| Title: | Calculates Goodness of Fit Statistics |
|---|---|
| Description: | Calculates 15 different goodness of fit criteria. These are; standard deviation ratio (SDR), coefficient of variation (CV), relative root mean square error (RRMSE), Pearson's correlation coefficients (PC), root mean square error (RMSE), performance index (PI), mean error (ME), global relative approximation error (RAE), mean relative approximation error (MRAE), mean absolute percentage error (MAPE), mean absolute deviation (MAD), coefficient of determination (R-squared), adjusted coefficient of determination (adjusted R-squared), Akaike's information criterion (AIC), corrected Akaike's information criterion (CAIC), Mean Square Error (MSE), Bayesian Information Criterion (BIC) and Normalized Mean Square Error (NMSE). |
| Authors: | Alper Gulbe [cre], Ecevit Eyduran [aut] |
| Maintainer: | Alper Gulbe <[email protected]> |
| License: | GPL-2 |
| Version: | 0.1.1 |
| Built: | 2025-02-13 03:41:15 UTC |
| Source: | https://github.com/cran/ehaGoF |
Tests predicted and observed values for the goodness of fit with various criteria. The goodness of fit tests are used to test how well the model fits. Measures of goodness of fit typically summarize the argument between targets or observed values and the values expected or predicted under the model in question.
GoF(Observations, Predicts, nTermInAppr = 2, ndigit = 3, RMSE = TRUE, RRMSE = TRUE, SDR = TRUE, CV = TRUE, PC = TRUE, PI = TRUE, ME = TRUE, RAE = TRUE, MRAE = TRUE, MAPE = TRUE, MAD = TRUE, RSq = TRUE, ARSq = TRUE, AIC = TRUE, CAIC = TRUE)GoF(Observations, Predicts, nTermInAppr = 2, ndigit = 3, RMSE = TRUE, RRMSE = TRUE, SDR = TRUE, CV = TRUE, PC = TRUE, PI = TRUE, ME = TRUE, RAE = TRUE, MRAE = TRUE, MAPE = TRUE, MAD = TRUE, RSq = TRUE, ARSq = TRUE, AIC = TRUE, CAIC = TRUE)
Observations |
Observed values or target vector. |
Predicts |
Predicted values. Values produced or fitted by approximation or regression. |
nTermInAppr |
Number of terms used in approximation or regression model. Generally 2 for simple linear model. Default is 2. |
ndigit |
Number of digits in decimal places. Default is 3. |
RMSE |
Whether to show Root Mean Square Error statistics. Default is TRUE. |
RRMSE |
Whether to show Relative Root Mean Square Error statistics. Default is TRUE. |
SDR |
Whether to show Standard Deviation Ratio statistics. Default is TRUE. |
CV |
Whether to show Coefficient of Variance statistics. Default is TRUE. |
PC |
Whether to show Pearson's Correlation Coefficients statistics. Default is TRUE. |
PI |
Whether to show Performance Index statistics. Default is TRUE. |
ME |
Whether to show Mean Error statistics. Default is TRUE. |
RAE |
Whether to show Global Relative Approximation Error statistics. Default is TRUE. |
MRAE |
Whether to show Modified Relative Approximation Error statistics. Default is TRUE. |
MAPE |
Whether to show Mean Absolute Percentage Error statistics. Default is TRUE. |
MAD |
Whether to show Mean Absolute Deviation statistics. Default is TRUE. |
RSq |
Whether to show Coefficient of Determination (R-Squared) statistics. Default is TRUE. |
ARSq |
Whether to show Adjusted Coefficient of Determination (Adjusted R-Squared) statistics. Default is TRUE. Warning: nTermInAppr must be supplied. |
AIC |
Whether to show Akaike's Information Criterion statistics. Default is TRUE. Warning: nTermInAppr must be supplied. |
CAIC |
Whether to show Corrected Akaike's Information Criterion statistics. Default is TRUE. Warning: nTermInAppr must be supplied. |
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan, Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas and Wilhelm Grzesiak, Pakistan J. Zool., vol. 49(1), pp 257-265, 2017.
