【SPSS】Validity Analysis

Three Types

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Validity analysis is mainly divided into exploratory factor analysis (EFA), principal component analysis (PCA), and confirmatory factor analysis (CFA).

Exploratory Factor Analysis (EFA) — SPSS

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Exploratory factor analysis (EFA) is used to explore the latent factor structure in data when there is no clear prior hypothesis. Its main purpose is to identify the number of latent factors that affect observed variables and reveal the relationship between each factor and the observed variables. EFA is usually used in the early stages of research to help researchers understand the internal structure of the data and provide a basis for later theory building or hypothesis generation.

Principal Component Analysis (PCA) — SPSS

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Principal component analysis (PCA) is a common dimensionality-reduction method. It aims to transform the original high-dimensional data into a set of uncorrelated new variables, namely principal components, through linear transformation. PCA is often used to explore potential factors behind variables, especially when the data structure is unclear, such as when developing a new scale.

Confirmatory Factor Analysis (CFA) — AMOS

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Confirmatory factor analysis (CFA) is used to verify whether a researcher-specified factor-structure model fits the actual data. In CFA, researchers need to clearly specify the number of factors, correlations among factors, and the relationships between observed variables and factors. CFA is usually used in the theory-verification stage to test the structural validity of a scale or model.

Steps

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Calculate the KMO Value

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Steps:

1. Open SPSS and import the data: start SPSS, click “File” > “Open” > “Data,” and select your data file.
2. Select factor analysis: click “Analyze” > “Dimension Reduction” > “Factor.”
3. Select variables: in the dialog box, add the variables that need analysis to the “Variables” box.
4. Set descriptives: click the “Descriptives” button, select “Coefficients” and “KMO and Bartlett’s test of sphericity,” then click “Continue.”
5. Run the analysis: click “OK” to run the analysis.

Run Principal Component Analysis

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Steps:

1. Select factor analysis: click “Analyze” > “Dimension Reduction” > “Factor.”
2. Select variables: in the dialog box, add the variables that need analysis to the “Variables” box.
3. Set descriptives: click the “Descriptives” button, select “Coefficients” and “KMO and Bartlett’s test of sphericity,” then click “Continue.”
4. Set extraction method: click the “Extraction” button and choose “Principal components” as the extraction method.
5. Set rotation method: click the “Rotation” button and choose “Varimax” as the rotation method.
6. Options: select “Suppress small coefficients” and enter “0.4”. The exact value depends on the factor-loading standard.
7. Run the analysis: click “OK” to run the analysis.

Concept Explanation and Result Interpretation

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KMO and Bartlett’s Test of Sphericity

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1. KMO value

   • Below 0.5 means unsuitable for factor analysis; 0.5–0.7 is mediocre; 0.7–0.8 is good; 0.8–0.9 is very good; above 0.9 is excellent.

   Bartlett, M. S. (1950). “Tests of significance in factor analysis.” British Journal of Mathematical and Statistical Psychology, 3(2), 77–85.

2. Significance

   • When the test significance level is less than 0.05, the “identity matrix” hypothesis can be rejected, indicating that the data are suitable for factor analysis. You can make a table like this:

Principal Component Analysis

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Is It Always Necessary?

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Not every scale must undergo principal component analysis (PCA). In actual research, many papers only conduct the KMO test:

1. Different research purposes:
   • If the main purpose of the study is to evaluate scale reliability or other indicators rather than explore latent factor structure, only the KMO test may be performed.
2. Data characteristics:
   • If the scale has few items or weak correlations among items, principal component analysis may not be suitable.
3. Disciplinary conventions:
   • In some research fields, researchers may prefer other methods to evaluate scale validity rather than principal component analysis.
4. Use of a mature scale:
   • If the study uses a mature scale that has already been widely validated and used, such as commonly used psychological or educational measurement scales, and its validity and reliability have been fully demonstrated, repeated validity analysis may not be necessary. In that case, directly cite the scale’s previous validity-analysis results.
5. Pilot survey or preliminary study:
   • Some studies conduct a pilot survey or preliminary study before the formal study to test the scale’s validity and reliability. If the pilot results show that the scale is valid and reliable, the researcher may choose not to run a full validity analysis again, especially when the scale has already been fully validated.

Key Concept Explanations

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1. Communality:
   • Measures what proportion of a variable’s variance can be explained by the extracted factors.
   • If a variable’s communality is low, it means the variable contains more unique information that cannot be explained by factor analysis, and deleting the variable may need to be considered.
   • The general requirement is greater than 0.4.
2. Factor loading coefficient:
   • Indicates the correlation between each variable and each factor.
   • Standards vary: 0.5, 0.45, and 0.35 are all used; generally, 0.4 is accepted.
   • An absolute value greater than 0.4 is considered significant, meaning the variable has a strong association with the corresponding factor.
   • An absolute value below 0.4 may indicate a weak association between the variable and the factor, so deleting or reassessing the variable is recommended.
3. Variance explained and cumulative variance explained:
   • Variance explained: the proportion of total variance explained by each factor or principal component.
   • Cumulative variance explained: the sum of the variance-explanation rates of the first n factors or principal components. For example, if the first two factors explain 75% and 15% of the variance respectively, the cumulative variance explained is 90%, meaning the two factors together explain 90% of the original data variance.
     • Above 50% is acceptable.

What If Validity Does Not Meet the Standard?

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1. Handle abnormal data: check and remove questionnaires with very short completion time, such as under 60 seconds, or excessive repeated answers to ensure data quality.
2. Delete low-quality items:
   • Identify and delete low-communality items: in factor analysis, items with communality below 0.4 should be deleted to improve factor-analysis validity.
   • Evaluate item validity: delete items that load under other items or have factor-loading coefficients below 0.4, thereby improving the scale’s internal consistency.
   • Delete items that show serious deviation from their intended dimensions, meaning they are assigned to the wrong construct.
3. Extraction — select “Fixed number of factors (N)” — enter your number of dimensions in “Number of factors to extract (I)” to force the factor analysis to extract that number of factors.

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