**.16. Draw these arrows from each circle on the right hand side of the editor to its corresponding rectangle next to it.

17. Draw an arrow starting from the larger circle to each of the rectangles.

18. In the end, each rectangle should have two arrows pointing at it, one from the small circle on the right side of graphics editor, and one arrow pointing at it from the large circle on the left hand side of the graphics editor.

19. Click

**View**.20. Click

**Variables in the Dataset**.21. In the table that appears, click on the first subscale or factor score from the validation study to highlight it.

22. Click and drag the variable into the first rectangle drawn earlier.

23. Click on the second subscale or factor score from the validation study to highlight it.

24. Click and drag the variable into the second rectangle drawn earlier.

25. Repeat these steps until each rectangle has a subscale or factor score in it.

26. Click on the first circle next to the first rectangle to highlight it.

27. Click on the button in the menu on the left-hand side of the screen, denoted as

**Object properties**.28. Under the

**Text**tab, type the variable name,**"e1"**into the**Variable name**box.29. Click on the second circle next to the second rectangle to highlight it.

30. Click on the button in the menu on the left-hand side of the screen, denoted as

**Object properties**.31. Under the

**Text**tab, type the variable name,**"e2"**into the**Variable name**box.32. Repeat these steps until all of the circles have a variable name.

33. Double click on the

**arrow**pointing from the large circle to the rectangle at the highest point of the diagram.34. In the

**Regression weight**box, type the number,**"1"**35. Double-click on the

**arrow**pointing from the first circle to the first rectangle.36. In the

**Regression weight**box, type the number,**"1"**37. Repeat Steps 35 and 36 until all of the arrows from the little circles have a

**Regression weight of 1**showing above it in the graphics editor.38. Click

**View**.39. Click

**Analysis Properties**.40. Under the

**Output**tab, click on the**Standardized estimates**and**Squared multiple correlations**boxes to select them.41. Click

**Analyze**.42. Click

**Calculate estimates**.43. Click on

**Standardized estimates**in the third box to the left of the graphics editor to highlight it.44. Click on

**View the output path diagram**button.45. Click

**View**.46. Click

**Text Output**.47. Click on the

**View the output path diagram**button.48. Click

**View text**.### The steps for interpreting the SPSS AMOS output for CFA

1. Look in the graphics editor for the squared multiple correlation values between the overall construct in the large circle and each subscale or factor score. They will above each arrow pointing from the overall construct to the subscale or factor variable.

2. Click

3. Click

4. Save the path diagram for publication purposes.

5. Click on the

6. Look in the

7. Look in the

8. Click on the

9. There are many different types of model fit indexes to choose from for your CFA. Choose the model fit statistic that best answers your research question. The most prevalent types of model fit indexes are GFI, CFI, RMR, and RMSEA.

2. Click

**File**.3. Click

**Save As**.4. Save the path diagram for publication purposes.

5. Click on the

**Estimates**drop-down menu of the**AMOS Output**.6. Look in the

**Standardized Regression Weights**table. These are the same values seen in the path diagram.7. Look in the

**Squared Multiple Correlations**table. These are the same values seen in the path diagram.8. Click on the

**Model Fit**drop-down menu.9. There are many different types of model fit indexes to choose from for your CFA. Choose the model fit statistic that best answers your research question. The most prevalent types of model fit indexes are GFI, CFI, RMR, and RMSEA.

Click on the

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- Statistical Analysis
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*SPSS Amos 23 (Armonk, NY: IBM Corp.)