# dummy inputs, independent variable # integers from 0 to 9 inputs <- 0:9 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*2 + rnorm(10) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # Number of Terms n = length(model$coefficients) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit statistics GoF(targets, predicted, nTermInAppr=n)# dummy inputs, independent variable # integers from 0 to 9 inputs <- 0:9 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*2 + rnorm(10) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # Number of Terms n = length(model$coefficients) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit statistics GoF(targets, predicted, nTermInAppr=n)
Calculates and returns goodness of fit - coefficient of variation (CV).
gofCV(Obs, Prd, dgt=3)gofCV(Obs, Prd, dgt=3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
dgt |
Number of digits in decimal places. Default is 3. |
CoeficientOfVariation |
Goodness of fit - coefficient of variation (CV). |
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz
# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit - coefficient of variation (CV) gofCV(targets, predicted)# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit - coefficient of variation (CV) gofCV(targets, predicted)
Calculates and returns the goodness of fit criterion: mean absolute percentage error (MAPE), a.k.a. mean absolute percentage deviation or MAPD.
gofMAPE(Obs, Prd, dgt=3)gofMAPE(Obs, Prd, dgt=3)
Obs |
Observed values or targets. |
Prd |
Predicted or expre-ected values produced by the model. |
dgt |
Number of digits in decimal places. Default is 3. |
Mean absolute percentage error (MAPE) is a measure of prediction accuracy of a forecasting method in statistics. It is commonly used as a loss function for regression problems and in model evaluation, for its very intuitive interpretation in terms of relative error. It usually expresses accuracy as a percentage.
MAPE |
Mean absolute percentage error (MAPE) of given set. |
For more information look at these papers:
Rob J. Hyndman, Anne B. Koehler, Another look at measures of forecast accuracy, International Journal of Forecasting, Volume 22, Issue 4, 2006, Pages 679-688, ISSN 0169-2070,
Arnaud de Myttenaere, Boris Golden, Bénédicte Le Grand, Fabrice Rossi, Mean Absolute Percentage Error for regression models, Neurocomputing, Volume 192, 2016, Pages 38-48, ISSN 0925-2312,
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan, Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas and Wilhelm Grzesiak, Pakistan J. Zool., vol. 49(1), pp 257-265, 2017.
Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019
Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz
# dummy inputs, independent variable # integers from 0 to 9 inputs <- 0:9 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*2 + rnorm(10) # linear regression model model<-lm(targets~inputs) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit - mean absolute percentage error statistics gofMAPE(targets, predicted)# dummy inputs, independent variable # integers from 0 to 9 inputs <- 0:9 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*2 + rnorm(10) # linear regression model model<-lm(targets~inputs) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit - mean absolute percentage error statistics gofMAPE(targets, predicted)
Calculates and returns Pearson's correlation coefficients (PC).
gofPC(Obs, Prd, dgt = 3)gofPC(Obs, Prd, dgt = 3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
dgt |
Number of digits in decimal places. Default is 3. |
PearsonCorrelation |
Pearson's correlation coefficients (PC) |
Prof. Dr. Ecevit EYDURAN, TA. Alper GULBE
OBILOR Esezi Isaac, AMADI Eric Chikweru, Test for Significance of Pearson’s Correlation Coefficient, International Journal of Innovative Mathematics, Statistics & Energy Policies 6(1):11-23, Jan-Mar, 2018.
Reza Soleimani, Amir Hossein Saeedi Dehaghani, Alireza Bahadori, A new decision tree based algorithm for prediction of hydrogen sulfide solubility in various ionic liquids, Journal of Molecular Liquids, Volume 242, 2017, Pages 701-713, ISSN 0167-7322, https://doi.org/10.1016/j.molliq.2017.07.075. (http://www.sciencedirect.com/science/article/pii/S0167732217305123)
# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit - Pearson's correlation coefficient gofPC(targets, predicted)# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit - Pearson's correlation coefficient gofPC(targets, predicted)
Calculates and returns relative root mean square error (RRMSE) of the model. The ratio of the mean of square root of residuals squared to the mean of observed values.
gofRRMSE(Obs, Prd, dgt = 3)gofRRMSE(Obs, Prd, dgt = 3)
Obs |
Observed values or target vector. |
Prd |
Predicted values. Values produced by approximation or regression. |
dgt |
Number of digits in decimal places. Default is 3. |
RRMSE is calculated by dividing RMSE by the mean of observed values.
