# Risk perception measurement using CFA - Items with different scale

I am working on my risk perception model using three measures- probability, affection, and severity. I have one item on a Likert scale (1-5) for each probability and affection. However, for the severity part, I have one item on the Likert scale (1-5) and 7 items of binary types (0,1). The Sample size is 203. I want to use CFA for risk perception measures because existing studies suggest the importance of three measures on risk perception. I use lavaan package in r to compute CFA. Prior to this, I change all variables to ordered factor variables and run an analysis. I started by including only three items with the same scale (1-5). When I run the analysis and calculate the model fitness, I got srmr=0 rmsea=0 cfi=1 tli=1. It looks like a perfect model. I feel like something is wrong. Is it because the model is just identified?

Next approach, in my model, I compute the latent variable `severity' by combining all binary variables which is an ordered, factor. Then fit that variable along with the other 3 items of the same scale in the risk measure. When I run cfa I got this warning message: In lav_object_post_check(object) : lavaan WARNING: some estimated ov variances are negative.

I can see the negative variance in one of the items. I am not sure what can I do about that. I checked the no. of model parameters= 30. Does the error indicate a larger parameter compared to the sample size? For second model, srmr= 0.166, rmsea= 0.086, cfi=0.817 and tli=0.767

I would request your help. How can I resolve it? Should I take a different approach like PCA?

Thank you.

1. Yes, a single factor model with 3 indicators and free loadings is just identified (saturated, df = 0). Therefore, it trivially fits your data perfectly.

2. A negative residual variance estimate (Heywood case/improper solution) is often a sign of model misspecification/misfit. Your fit indices for this model don't look good, indicating that your model may be incorrect/misspecified. Another common reason for a Heywood case is a sample size that is too small. However, your sample size looks pretty OK.

• Thank you @Christian for your response. I want to follow up with your first response regarding the single-factor model with 3 indicators. Since the model fits perfectly, will there be any concern if I use it to obtain risk index value? I plan to use it as my dependent value in the regression model to assess the factors that influence risk perception. Jun 1 at 14:22

There is no concern per se--it just means the single factor, 3-indicator model with different loadings cannot be falsified--except if some or all covariances between the three indicators were (near) zero or negative (in which case you'd run into estimation problems).

A model in which the single factor with the three indicators serves as outcome (dependent) variable would be overidentified with > 0 degrees of freedom and would contain testable restrictions.