Package 'ConfZIC'

Concrete Compressive Strength Data Set

Description

Concrete strength is very important in civil engineering and is a highly nonlinear function of age and ingredients. This dataset contains 1030 instances and there are 8 features relevant to concrete strength.

Usage

Concrete

Format

A data frame with 1030 rows and 8 covariate variables and 1 response variable

Source

https://archive.ics.uci.edu/ml/datasets/Concrete+Compressive+Strength

Examples

data(Concrete)

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Rank the regression models based on the confidence envelope for minimum ZIC

Description

Narrow down the number of models to look at in model selection using the confidence envelope based on the minimum ZIC values for regression data. Here, we compute the ZIC values ("AIC", "BIC", or "AICc") for regression data, confidence envelope for the minimum ZIC values for the given confidence limit, and rank the best models which lie in the confidence envelope.

Usage

RankReg(data,alphaval=0.95, model_ZIC="AIC")

Arguments

data	a matrix of $n$ by $(m+1)$ where $m$ is the number of independent variables. First column should be the dependent variable and the rest of the $m$ columns should be the independent variables of the dataset. Maximum of $m$ should be 10.
alphaval	confidence limit of the confidence envelope (Default is 0.95).
model_ZIC	type of the information criterion, it can be "AIC", "BIC", or "AICc" (Default is the "AIC").

Details

This program involves the computation of multivariate normal-probabilities with covariance matrices based on minimum ZIC inverting the CDF of the minimum ZIC. It involves both the computation of singular and nonsingular probabilities. The methodology is described in Genz (1992).

Let $X_j$ be the ZIC value for the $j^{th}$ fitted model. Compute the cdf values of the minimum ZIC, $F_{X_{(1)}}(\cdot)$ numerically and then obtain the $100\cdot (1-\alpha)\%$ confidence envelope:

$CE(\alpha)=F^{-1}_{X_{(1)}}(1-\alpha)$

See details:

Jayaweera I.M.L.N, Trindade A.A., “How Certain are You in Your Minimum AIC and BIC Values?", Sankhya A (2023+)

Value

A list containing at least the following components.

Ranked_Models	A set of top ranked models which lie in the confidence envelop $CE(\alpha)$ (with variables list and the ranked ZIC values ("AIC", "BIC", or "AICc")) for regression data. $0$ represents the coefficient while $1,2,...,m$ give the corresponding columns of independent variables $X_1,X_2,...,X_m$ respectively.
Confidence_Envelope	gives the confidence envelope $CE(\alpha)$ for the minimum ZIC.
Confidence_Limit	the confidence limit, $1-\alpha$.
Total_Models	number of total fitted models.

References

Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of computational and graphical statistics, 1(2), 141-149.

Examples

library("ConfZIC")
data(Concrete)
x=Concrete
Y=x[,9] #dependent variable
#independent variables
X1=x[,1];X2=x[,2];X3=x[,3];X4=x[,4];
X5=x[,5];X6=x[,6];X7=x[,7];X8=x[,8];
mydata=cbind(Y,X1,X2,X3,X4,X5,X6,X7,X8) #data matrix
RankReg(mydata,0.95,"BIC")

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Rank the time series (ARMA) models based on the confidence envelope for minimum ZIC

Description

Narrow down the number of models to look at in model selection using the confidence envelope based on the minimum ZIC values for time series data. Here, we compute the ZIC values ("AIC", "BIC", or "AICc") for time-series data, confidence envelope for the minimum ZIC values for the given confidence limit, and rank the top models which lie in the confidence envelope.

Usage

RankTS(x,max.p,max.q,alphaval=0.95,model_ZIC="AIC")

Arguments

x	a vector of time series data (should be included with the maximum of 1000 data points).
max.p	maximum value for AR coefficient.
max.q	maximum value for MA coefficient.
alphaval	confidence limit $(1-\alpha)$ (Default is 0.95).
model_ZIC	type of the information criterion, it can be "AIC", "BIC", or "AICc" (Default is the "AIC").

Details

This program involves the computation of multivariate normal-probabilities with covariance matrices based on minimum ZIC inverting the CDF of the minimum ZIC. It involves both the computation of singular and non-singular probabilities. The methodology is described in Genz (1992).

