columbus_sub2

#two submarkets

rm(list=ls())

library(mvtnorm)

data <- read.csv("columbus.csv")

data <- data[!(data$price_000s==87.06),]

set.seed(5)

data <- sample_n(data, 500)

data <- data[complete.cases(data), ]

#path <- "C:/Users/Syed Fuad/Desktop/Spatial/Shiroya/"

Y <- I(data$price_000s)

#house attributes

X <- cbind(1,I(data$onestory), I(data$air), I(data$rooms), I(data$fullbath), 
           I(data$agehouse)/100, I(data$buildingsqft)/1000, I(data$lotsize)/10000)

#demographic variables/mixing variables

Z <- cbind(1,I(data$pctblack), I(data$college), I(data$bluecoll_cbg)/100, I(data$mediany_cbg)/100000, 
           I(data$gradrate), I(data$math12), I(data$science12), I(data$staterevpct))

ols_agg <- lm(Y~X-1);
summary(ols_agg)

k = ncol(X)
n=nrow(X)
beta = matrix(NA,nrow=n,ncol=k)
sigma = c(1,rep(NA,n))
psi = rep(NA,n)

#starting values for the hedonic estimates/betas for each type i.e. for mixing algorithm

types <- 2;

beta_start <- matrix(ols_agg$coef,(types*ncol(X)),1);  

#starting values for the gamma estimates for the demographic variables

gamma_start <- matrix(0.01,(1*ncol(Z)),1);

#starting values for sigma
sigma_start <- matrix(sqrt(mean(ols_agg$residuals^2)),types,1)     

#collecting initializing values

val_start <- c(beta_start,gamma_start,sigma_start);

vals <- val_start;
types <- 2;

#convergence criteria comparing new and old estimates:

Iter_conv <- 0.0001;
j <- types; 

#number of independent variables or beta estimates we need to keep track of - so to use when indexing

niv <- ncol(X); 

#number of demographic variables to use when indexing

gvs <- ncol(Z); 

#row dim of aggregate

n <- nrow(X);
conv_cg = 5000; 
conv_cb = 5000; 

par <- val_start

#FnOne prob density  of observing prices given mean of cross product of house attributes and current 
#iteration of hedonic estimates and sigma

FnOne <- function(par,x,y) 
{
  #par[1] <- ifelse(par[1]>0, par[1], -1*par[1]) #this is for the NaNs
  dnorm(y, mean=x%*%par[-1], sd = par[1], log=FALSE)   
}

#FnTwo max prob densities over type probabilities

#beta_m <- optim(par1,FnTwo,d=d,x=X,y=Y,control=list(fnscale=-1,maxit=100000))

FnTwo <- function(par,d,x,y)   
{
  pdy <- matrix(0,n,j) 
  b <- par[1:(niv*j)] 
  s <- par[(niv*j+1):((niv+1)*j)]
  for (i in 1:j)
  {	
    pdy[,i] <- FnOne(c(s[i],b[((i-1)*niv+1):(i*niv)]),X,Y) 
  }
  pdy[pdy < 0.0005] <- 0.05 #this is for function cannot be evaluated at initial parameters 
  sum(d*log(pdy))
}

#FnThree logit for gamma estimates 

FnThree <- function(g,z)  
{ 
  L <- exp(z%*%g)  	
}

#FnFour max gamma estimates, type probabilities

FnFour <- function(par,d,z,y)   
{
  L <- matrix(0,n,j) 
  L[,1] <- 1
  for (m in 1:(j-1))   
  { 
    L[,(m+1)] <- FnThree(par[((m-1)*gvs+1):(m*gvs)],z)     
  }
  Pi <<- L / apply(L,1,sum) 
  sum(apply(d*log(Pi),1,sum))  
}

#mixing algorithm

FMM <- function(par,X,Z,y) 
{
  b <- par[1:(j*niv)]; 
  g <- par[(j*niv+1):((j*(niv+gvs)-gvs))]; 
  #g <- par[(j*niv+1):(length(par)-types)]; #three submarkets
  s <- par[-(1:(j*(niv+gvs)-gvs))];
  #s <- par[-(1:(length(par)-types))]; #three submarkets
  L <- matrix(0,n,j); 
  f <- L; 
  d <<- L;
  b <- matrix(b,niv,j); 
  iter <- 0
  
  while (abs(conv_cg) + abs(conv_cb) > Iter_conv)   {   
    
    #store parameter estimates of preceding iteration of mix through loop
    beta_old <- b; 
    gamma_old <- g; 
    
