I'm working with the train() function from the caret package to fit multiple regression and ML models to test their fit. I'd like to write a function that iterates through all model types and enters the best fit into a dataframe. Biggest issue is that caret doesn't provide all the model fit statistics that I'd like so they need to be derived from the raw output. Based on my exploration there doesn't seem to be a standardized way caret outputs each models fit.
Another post (sorry don't have a link) created this function which pulls from fit$results and fit$bestTune to get pre calculated RMSE, R^2, etc.
get_best_result <- function(caret_fit) {
best = which(rownames(caret_fit$results) == rownames(caret_fit$bestTune))
best_result = caret_fit$results[best, ]
rownames(best_result) = NULL
best_result
}
One example of another fit statistic I need to calculate using raw output is BIC. The two functions below do that. The residuals (y_actual - y_predicted) are needed along with the number of x variables (k) and the number of rows used in the prediction (n). k and n must be derived from the output not the original dataset due to the models dropping x variables (feature selection) or rows (omitting NAs) based on its algorithm.
calculate_MSE <- function(residuals){
# residuals can be replaced with y_actual-y_predicted
mse <- mean(residuals^2)
return(mse)
}
calculate_BIC <- function(n, mse, k){
BIC <- n*log(mse)+k*log(n)
return(BIC)
}
The real question is is there a standardized output of caret::train() for x variables or either y_actual, y_predicted, or residuals?
I tried fit$finalModel$model and other methods but to no avail.
Here is a reproducible example along with the function I'm using. Please consider the functions above a part of this reproducible example.
library(rlist)
library(data.table)
# data
df <- data.frame(y1 = rnorm(50, 0, 1),
y2 = rnorm(50, .25, 1.5),
x1 = rnorm(50, .4, .9),
x2 = rnorm(50, 0, 1.1),
x3 = rnorm(50, 1, .75))
missing_index <- sample(1:50, 7, replace = F)
df[missing_index,] <- NA
# function to fit models and pull results
fitModels <- function(df, Ys, Xs, models){
# empty list
results <- list()
# number of for loops
loops_counter <- 0
# for every y
for(y in 1:length(Ys)){
# for every model
for(m in 1:length(models)){
# track loops
loops_counter <- loops_counter + 1
# fit the model
set.seed(1) # seed for reproducability
fit <- tryCatch(train(as.formula(paste(Ys[y], paste(Xs, collapse = ' + '),
sep = ' ~ ')),
data = df,
method = models[m],
na.action = na.omit,
tuneLength = 10),
error = function(e) {return(NA)})
# pull results
results[[loops_counter]] <- c(Y = Ys[y],
model = models[m],
sample_size = nrow(fit$finalModel$model),
RMSE = get_best_result(fit)[[2]],
R2 = get_best_result(fit)[[3]],
MAE = get_best_result(fit)[[4]],
BIC = calculate_BIC(n = length(fit$finalModel),
mse = calculate_MSE(fit$finalModel$residuals),
k = length(fit$finalModel$xNames)))
}
}
# list bind
results_df <- list.rbind(results)
return(results_df)
}
linear_models <- c('lm', 'glmnet', 'ridge', 'lars', 'enet')
fits <- fitModels(df, c(y1, y2), c(x1,x2,x3), linear_models)
I would like to include person-item covariates in the item response model(eg:2PL model), but I am confused with how to interpret the output
(shown in the picture). Like how to understand the relationship between the coefficients of groupG1 and a1(or d)?
Below is my code:
#make some data
set.seed(1234)
N <- 750
a <- matrix(rlnorm(10,.3,1),10,1)
d <- matrix(rnorm(10), 10)
Theta <- matrix(sort(rnorm(N)))
pseudoIQ <- Theta * 5 + 100 + rnorm(N, 0 , 5)
pseudoIQ <- (pseudoIQ - mean(pseudoIQ))/10 #rescale variable for numerical stability
group <- factor(rep(c('G1','G2','G3'), each = N/3))
data <- simdata(a,d,N, itemtype = rep('2PL',10), Theta=Theta)
covdata <- data.frame(group, pseudoIQ)
#specify IRT model
model <- 'Theta = 1-10'
# 2PL model
mod2 <- mixedmirt(data, covdata, model, fixed = ~ 0 + group + items + pseudoIQ,itemtype = '2PL')
coef(mod2)
I have written a small function that simulates data from a normal distribution, how it is usual in linear models. My question is how to get a model with a pvalue of sim[, 1] == 0.05. I want to show that if I add a random variable even it is normal distributed around zero with small variance N(0,0.0023) , that pvalue of sim[,1] changes. The code below shows the true model.
