I wouldn't see RMSEA = 0.09 as "reasonable" under most circumstances. for testing a model, I would focus on the chi-square, df, and p value. One problem (among others) with approximate fit indices such as RMSEA is that they become less sensitive to model misspecification as the sample size increases (which is not what you want). Here is a reference to a study that showed this:

Marsh, H. W., Hau, K. T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler's (1999) findings. Structural Equation Modeling, 11(3), 320-341.

Article In Search of Golden Rules: Comment on Hypothesis-Testing App...

Overall, the fit of your model doesn't look good, even when relying on the approximate fit indices.

RMSEA below 0.08 is considered a good fit, while values between 0.08 and 0.10 suggest a reasonable fit. Values above 0.10 are often considered less acceptable. So, an RMSEA of 0.09 isn't necessarily terrible, but it's close to the threshold where you might want to aim for a better fit, especially with small sample sizes.

RMSEA tends to improve with larger sample sizes because a bigger sample provides more stable and reliable estimates. Smaller samples have a higher chance of unstable or biased results, which could explain why you're seeing slight improvements with a larger sample.

However, RMSEA can be sensitive to sample size. In small samples, it's common to observe higher RMSEA values, and this can also affect other fit indices.

The CMIN/df (Chi-Square divided by degrees of freedom) ratio is another important fit index. A value of 2 or 3 is typically considered acceptable. However, in smaller samples, the chi-square statistic may be inflated, leading to a higher CMIN/df ratio, which can be misleading. Since you're seeing an improvement in other indices (like RMSEA) with the larger sample size, the chi-square statistic may have been sensitive to the smaller sample size.

Check them

• Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55. https://doi.org/10.1080/10705519909540118
• Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). The Guilford Press.

Thank you very much for your response.