# Common Method Bias (CMB) in Confirmatory Factor Analysis (CFA)

## Common Method Bias (CMB)

• REF: Podsakoff, P.M., MacKenzie, S.B., Lee, J.Y., and Podsakoff, N.P. “Common method biases in behavioral research: a critical review of the literature and recommended remedies,” Journal of Applied Psychology (88:5) 2003, p 879.

Common method bias refers to a bias in your dataset due to something external to the measures. Something external to the question may have influenced the response given. For example, collecting data using a single (common) method, such as an online survey, may introduce systematic response bias that will either inflate or deflate responses. A study that has significant common method bias is one in which a majority of the variance can be explained by a single factor. To test for a common method bias you can do a few different tests. Each will be described below. For a step by step guide, refer to the video tutorials.

### Harman’s single factor test

• It should be noted that the Harman’s single factor test is no longer widely accepted and is considered an outdated and inferior approach.

A Harman’s single factor test tests to see if the majority of the variance can be explained by a single factor. To do this, constrain the number of factors extracted in your EFA to be just one (rather than extracting via eigenvalues). Then examine the unrotated solution. If CMB is an issue, a single factor will account for the majority of the variance in the model (as in the figure below).

### Common Latent Factor

This method uses a common latent factor (CLF) to capture the common variance among all observed variables in the model. To do this, simply add a latent factor to your AMOS CFA model (as in the figure below), and then connect it to all observed items in the model. Then compare the standardised regression weights from this model to the standardized regression weights of a model without the CLF. If there are large differences (like greater than 0.200) then you will want to retain the CLF as you either impute composites from factor scores, or as you move in to the structural model. The CLF video tutorial demonstrates how to do this. This approach is taken in this article:

• Serrano Archimi, C., Reynaud, E., Yasin, H.M. and Bhatti, Z.A. (2018), “How perceived corporate social responsibility affects employee cynicism: the mediating role of organizational trust”, Journal of Business Ethics, Vol. 151 No. 4, pp. 907-921.

### Marker Variable

This method is simply an extended, and more accurate way to do the common latent factor method. For this method, just add another latent factor to the model (as in the figure below), but make sure it is something that you would not expect to correlate with the other latent factors in the model (i.e., the observed variables for this new factor should have low, or no, correlation with the observed variables from the other factors). Then add the common latent factor. This method teases out truer common variance than the basic common latent factor method because it is finding the common variance between unrelated latent factors. Thus, any common variance is likely due to a common method bias, rather than natural correlations. This method is demonstrated in the common method bias video tutorial.

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### Zero and Equal Constraints

The most current and best approach is outlined below. Here is an article that recommends this approach (pg. 20):

1. Do an EFA, and make sure to include “marker” or specific bias (SB) constructs.
1. Specific bias constructs are just like any other multi-item constructs but measure specific sources of bias that may account for shared variance not due to a causal relationship between key variables in the study. A common one is Social Desirability Bias.
2. Do the CFA with SB constructs covaried to other constructs (this looks like a normal CFA).
3. Add a common latent factor (CLF), sometimes called an unmeasured method factor.
1. Make sure the CLF is connected to all observed items, including the items of the SB constructs.
2. If this breaks your model, then remove the CLF and proceed with the steps below.
3. If it does not break your model, then in the steps below, keep the SB constructs covaried to the other latent factors, and keep the CLF connected with regression lines to all observed factors.
4. The steps below assume the CLF will break the model, so some instructions that say to connect the SB to all observed variables should instead be CLF to all observed variables (if the CLF did not break your model).
4. Then conduct the CFA with the SB constructs shown to influence ALL indicators of other constructs in the study. Do not correlate the SB constructs with the other constructs of study. If there is more than one SB construct, they follow the same approach and can correlate with each other.
1. Retest validity, but be willing to accept lower thresholds.
2. If change in AVE is extreme (e.g., >.300) then there is too much shared variance attributable to a response variable. This means that variable is compromised and any subsequent analysis with it may be biased.
3. If the majority of factors have extreme changes to their AVE, you might consider rethinking your data collection instrument and how to reduce specific response biases.
5. If the validities are still sufficient, then conduct the zero-constrained test. This test determines whether the response bias is any different from zero.
1. To do this, constrain all paths from the SB constructs to all indicators (but do not constrain their own) to zero. Then conduct a chi-square difference test between the constrained and unconstrained models.
2. If the null hypothesis cannot be rejected (i.e., the constrained and unconstrained models are the same or “invariant”), you have demonstrated that you were unable to detect any specific response bias affecting your model. You can move on to causal modeling, but make sure to retain the SB construct(s) to include as control in the causal model. See the bottom of this subsection for how to do this.
3. If you changed your model while testing for specific bias, you should retest validities and model fit with this final (unconstrained) measurement model, as it may have changed.
6. If the zero-constrained chi-square difference test resulted in a significant result (i.e., reject null, i.e., response bias is not zero), then you should run an equal-constrained test. This test determines whether the response bias is evenly distributed across factors.
1. To do this, constrain all paths from the SB construct to all indicators (not including their own) to be equal. There are multiple ways to do this. One easy way is simply to name them all the same thing (e.g., “aaa”).
2. If the chi-square difference test between the constrained (to be equal) and unconstrained models indicates invariance (i.e., fail to reject null – that they are equal), then the bias is equally distributed. Make note of this in your report. e.g., “A test of equal specific bias demonstrated evenly distributed bias.”
3. Move on to causal modeling with the SB constructs retained (keep them).
4. If the chi-square test is significant (i.e., unevenly distributed bias), which is more common, you should still retain the SB construct for subsequent causal analyses. Make note of this in your report. e.g., “A test of equal specific bias demonstrated unevenly distributed bias.”
• What to do if you have to retain the specific bias factor
• You can do this either by imputing factor scores while the SB construct is connected to all observed variables (thereby essentially parceling out the shared bias with the SB construct), and then exclude from your causal model the SB construct that was imputed during your measurement model. Or you can disconnect the SB construct from all your observed variables, but covary it with all your latent variables, and then impute factor scores. If taking this latter approach, the SB will not be parceled out, so you will then need to include the factor score for the SB construct in the causal model as a control variable, connected to all other variables. If you also are able to retain the CLF (i.e., it does not break your model), then you keep it while imputing. If you have only connected the CLF to the observed variables (and not the SB construct), then make sure to use the SB construct as a control variable in the causal model.
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