RelativeRootMeanSquareError |
Relative root mean square error (RRMSE) of given set. |
For more information: Despotovic, M., Nedic, V., Despotovic, D., & Cvetanovic, S., Evaluation of empirical models for predicting monthly mean horizontal diffuse solar radiation, Renewable and Sustainable Energy Reviews, Volume 56, April 2016, Pages 246-260, ISSN 1364-0321, http://dx.doi.org/10.1016/j.rser.2015.11.058.
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan, Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas and Wilhelm Grzesiak, Pakistan J. Zool., vol. 49(1), pp 257-265, 2017.
Indirect Estimation of Structural Parameters in South African Forests Using MISR-HR and LiDAR Remote Sensing Data - Precious Nokuthula Wistebaar Mahlangu, Renaud Mathieu, Konrad Wessels, Laven Naidoo, Michel M Verstraete, Gregory P Asner, Russell Main
# Input values, independent variable input <- 0:4 # Target vector, observed values, dependent variable target <- c(1.9, 4.1, 5.89, 7.9, 10.01) # Simple linear regression, target across input like: target = a * input + b, # where a and b are coefficients. model <- lm(target~input) # Information about the model summary(model) # Values predicted by the model predicted <- predict(model) # using library ehaGoF for goodness of fit library(ehaGoF) # Goodness of fit - relative root mean square error (RRMSE) gofRRMSE(target, predicted)# Input values, independent variable input <- 0:4 # Target vector, observed values, dependent variable target <- c(1.9, 4.1, 5.89, 7.9, 10.01) # Simple linear regression, target across input like: target = a * input + b, # where a and b are coefficients. model <- lm(target~input) # Information about the model summary(model) # Values predicted by the model predicted <- predict(model) # using library ehaGoF for goodness of fit library(ehaGoF) # Goodness of fit - relative root mean square error (RRMSE) gofRRMSE(target, predicted)
Calculates and returns root mean square error (RMSE).
gofRMSE(Obs, Prd, dgt = 3)gofRMSE(Obs, Prd, dgt = 3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
dgt |
Number of digits in decimal places. Default is 3. |
RootMeanSquareError |
Root mean square error (RMSE) |
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan - Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas, Wilhelm Grzesiak
Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019
Indirect Estimation of Structural Parameters in South African Forests Using MISR-HR and LiDAR Remote Sensing Data - Precious Nokuthula Wistebaar Mahlangu, Renaud Mathieu, Konrad Wessels, Laven Naidoo, Michel M Verstraete, Gregory P Asner, Russell Main, Remote Sens. 2018, 10, 1537 ; doi:10.3390/rs10101537.
# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit - root mean square error (RMSE) gofRMSE(targets, predicted)# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit - root mean square error (RMSE) gofRMSE(targets, predicted)
Calculates and returns standard deviation ratio (SDR).
gofSDR(Obs, Prd, dgt=3)gofSDR(Obs, Prd, dgt=3)
Obs |
Observed values or target vector. |
Prd |
Predicted values. Values produced by approximation or regression. |
dgt |
Number of digits in decimal places. Default is 3. |
StandardDeviationRatio |
Standard deviation ratio (SDR) of given set. |
Prof. Dr. Ecevit Eyduran, TA. Alper Gülbe
Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan, Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas and Wilhelm Grzesiak, Pakistan J. Zool., vol. 49(1), pp 257-265, 2017.
Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019
Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz
##---- Should be DIRECTLY executable !! ---- ##-- ==> Define data, use random, ##-- or do help(data=index) for the standard data sets. # Input values, independent variable input <- 0:4 # Target vector, observed values target <- c(1.9, 4.1, 5.89, 7.9, 10.01) # Simple linear regression target across input like target = a * input + b, # where a and b are coefficients. model <- lm(target~input) # Information about the model summary(model) # Values predicted by the model predicted <- predict(model) # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit - standard deviation ratio (SDR) gofSDR(target, predicted)##---- Should be DIRECTLY executable !! ---- ##-- ==> Define data, use random, ##-- or do help(data=index) for the standard data sets. # Input values, independent variable input <- 0:4 # Target vector, observed values target <- c(1.9, 4.1, 5.89, 7.9, 10.01) # Simple linear regression target across input like target = a * input + b, # where a and b are coefficients. model <- lm(target~input) # Information about the model summary(model) # Values predicted by the model predicted <- predict(model) # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit - standard deviation ratio (SDR) gofSDR(target, predicted)
Calculates and returns adjusted coefficient of determination (adjusted R-squared).