set.seed(37) # seed for reproducability
simulation <- function(b_0, b_1,n,min_x_1 ,max_x_1,sd_e){
mat <- NA
x_1 <- runif(n = n, min = min_x_1, max =max_x_1)
error <- rnorm(mean = 0,sd = sd_e, n = n )
y <- b_0 + b_1*x_1 + error
mat <- matrix(cbind(x_1,y), ncol = 2)
return(mat)
#plot(mat[,1],mat[,2])
}
sim <- simulation(10,-2,10000,-10,70,0.003)
summary(lm(sim[,2] ~ sim[,1] ))
I'm working on a binomial mixture model using OpenBUGS and R package R2OpenBUGS. I've successfully built simpler models, but once I add another level for imperfect detection, I consistently receive the error variable X is not defined in model or in data set. I've tried a number of different things, including changing the structure of my data and entering my data directly into OpenBUGS. I'm posting this in the hope that someone else has experience with this error, and perhaps knows why OpenBUGS is not recognizing variable X even though it is clearly defined as far as I can tell.
I've also gotten the error expected the collection operator c error pos 8 - this is not an error I've been getting previously, but I am similarly stumped.
Both the model and the data-simulation function come from Kery's Introduction to WinBUGS for Ecologists (2010). I will note that the data set here is in lieu of my own data, which is similar.
I am including the function to build the dataset as well as the model. Apologies for the length.
# Simulate data: 200 sites, 3 sampling rounds, 3 factors of the level 'trt',
# and continuous covariate 'X'
data.fn <- function(nsite = 180, nrep = 3, xmin = -1, xmax = 1, alpha.vec = c(0.01,0.2,0.4,1.1,0.01,0.2), beta0 = 1, beta1 = -1, ntrt = 3){
y <- array(dim = c(nsite, nrep)) # Array for counts
X <- sort(runif(n = nsite, min = xmin, max = xmax)) # covariate values, sorted
# Relationship expected abundance - covariate
x2 <- rep(1:ntrt, rep(60, ntrt)) # Indicator for population
trt <- factor(x2, labels = c("CT", "CM", "CC"))
Xmat <- model.matrix(~ trt*X)
lin.pred <- Xmat[,] %*% alpha.vec # Value of lin.predictor
lam <- exp(lin.pred)
# Add Poisson noise: draw N from Poisson(lambda)
N <- rpois(n = nsite, lambda = lam)
table(N) # Distribution of abundances across sites
sum(N > 0) / nsite # Empirical occupancy
totalN <- sum(N) ; totalN
# Observation process
# Relationship detection prob - covariate
p <- plogis(beta0 + beta1 * X)
# Make a 'census' (i.e., go out and count things)
for (i in 1:nrep){
y[,i] <- rbinom(n = nsite, size = N, prob = p)
}
# Return stuff
return(list(nsite = nsite, nrep = nrep, ntrt = ntrt, X = X, alpha.vec = alpha.vec, beta0 = beta0, beta1 = beta1, lam = lam, N = N, totalN = totalN, p = p, y = y, trt = trt))
}
data <- data.fn()
And here is the model:
sink("nmix1.txt")
cat("
model {
# Priors
for (i in 1:3){ # 3 treatment levels (factor)
alpha0[i] ~ dnorm(0, 0.01)
alpha1[i] ~ dnorm(0, 0.01)
}
beta0 ~ dnorm(0, 0.01)
beta1 ~ dnorm(0, 0.01)
# Likelihood
for (i in 1:180) { # 180 sites
C[i] ~ dpois(lambda[i])
log(lambda[i]) <- log.lambda[i]
log.lambda[i] <- alpha0[trt[i]] + alpha1[trt[i]]*X[i]
for (j in 1:3){ # each site sampled 3 times
y[i,j] ~ dbin(p[i,j], C[i])
lp[i,j] <- beta0 + beta1*X[i]
p[i,j] <- exp(lp[i,j])/(1+exp(lp[i,j]))
}
}
# Derived quantities
}
",fill=TRUE)
sink()
# Bundle data
trt <- data$trt
y <- data$y
X <- data$X
ntrt <- 3
# Standardise covariates
s.X <- (X - mean(X))/sd(X)
win.data <- list(C = y, trt = as.numeric(trt), X = s.X)
# Inits function
inits <- function(){ list(alpha0 = rnorm(ntrt, 0, 2),
alpha1 = rnorm(ntrt, 0, 2),
beta0 = rnorm(1,0,2), beta1 = rnorm(1,0,2))}
# Parameters to estimate
parameters <- c("alpha0", "alpha1", "beta0", "beta1")
# MCMC settings
ni <- 1200
nb <- 200
nt <- 2
nc <- 3
# Start Markov chains
out <- bugs(data = win.data, inits, parameters, "nmix1.txt", n.thin=nt,
n.chains=nc, n.burnin=nb, n.iter=ni, debug = TRUE)
Note: This answer has gone through a major revision, after I noticed another problem with the code.
