In RSM, 'MPE' are a statistical indicator for the output response. Then, how can we calculate the 'MPE' (relative model predictive percentage error) for an output response? And what is the acceptable limits?
Thank you in advance
Dear Lakhdar,
In statistics, the mean percentage error (MPE) is the computed average of percentage errors by which forecasts of a model differ from actual values of the quantity being forecast.
The formula for the mean percentage error is:
To view the formula, please use the following link:
https://en.wikipedia.org/wiki/Mean_percentage_error
where at is the actual value of the quantity being forecast, ft is the forecast, and n is the number of different times for which the variable is forecast.
Because actual rather than absolute values of the forecast errors are used in the formula, positive and negative forecast errors can offset each other; as a result the formula can be used as a measure of the bias in the forecasts.
A disadvantage of this measure is that it is undefined whenever a single actual value is zero.
An example is a recent article contained in the following link :
Alexandria Engineering Journal
Volume 52, Issue 3, September 2013, Pages 507–516
Open Access
ORIGINAL ARTICLE
Artificial neural network and response surface methodology modeling in mass transfer parameters predictions during osmotic dehydration of Carica papaya L.
J. Prakash Marana, V. Sivakumara, K. Thirugnanasambandhama, R. Sridharb,
Abstract
In this study, a comparative approach was made between artificial neural network (ANN) and response surface methodology (RSM) to predict the mass transfer parameters of osmotic dehydration of papaya. The effects of process variables such as temperature, osmotic solution concentration and agitation speed on water loss, weight reduction, and solid gain during osmotic dehydration were investigated using a three-level three-factor Box-Behnken experimental design. Same design was utilized to train a feed-forward multilayered perceptron (MLP) ANN with back-propagation algorithm. The predictive capabilities of the two methodologies were compared in terms of root mean square error (RMSE), mean absolute error (MAE), standard error of prediction (SEP), model predictive error (MPE), chi square statistic (χ2), and coefficient of determination (R2) based on the validation data set. The results showed that properly trained ANN model is found to be more accurate in prediction as compared to RSM model.
http://www.sciencedirect.com/science/article/pii/S1110016813000604
Hoping this will be helpful,
Rafik
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