gofACoD(Obs, Prd, nTermInAppr = 2, dgt = 3)gofACoD(Obs, Prd, nTermInAppr = 2, dgt = 3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
nTermInAppr |
Number of terms in approximation or regression models formula, interception included. For simple linear regression with one independent variable is simply 2. Default is 2. |
dgt |
Number of digits in decimal places. Default is 3. |
AdjustedCoefficientofDetermination |
Goodness of fit - adjusted coefficient of determination (adjusted R-squared) |
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz.
A new decision tree based algorithm for prediction of hydrogen sulfide solubility in various ionic liquids - Reza Soleimani, Amir Hossein Saeedi Dehaghani, Alireza Bahadori.
# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # Number of Terms n = length(model$coefficients) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : adjusted coefficient of determination (adjusted R-squared) gofACoD(targets, predicted, dgt=4,nTermInAppr=n)# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # Number of Terms n = length(model$coefficients) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : adjusted coefficient of determination (adjusted R-squared) gofACoD(targets, predicted, dgt=4,nTermInAppr=n)
Caclulates and returns adjusted coefficient of determination (adjusted R-squared).
gofARSq(Obs, Prd, nTermInAppr = 2, dgt = 3)gofARSq(Obs, Prd, nTermInAppr = 2, dgt = 3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
nTermInAppr |
Number of terms in approximation or regression models formula, interception included. For simple linear regression with one independent variable is simply 2. Default is 2. |
dgt |
Number of digits in decimal places. Default is 3. |
ARsquared |
Goodness of fit - adjusted coefficient of determination (adjusted R-squared) |
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz.
A new decision tree based algorithm for prediction of hydrogen sulfide solubility in various ionic liquids - Reza Soleimani, Amir Hossein Saeedi Dehaghani, Alireza Bahadori.
# dummy inputs, independent variable # integers from 0 to 99 inputs <- 0:99 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(100) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # Number of Terms n = length(model$coefficients) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : adjusted R-squared gofARSq(targets, predicted, dgt=4, nTermInAppr=n)# dummy inputs, independent variable # integers from 0 to 99 inputs <- 0:99 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(100) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # Number of Terms n = length(model$coefficients) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : adjusted R-squared gofARSq(targets, predicted, dgt=4, nTermInAppr=n)
Calculates and returns Akaike's information criterion (AIC).
gofAIC(Obs, Prd, nTermInAppr=2, dgt = 3)gofAIC(Obs, Prd, nTermInAppr=2, dgt = 3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
nTermInAppr |
Number of terms in approximation or regression models formula, including interception. For simple linear regression with one independent variable is simply 2. Default is 2. |
dgt |
Number of digits in decimal places. Default is 3. |
AkaikesInformationCriterion |
Akaike's information criterion (AIC) |
When n/k is not greater than 40, where n is the number of observations and k is the number of terms in approximation, Corrected Akaike's Information Criterion (gofCAIC) is used.
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan - Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas, Wilhelm Grzesiak.
Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019.
# dummy inputs, independent variable # integers from 0 to 99 inputs <- 0:99 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(100) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # Number of Terms n = length(model$coefficients) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : Akaike's information criterion (AIC) gofAIC(targets, predicted, dgt=4, nTermInAppr=n)# dummy inputs, independent variable # integers from 0 to 99 inputs <- 0:99 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(100) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # Number of Terms n = length(model$coefficients) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : Akaike's information criterion (AIC) gofAIC(targets, predicted, dgt=4, nTermInAppr=n)
Calculates and returns coefficient of determination (R-squared).
gofCoD(Obs, Prd, dgt = 3)gofCoD(Obs, Prd, dgt = 3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
dgt |
Number of digits in decimal places. Default is 3. |
CoefficientofDetermination |
Goodness of fit - coefficient of determination (R-squared) |
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz.
