Calculate Confidence Interval and Prediction Interval for Non Linear fits

Emmanuel_Romeu

Hello,

a customer wants to visualize if their curves are within the expected tolerance. She uses Non Linear fit for which JMP does not provide neither Confidence Interval nor Prediction Interval. To achieve that goal I’ve been through Non Linear Fit and used the predictor formula. I created a new table with 200,000 rows and 3 columns :Y-formula, :Y_formula_Conf_Int and :Y_formula_Pred_Int.

:Y-formula depict the fit using parameter estimates. 

:Y_formula_Conf_Int depict the confidence interval around the fit using a normal random distribution for each parameter based on their estimate and ApproxStdErr.  

:Y_formula_Pred_Int depict the prediction interval using a normal random distribution for each parameter based on their estimate and ApproxStdErr + the RMSE.

In order to visualize the 95% Conf. Int. & Pred. Int. I selected values within -2.2 and -1.8 SD (Lower Limit) and values within 1.8 and 2.2 SD (Upper Limit) for both :Y_formula_Conf_Int and :Y_formula_Pred_Int.

 Is that a reasonable way of getting 95% intervals ? I used a normal random distribution but I’m wondering if parameters are supposed to be normally (or something else) distributed ?

The script and dataset are for illustration.

Is that correct ? good enough approximation ? totally wrong ?

Keep in mind that the 3P exponential used on this data is just as example, I would like something working for any fit (if possible).

Thanks for the help.

Emmanuel

Cell growth with Time.jmp

Confidence and Prediction Interval script.jsl

yuichi_katsumur

Hi Emmanuel,

You could consider the following steps:
1. fit the model in the fit curve personality and save the Parametric Prediction Formula to the data table.
2. go to  nonlinear personality (not fit curve), then use the newly created prediction formula column in the X role. 
3. you can then save either the prediction confidence limits or the individual confidence limits to the data table.
4. finally, you can use the prediction formula and confidence limits in graph builder to create graph with the data, model, and confidence limits.

Please see the attached data table.

I hope this information is helpful. If my understanding is not correct, please let me know.

Yuichi

Cell growth with Time2.jmp