I developed two prediction models using non-linear regression analysis to predict a set of values using sigmoidal and power functions. I was wondering how I can evaluate the accuracy of these individual models (Sigmoid predictions vs Power predictions) besides RMSE? Also, are there any other hypothesis tests such as Chi-Square Goodness of Fit Test that I can use to evaluate the prediction accuracy of these models?
There are many measures of point prediction accuracy, like the mae, the rmse, or the mape. You may want to browse through our questions with these tags. Why use a certain measure of forecast error (e.g. MAD) as opposed to another (e.g. MSE)? is likely helpful, as may be What are the shortcomings of the Mean Absolute Percentage Error (MAPE)? and Mean absolute error OR root mean squared error?
This page and discusses some of these KPIs in the context of time series forecasting.
You can evaluate the accuracy of a regression model (including nonlinear ones) by comparing the predicted values to the actual values. I'd say the best way to do this is graphically with e.g. boxplots of the residuals, a scatterplot of actual vs. predicted values, a quantile quantile plot of those and a Tukey mean difference plot.
You can also look at the values of the residuals numerically and see if any are unacceptable large.