MeasureAccuracy {CvmortalityMult}

Measures of Accuracy

Description

R function to estimate different measures of accuracy.

1. the sum of squared errors (SSE) for the mortality rates:

   \sum_{x}^{} \sum_{t} \left( qxt1 - qxt2 \right)^{2}

   where qxt1 is the real mortality rates qxt_re, and qxt2 is the adjusted mortality rates qxt_aju.

2. The mean squared errors (MSE) for the mortality rates:

   \frac{1}{n}\sum_{x} \sum_{t} \left( qxt1 - qxt2 \right)^2 = \frac{1}{n} SSE

   where qxt1 is the real mortality rates qxt_re, and qxt2 is the adjusted mortality rates qxt_aju.

3. The mean absolute errors (MAE) for the mortality rates:

   \frac{1}{n}\sum_{x} \sum_{t} \left| qx1 - qxt2 \right|

   . where qxt1 is the real mortality rates qxt_re, and qxt2 is the adjusted mortality rates qxt_aju.

4. The mean absolute percentage error (MAPE) for the mortality rates:

   \frac{1}{n}\sum_{x} \sum_{t}\left| \frac{\left(qxt1 - qxt2\right) }{qxt2} \right|

   where qxt1 is the real mortality rates qxt_re, and qxt2 is the adjusted mortality rates qxt_aju. You only have to provide the real value, the fitted or forecasted value for your mortality rates and the measure of accuracy chosen. However, the function is constructed to provide the real value and the fitted or forecasted value of your independent variable. These variables must have the same dimensions to be compared.

Usage

MeasureAccuracy(
  measure = c("SSE", "MSE", "MAE", "MAPE", "All"),
  qxt_re,
  qxt_aju,
  wxt
)

Arguments

measure

choose the non-penalized measure of accuracy that you want to use; c("SSE", "MSE", "MAE", "MAPE", "All"). Check the function. In case you do not provide any value, the function will apply the "SSE" as measure of forecasting accuracy.

qxt_re

real mortality rates used to check the goodness of fit measure.

qxt_aju

adjusted mortality rates using a specific mode.

wxt

weights of the mortality rates or data provided.

Value

An object with class "MoA" including the value of the measure of accuracy for the data provided.

References

Atance, D., Debón, A., & Navarro, E. (2020). A comparison of forecasting mortality models using resampling methods. Mathematics, 8(9), 1550.

See Also

fitLCmulti, forecast.fitLCmulti, multipopulation_cv, multipopulation_loocv.

Examples

#The example takes more than 5 seconds because it includes
#several fitting and forecasting process and hence all
#the process is included in donttest

#To show how the function works, we need to provide fitted or forecasted data and the real data.
#In this case, we employ the following data of the library:
SpainRegions

library(gnm)
library(forecast)
ages <- c(0, 1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90)
#In this case, we fit for males providing the lxt
multiplicative_Spainmales <- fitLCmulti(model = "multiplicative",
                              qxt = SpainRegions$qx_male,
                              periods = c(1991:2020),
                              ages = c(ages),
                              nPop = 18,
                              lxt = SpainRegions$lx_male)

multiplicative_Spainmales
plot(multiplicative_Spainmales)

#Once, we have the fitted data, we will obtain different measures of accuracy
#for the first population.
#We need to obtain wxt (weight of the mortality rates or data provided) using a
library(StMoMo)
wxt_1pob <- genWeightMat(ages = ages, years = c(1991:2020), clip = 0)

##########################
#SSE#
##########################
SSE_multSpmales <- MeasureAccuracy(measure = "SSE",
                       qxt_re = multiplicative_Spainmales$qxt.real$pob1,
                       qxt_aju = multiplicative_Spainmales$qxt.fitted$pob1,
                       wxt = wxt_1pob)
SSE_multSpmales
##########################
#MSE#
##########################
MSE_multSpmales <- MeasureAccuracy(measure = "MSE",
                       qxt_re = multiplicative_Spainmales$qxt.real$pob1,
                       qxt_aju = multiplicative_Spainmales$qxt.fitted$pob1,
                       wxt = wxt_1pob)
MSE_multSpmales
##########################
#MAE#
##########################
MAE_multSpmales <- MeasureAccuracy(measure = "MSE",
                       qxt_re = multiplicative_Spainmales$qxt.real$pob1,
                       qxt_aju = multiplicative_Spainmales$qxt.fitted$pob1,
                       wxt = wxt_1pob)
MAE_multSpmales
##########################
#MAPE#
##########################
MAPE_multSpmales <- MeasureAccuracy(measure = "MSE",
                        qxt_re = multiplicative_Spainmales$qxt.real$pob1,
                        qxt_aju = multiplicative_Spainmales$qxt.fitted$pob1,
                        wxt = wxt_1pob)
MAPE_multSpmales