Let $X_j$ be the ZIC value for the $j^{th}$ fitted model. Compute the cdf values of the minimum ZIC, $F_{X_{(1)}}(\cdot)$ numerically and then obtain the $100\cdot (1-\alpha)\%$ confidence envelope:

$CE(\alpha)=F^{-1}_{X_{(1)}}(1-\alpha)$

See details:

Jayaweera I.M.L.N, Trindade A.A., “How Certain are You in Your Minimum AIC and BIC Values?", Sankhya A (2023+)

Value

a list of ranked models which lies in the confidence envelope, $CE(\alpha).$

Ranked_Models	A set of top ranked time series models which lie in the confidence envelope $CE(\alpha)$ (with AR and MA coefficients, ZIC values ("AIC", "BIC", or "AICc")).
Confidence_Envelope	gives the confidence envelope $CE(\alpha)$ for the minimum ZIC.
Confidence_Limit	the confidence limit, $1-\alpha$.
Total_Models	number of total fitted models.

References

Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of computational and graphical statistics, 1(2), 141-149.

Examples

library("ConfZIC")
data(Sunspots)
x=Sunspots
RankTS(x,max.p=13,max.q=13,0.95,"AICc")

---

Test whether two ZIC values differ significantly based on minimum ZIC for regression data

Description

Test whether two ZIC values differ significantly based on minimum ZIC for regression data.

Usage

regZIC.test(model1,model2,model_ZIC="AIC",data,alpha=0.05)

Arguments

model1	an object of class “lm".
model2	an object of class “lm".
model_ZIC	type of the information criterion, it can be "AIC", "BIC", or "AICc" (Default is the "AIC").
data	a matrix of $n$ by $(m+1)$ where $m$ is the number of independent variables.First column should be the dependent variable and the rest of the $m$ columns should be the independent variables of the dataset. Maximum of $m$ should be 10.
alpha	significance level $\alpha$ for the hypothesis testing (Default is 0.05).

Details

Consider the hypothesis: Under the null hypothesis that the two expected discrepancies are equal.

$H_0: ZIC_i=ZIC_j , H_1: ZIC_i\neq ZIC_j$

$Z_0=\frac{(\hat{ZIC_i}-\hat{ZIC_j})-0}{\sqrt{SD(ZIC_i,ZIC_j)}}\sim N(0,1)$

is calculated empirically.

Value

p-value with significance status.

References

Linhart, H. (1988). A test whether two AIC's differ significantly. South African Statistical Journal, 22(2), 153-161.

Examples

library(ConfZIC)
data(Concrete)
x=Concrete
Y=x[,9] #dependent variable
#independent variables
X1=x[,1];X2=x[,2];X3=x[,3];X4=x[,4];
X5=x[,5];X6=x[,6];X7=x[,7];X8=x[,8];
mydata=cbind(Y,X1,X2,X3,X4,X5,X6,X7,X8) #data matrix
model1=lm(Y~X1); model2=lm(Y~X1+X2)
regZIC.test(model1,model2,model_ZIC="BIC",data=mydata,alpha=0.05)

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Number of sunspots, 1770 to 1869

Description

Number of sunspots, 1770 to 1869

Usage

Sunspots

Format

Number of sunspots, 1770 to 1869

Source

Brockwell, P. J., & Davis, R. A. (Eds.). (2002). Introduction to time series and forecasting. New York, NY: Springer New York.

Examples

data(Sunspots)

---

Test whether two ZIC values differ significantly based on minimum ZIC for time series data

Description

Test whether two ZIC values differ significantly based on minimum ZIC for time series data.

Usage

tsZIC.test(x,model1,model2,model_ZIC="AIC",alpha=0.05)

Arguments

x	time series data (maximum of 1000 data points).
model1	AR and MA coefficients of Model 1.
model2	AR and MA coefficients of Model 2.
model_ZIC	type of the information criterion, it can be "AIC", "BIC", or "AICc" (Default is the "AIC").
alpha	significance level $\alpha$ for the hypothesis testing (Default is 0.05).

Details

Consider the hypothesis: Under the null hypothesis that the two expected discrepancies are equal.

$H_0: ZIC_i=ZIC_j , H_1: ZIC_i\neq ZIC_j$

$Z_0=\frac{(\hat{ZIC_i}-\hat{ZIC_j})-0}{\sqrt{SD(ZIC_i,ZIC_j)}} \sim N(0,1)$

is calculated empirically.

Value

p-value with significance status.

References

Linhart, H. (1988). A test whether two AIC's differ significantly. South African Statistical Journal, 22(2), 153-161.

Examples

library(ConfZIC)
data(Sunspots)
x=Sunspots
model1=try(arima(x,order=c(1,0,1),method="ML",include.mean=FALSE),silent = TRUE)
model2=try(arima(x,order=c(1,0,0),method="ML",include.mean=FALSE),silent = TRUE)
tsZIC.test(x,model1,model2,model_ZIC="AIC",alpha=0.05)

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