    #counter for while loop
    iter <- iter+1     
    
    for (i in 1:j) 
    { 
      f[,i] <- FnOne(c(s[i],b[,i]),X,Y)		
    }
    for (i in 1:(j-1)) 
    { 
      L[,1] <- 0
      L[,(i+1)] <- Z%*%g[((i-1)*gvs+1):(i*gvs)] 
    }
    
    #estimate Pi (P) and individual probabilities of belonging to a certain type (d):
    
    P <- exp(L)/(1+apply(exp(L[,(1:j)]),1,sum))
    P[is.nan(P)] <- 1
    
    for (i in 1:n) 
    {	
      d[i,] <- P[i,]*f[i,]/sum(P[i,]*f[i,]) 
    }
    
    #use individual probs (d) to estimate beta (b), gamma (g)
    
    b1 <- matrix(b,(niv*j),1); par1 <- c(b1,s);
    beta_m <- optim(par1,FnTwo,d=d,x=X,y=Y,control=list(fnscale=-1,maxit=100000))
    b <- matrix(beta_m$par[1:(j*niv)],niv,j) 
    
    s <- beta_m$par[(j*niv+1):(j*(niv+1))]
    
    gam_m <- optim(g,FnFour,d,z=Z,Y,control=list(fnscale=-1,maxit=100000))
    #gam_m <- optim(g,FnFour,d,z=Z,control=list(fnscale=-1,maxit=100000))
    g <- gam_m$par
    
    #setting up convergence check
    
    conv_cg <- sum(abs(g-gamma_old)) 
    conv_cb <- sum(abs(b-beta_old))  
    
    #collecting parameter estimates to use to impute LL
    
    par2 <- matrix(b,(niv*j),1)
    par2 <- c(par2,s)
    LL <- FnTwo(par2,d=d,x=X,y=Y) + FnFour(g,d=d,z=Z,y=Y);
    
    #storing 
    
    bvector <- matrix(b,j*niv,1)
    vals_fin <- c(bvector,g,s)	
    dvector <- d
  }
  #collecting parameters for output
  
  out_pars <- list("vals_fin" = vals_fin, "i_type" = d)
  print(b)
  print(g)
  print(iter)
  #f <<- f
  
  #return list of estimates - index for subsetting in final updating 
  return(out_pars)
}

#calling:

mix <- FMM(val_start,X=X,Z=Z,y=Y)

#final updating:

d <- mix$i_type

b <- mix$vals_fin[1:(j*niv)]; 

#g <- mix$vals_fin[(j*niv+1):((j*(niv+gvs)-gvs))]; 

s <- mix$vals_fin[-(1:(j*(niv+gvs)-gvs))];

b <- matrix(b,niv,j);

b1 <- matrix(b,(niv*j),1); 
par3 <- c(b1,s);

#standard errors

#beta_opt <- optim(par3,FnTwo,d=d,x=X,y=Y,control=list(fnscale=-1,maxit=10000),hessian=TRUE, method = c("Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", "Brent"))

beta_opt <- optim(par3,FnTwo,d=d,x=X,y=Y,control=list(fnscale=-1,maxit=10000),hessian=TRUE)

b <- matrix(beta_opt$par[1:(j*niv)],niv,j); 
bse1 <- sqrt(-diag(solve(beta_opt$hessian[1:niv,1:niv])))
bse2 <- sqrt(-diag(solve(beta_opt$hessian[(niv+1):(2*niv),(niv+1):(2*niv)])))

s <- beta_opt$par[(j*niv+1):(j*(niv+1))]

#gamma_opt <- optim(g,FnFour,d=d,z=Z,y=Y,control=list(fnscale=-1,maxit=100000),hessian=TRUE)
#g <- gamma_opt$par
#gse1 <- sqrt(-diag(solve(gamma_opt$hessian[1:gvs,1:gvs])))

par2 <- matrix(b,(niv*j),1);  
par2 <- c(par2,s)

LL <- FnTwo(par2,d=d,x=X,y=Y) + FnFour(g,d=d,z=Z,y=Y);
AIC <- -2*LL+2*niv

Ds=d;
beta=b;
bse=cbind(bse1,bse2);
#gamma=cbind(g[1:gvs],g[(gvs+1):(2*gvs)]);
#gse=cbind(gse1)