If I understand your model correctly, you are mixing up the y and N from the simulated data, and what is passed as C to Bugs. You are passing the y variable (a matrix) to the C variable in the Bugs model, but this is accessed as a vector. From what I can see C is representing the number of "trials" in your binomial draw (actual abundances), i.e. N in your data set. The variable y (a matrix) is called the same thing in both the simulated data and in the Bugs model.
This is a reformulation of your model, as I understand it, and this runs ok:
sink("nmix1.txt")
cat("
model {
# Priors
for (i in 1:3){ # 3 treatment levels (factor)
alpha0[i] ~ dnorm(0, 0.01)
alpha1[i] ~ dnorm(0, 0.01)
}
beta0 ~ dnorm(0, 0.01)
beta1 ~ dnorm(0, 0.01)
# Likelihood
for (i in 1:180) { # 180 sites
C[i] ~ dpois(lambda[i])
log(lambda[i]) <- log.lambda[i]
log.lambda[i] <- alpha0[trt[i]] + alpha1[trt[i]]*X[i]
for (j in 1:3){ # each site sampled 3 times
y[i,j] ~ dbin(p[i,j], C[i])
lp[i,j] <- beta0 + beta1*X[i]
p[i,j] <- exp(lp[i,j])/(1+exp(lp[i,j]))
}
}
# Derived quantities
}
",fill=TRUE)
sink()
# Bundle data
trt <- data$trt
y <- data$y
X <- data$X
N<- data$N
ntrt <- 3
# Standardise covariates
s.X <- (X - mean(X))/sd(X)
win.data <- list(y = y, trt = as.numeric(trt), X = s.X, C= N)
# Inits function
inits <- function(){ list(alpha0 = rnorm(ntrt, 0, 2),
alpha1 = rnorm(ntrt, 0, 2),
beta0 = rnorm(1,0,2), beta1 = rnorm(1,0,2))}
# Parameters to estimate
parameters <- c("alpha0", "alpha1", "beta0", "beta1")
# MCMC settings
ni <- 1200
nb <- 200
nt <- 2
nc <- 3
# Start Markov chains
out <- bugs(data = win.data, inits, parameters, "nmix1.txt", n.thin=nt,
n.chains=nc, n.burnin=nb, n.iter=ni, debug = TRUE)
Overall, the results from this model looks ok, but there are long autocorrelation lags for beta0 and beta1. The estimate of beta1 also seems a bit off(~= -0.4), so you might want to recheck the Bugs model specification, so that it is matching the simulation model (i.e. that you are fitting the correct statistical model). At the moment, I'm not sure that it does, but I don't have the time to check further right now.
I got the same message trying to pass a factor to OpenBUGS. Like so,
Ndata <- list(yrs=N$yrs, site=N$site), ... )
The variable "site" was not passed by the "bugs" function. It simply was not in list passed
to OpenBUGS
I solved the problem by passing site as numeric,
Ndata <- list(yrs=N$yrs, site=as.numeric(N$site)), ... )
I have a time-series which I need to fit onto an AR (auto-regression) model.
The AR model has the form:
x(t) = a0 + a1*x(t-1) + a2*x(t-2) + ... + aq*x(t-q) + noise.
I have two contraints:
Find the best AR fit when lag.max = 50.
Sum of all coefficients a0 + a1 + ... + aq = 1
I wrote the below code:
require(FitAR)
data(lynx) # my real data comes from the stock market.
z <- -log(lynx)
#find best model
step <- SelectModel(z, ARModel = "AR" ,lag.max = 50, Criterion = "AIC",Best=10)
summary(step) # display results
# fit the model and get coefficients
arfit <- ar(z,p=1, order.max=ceil(mean(step[,1])), aic=FALSE)
#check if sum of coefficients are 1
sum(arfit$ar)
[1] 0.5784978
My question is, how to add the constraint: sum of all coefficients = 1?
I looked at this question, but I do not realize how to use it.
**UPDATE**
I think I manage to solve my question as follow.
library(quadprog)
coeff <- arfit$ar
y <- 0
for (i in 1:length(coeff)) {
y <- y + coeff[i]*c(z[(i+1):length(z)],rep(0,i))
ifelse (i==1, X <- c(z[2:length(z)],0), X <- cbind(X,c(z[(i+1):length(z)],rep(0,i))))
}
Dmat <- t(X) %*% X
s <- solve.QP(Dmat , t(y) %*% X, matrix(1, nr=15, nc=1), 1, meq=1 )
s$solution
# The coefficients should sum up to 1
sum(s$solution)