There is no general way to answer this question because it depends on many factors such as the model structure, specific parameter values, and effect sizes. The best way to address this issue is to simulate your specific model for the given sample size using a Monte Carlo simulation. This allows you to study the accuracy of parameter estimates, standard errors, and test statistics as well as the rate of improper solutions and/or convergence problems.

The sample size required for estimating a specific number of parameters in an SEM model depends on several factors, including the model's complexity, the data's distributional properties, and the desired statistical power. While there is no fixed rule for determining an exact sample size requirement, general guidelines and considerations can be taken into account.

In SEM, as a rule of thumb, having a minimum of 10-20 observations per estimated parameter is often suggested. This guideline helps ensure a sufficient sample size for stable and reliable parameter estimates.

In your case, you mentioned estimating 50 parameters with a sample size of 220. As a rough guideline, the minimum recommended sample size for estimating 50 parameters would be around 500 to 1000 cases. However, it is important to note that this is a general guideline and might vary based on the complexity of the model and other factors.

With a sample size of 220, estimating 50 parameters might be challenging. You may face issues related to model identification, poor model fit, or unstable parameter estimates. It is advisable to consider reducing the number of parameters if possible or increasing the sample size to obtain more reliable results.

Additionally, conducting a power analysis to assess the adequacy of the sample size for your specific research context is recommended. A power analysis can help determine if the sample size is sufficient to detect meaningful effects in your SEM model.

Overall, while a sample size of 220 is relatively small for estimating 50 parameters in an SEM model, the adequacy of the sample size also depends on other factors. It is advisable to consult with a statistical expert or consider conducting a power analysis to determine the suitability of your sample size for the specific SEM analysis you are conducting.

Hi,

The thumb rule is to have ration as 1:10 , means if you have 50 items its recommended to have min 500 sample size.

You can check my paper for journal reference on this.

Regards,