RTransProb (version 0.1.0)

transForecast_mnl: Forecast - using Multinomial Logistic Regression

Description

This model implements a forecasting method using multinomial logistic regression (also known as Softmax Regression in machine learning parlance).

Usage

transForecast_mnl(transData, histData, predData, startDate,
                        endDate, ref, depVar, indVars, ratingCat, wgt)

Arguments

transData

dataframe containing date, beginning ratings, ending ratings, and transition counts.

histData

historical macroeconomic,financial and non-financial data.

predData

forecasting data.

startDate

start date of the estimation time window, in string or numeric format.

endDate

end date of the estimation time window, in string or numeric format.

ref

base or reference category for the dependent variable.

depVar

dependent variable, as a string.

indVars

list containing the independent variables

ratingCat

list containing the unique rating categories

wgt

weights

Value

The output consists of a forecasted transition matrix.

Details

Multinomial logistic regression is a simple extension of binary logistic regression that allows for more than two categories of the dependent or outcome variable. Whereas, a binary logistic regression model compares one dichotomy, the multinomial logistic regression model compares a number of dichotomies. Like binary logistic regression, multinomial logistic regression uses maximum likelihood estimation to evaluate the probability of categorical membership.

Assume there are 1,2,3 ...K groups in a dataset, and group 1 is the one chosen as the reference category. The logistic model states that the probability of falling into group j given the set of predictor values x is given by the general expression $$P(y=k|\emph{X}) = \frac{exp(\emph{X}\beta_{k})}{1+\sum_{j=2}^{N}exp(\emph{X}\beta_{j})}$$

Examples

# NOT RUN {
#(1) Import Data
startDate <-"2000-01-01"
endDate   <-"2002-01-01"
TotalDateRange <- seq(as.Date(startDate), as.Date(endDate), "years")


#(2) Create quarterly transition matrices for the entire date range selected using the normal
#   procedures

#Set parameters
snapshots <- 4   #4,#12    #monthly transition matrices
interval <-  1   #1/12    #1 month transition matrices

#define list to hold initial counts and transition counts
lstCnt <-rep(list(list()), length(TotalDateRange)-1)
lstInit <-rep(list(list()), length(TotalDateRange)-1)

#initialize counters
n <- 1
k <- 1
for (l in 1:(length(TotalDateRange)-1)){

  istartDate = POSIXTomatlab(as.POSIXlt(as.Date(TotalDateRange[l],format = "%Y-%m-%d")))
  iendDate = POSIXTomatlab(as.POSIXlt(as.Date(TotalDateRange[l+1],format = "%Y-%m-%d")))
  DateRange        <- as.Date(matlabToPOSIX(cfdates(istartDate,iendDate,snapshots)))

  for(i in 1:(length(DateRange)-1)){

    sDate  <- as.Date(DateRange[i])
    eDate    <- as.Date(DateRange[i+1])

    Example1<-TransitionProb(data,sDate, eDate, 'cohort', snapshots, interval)

    lstCnt[[k]][[n]] <- Example1$sampleTotals$totalsMat      #list of monthly transition counts
    lstInit[[k]][[n]]  <- Example1$sampleTotals$totalsVec    #list of monthly initial counts
    n <- n+1

    if(n>snapshots){
      n <- 1
      k <- k+1
    }

  }

}

#(3) extract the aggregate transition counts by date and transition type (i.e, AAA to AA,
#   AAA to A, AAA to BBB, etc...)
ratingCat <- c("A","B", "C", "D", "E", "F", "G", "N")

df <- VecOfTransData(lstCnt,ratingCat,startDate,endDate,snapshots)
df <- subset(df, df[["start_Rating"]] !="N")   #Notes: remove any record having a default
                                               #rating in the 'start_Rating'
#(4) Construct parameters for MNL model
startDate <- as.Date("2000-01-01")
endDate <- as.Date("2005-01-01")

ref <- "A"   #"AAA"
depVar <- c("end_rating")
indVars <-c("Macro1", "Financial1","Industry1")
wgt <-  "mCount"
ratingCat <- c("A","B", "C", "D", "E", "F", "G")  #NOTE: 'N' (Default Rating) is excluded
                                                  #(VBA book count data)
#(5) run mnl model
# }
# NOT RUN {
mnl_T<-transForecast_mnl(df, histData, predData_mnl, startDate, endDate, ref, depVar,
                         indVars, ratingCat, wgt)
# }
# NOT RUN {

# }