A new decision tree based algorithm for prediction of hydrogen sulfide solubility in various ionic liquids - Reza Soleimani, Amir Hossein Saeedi Dehaghani, Alireza Bahadori.
# dummy inputs, independent variable # integers from 0 to 99 inputs <- 0:99 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(100) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : coefficient of determination (R-squared) gofCoD(targets, predicted)# dummy inputs, independent variable # integers from 0 to 99 inputs <- 0:99 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(100) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : coefficient of determination (R-squared) gofCoD(targets, predicted)
Calculates and returns corrected Akaike's information criterion.
gofCAIC(Obs, Prd, nTermInAppr = 2, dgt = 3)gofCAIC(Obs, Prd, nTermInAppr = 2, dgt = 3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
nTermInAppr |
Number of terms in approximation or regression models formula, interception included. For simple linear regression with one independent variable is simply 2. Default is 2. |
dgt |
Number of digits in decimal places. Default is 3. |
CorrectedAkaikesInformationCriterion |
Goodness of fit - corrected Akaike's information criterion (cAIC) |
When n/k is greater than 40, where n is the umber of observations and k is the number of terms in approximation, Akaike's Information Criterion (gofAIC) is used.
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan - Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas, Wilhelm Grzesiak.
Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019.
# dummy inputs, independent variable # integers fron 0 to 79 inputs <- 0:79 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(80) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # Number of Terms n = length(model$coefficients) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for Goodness of Fit function (GoF) library(ehaGoF) # Goodness of Fit : Corrected Akaike's Information Criterion gofCAIC(targets, predicted, dgt=4, nTermInAppr=n)# dummy inputs, independent variable # integers fron 0 to 79 inputs <- 0:79 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(80) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # Number of Terms n = length(model$coefficients) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for Goodness of Fit function (GoF) library(ehaGoF) # Goodness of Fit : Corrected Akaike's Information Criterion gofCAIC(targets, predicted, dgt=4, nTermInAppr=n)
Calculates and returns global relative approximation error (RAE).
gofRAE(Obs, Prd, dgt = 3)gofRAE(Obs, Prd, dgt = 3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
dgt |
Number of digits in decimal places. Default is 3. |
RelativeApproximationError |
Global relative approximation error (RAE) |
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan - Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas, Wilhelm Grzesiak.
Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019.
Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz.
The Connection Dependent Threshold Model for Finite Sources -A Generalization of the Engset Multirate Loss Model - Ioannis D. Moscholios and Michael D. Logothetis.
# dummy inputs, independent variable # integers from 0 to 99 inputs <- 0:99 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(100) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : global relative approximation error (RAE) gofRAE(targets, predicted)# dummy inputs, independent variable # integers from 0 to 99 inputs <- 0:99 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(100) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : global relative approximation error (RAE) gofRAE(targets, predicted)
Calculates and returns mean absolute deviation (MAD).
gofMAD(Obs, Prd, dgt = 3)gofMAD(Obs, Prd, dgt = 3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
dgt |
Number of digits in decimal places. Default is 3. |
MeanAbsoluteDeviation |
Goodness of fit - mean absolute deviation (MAD) |
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan - Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas, Wilhelm Grzesiak.
Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019.
Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz.
# dummy inputs, independent variable # integers from 0 to 99 inputs <- 0:99 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(100) # linear regression model model<-lm(targets~inputs) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for Goodness of Fit function (GoF) library(ehaGoF) # Goodness of Fit : Mean Absolute Deviation gofMAD(targets, predicted, dgt=4)# dummy inputs, independent variable # integers from 0 to 99 inputs <- 0:99 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(100) # linear regression model model<-lm(targets~inputs) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for Goodness of Fit function (GoF) library(ehaGoF) # Goodness of Fit : Mean Absolute Deviation gofMAD(targets, predicted, dgt=4)
Calculates and returns mean error (ME).
gofME(Obs, Prd, dgt = 3)gofME(Obs, Prd, dgt = 3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
dgt |
Number of digits in decimal places. Default is 3. |
MeanError |
Goodness of fit - mean error (ME) |
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of the Predictive Capabilities of Several Data Mining Algorithms and Multiple Linear Regression in the Prediction of Body Weight by Means of Body Measurements in the Indigenous Beetal Goat of Pakistan - Ecevit Eyduran, Daniel Zaborski, Abdul Waheed, Senol Celik, Koksal Karadas, Wilhelm Grzesiak.
Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019.
# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : mean error (ME) gofME(targets, predicted)# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : mean error (ME) gofME(targets, predicted)
Calculates and returns mean relative approximation error (MRAE).
gofMRAE(Obs, Prd, dgt = 3)gofMRAE(Obs, Prd, dgt = 3)
Obs |
Observed values or target vector. |
Prd |
Predicted values. Values produced by approximation or regression. |
dgt |
Number of digits in decimal places. Default is 3. |
MeanRelativeApproximationError |
Goodness of fit - mean relative approximation error (MRAE) |
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
The Connection Dependent Threshold Model for Finite Sources -A Generalization of the Engset Multirate Loss Model - Ioannis D. Moscholios and Michael D. Logothetis.
Competitive adsorption equilibrium modeling of volatile organic compound (VOC) and water vapor onto activated carbon - Imranul I. Laskara, Zaher Hashishoa,⁎, John H. Phillipsb, James E. Andersonc, Mark Nichols.
A new decision tree based algorithm for prediction of hydrogen sulfide solubility in various ionic liquids - Reza Soleimani, Amir Hossein Saeedi Dehaghani, Alireza Bahadori.
# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2 times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : mean relative approximation error (MRAE) gofMRAE(targets, predicted)# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2 times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : mean relative approximation error (MRAE) gofMRAE(targets, predicted)
Calculates and returns performance index (PI).
gofPI(Obs, Prd, dgt = 3)gofPI(Obs, Prd, dgt = 3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
dgt |
Number of digits in decimal places. Default is 3. |
PerformanceIndex |
Goodness of fit: performance index (PI) |
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Prediction of Selected Reproductive Traits of Indigenous Harnai Sheep under the Farm Management System via various Data Mining Algorithms - Daniel Zaborski, Muhammad Ali, Ecevit Eyduran, Wilhelm Grzesiak, Mohammad Masood Tariq, Ferhat Abbas, Abdul Waheed, Cem Tirink - Pakistan journal of zoology, 2019
# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit - performance index (PI) gofPI(targets, predicted)# dummy inputs, independent variable # integers from 0 to 19 inputs <- 0:19 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(20) # linear regression model model<-lm(targets~inputs) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit - performance index (PI) gofPI(targets, predicted)
Calculates and returns R-squared (coefficient of determination).
gofRSq(Obs, Prd, dgt = 3)gofRSq(Obs, Prd, dgt = 3)
Obs |
Observed or measured values or target vector. |
Prd |
Predicted or fitted values by the model. Values produced by approximation or regression. |
dgt |
Number of digits in decimal places. Default is 3. |
RSquared |
Goodness of fit - coefficient of determination (R-squared) |
Prof. Dr. Ecevit Eyduran, TA. Alper Gulbe
Comparison of Different Data Mining Algorithms for Prediction of Body Weight From Several Morphological Measurements in Dogs - S Celik, O Yilmaz.
A new decision tree based algorithm for prediction of hydrogen sulfide solubility in various ionic liquids - Reza Soleimani, Amir Hossein Saeedi Dehaghani, Alireza Bahadori.
# dummy inputs, independent variable # integers from 0 to 99 inputs <- 0:99 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(100) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : coefficient of determination (R-squared) gofRSq(targets, predicted)# dummy inputs, independent variable # integers from 0 to 99 inputs <- 0:99 # dummy targets/observed values, dependent variable # a product of 2*times inputs minus 5 with some normal noise targets <- -5 + inputs*1.2 + rnorm(100) # linear regression model model<-lm(targets~inputs) # About the model summary(model) # model's predicted values against targets predicted<-model$fitted.values # using library ehaGoF for goodness of fit. library(ehaGoF) # Goodness of fit : coefficient of determination (R-squared) gofRSq(targets, predicted)