I am able to change the coefficients of my linear model. Then i want to compare the results of my "new" model with the new coefficients, but R is not calculating the results with the new coefficients.
As you can see in my following example the summary of my models fit and fit1 are excactly the same, though results like multiple R-squared should or fitted values should change.
set.seed(2157010) #forgot set.
x1 <- 1998:2011
x2 <- x1 + rnorm(length(x1))
y <- 3*x2 + rnorm(length(x1)) #you had x, not x1 or x2
fit <- lm( y ~ x1 + x2)
# view original coefficients
coef(fit)
# generate second function for comparing results
fit1 <- fit
# replace coefficients with new values, use whole name which is coefficients:
fit1$coefficients[2:3] <- c(5, 1)
# view new coefficents
coef(fit1)
# Comparing
summary(fit)
summary(fit1)
Thanks in advance
It might be easier to compute the multiple R^2 yourself with the substituted parameters.
mult_r2 <- function(beta, y, X) {
tot_ss <- var(y) * (length(y) - 1)
rss <- sum((y - X %*% beta)^2)
1 - rss/tot_ss
}
(or, more compactly, following the comments, you could compute p <- X %*% beta; (cor(y,beta))^2)
mult_r2(coef(fit), y = model.response(model.frame(fit)), X = model.matrix(fit))
## 0.9931179, matches summary()
Now with new coefficients:
new_coef <- coef(fit)
new_coef[2:3] <- c(5,1)
mult_r2(new_coef, y = model.response(model.frame(fit)), X = model.matrix(fit))
## [1] -343917
That last result seems pretty wild, but the substituted coefficients are very different from the true least-squares coeffs, and negative R^2 is possible when the model is bad enough ...
I am trying to fit following model:
mod <- jagam(y_freq ~
s(x, bs="cr", fx=FALSE, k=5) +
s(x, by=a, bs="cr", fx=FALSE, k=5) +
s(x, by=b, bs="cr", fx=FALSE, k=5) +
s(x, by=c, bs="cr", fx=FALSE, k=5),
family = binomial(), data = dt,
file = "file.jags",
weights = dt$total)
where 'a' is a numeric variable with 0 and 1 as potential values, 'b' is another numeric variable with 0 and 1 as potential values, and 'c' is the interaction between 'a' and 'b'.
As I would like to correct for overdispersion, I update the jags file that gets created by the jagam function as follows:
model {
eta <- X %*% b
for (i in 1:n) {
y[i] ~ dbin(p[i],w[i])
p[i] ~ dbeta(alpha[i], beta[i]) T(0.001,0.999)
alpha[i] = phi[i] * mu[i]
beta[i] = phi[i] * (1 - mu[i])
phi[i] ~ dexp(1/250)
mu[i] <- ilogit(eta[i])
}
#splines are defined below here
}
After updating the file, I use the functions jags.model, jags.sample (for parameters: b, rho and mu) with 100k iterations and 3 chains, and sim2jam.
After I check for convergence with the coda package, I get for all three chains following results (only one shown here):
example plot for one chain for rho parameter
I get traces for 8 rho parameters, for which only two seem to converge. I cannot show the results for the other parameters (b and mu) as there are too many (40 for b) to show on a plot.
I would like to know which of these 8 parameters for rho correspond to the null-space parameters, and what the cause of the convergence issue could be (too many parameters, too many splines, ...) and how to fix it?
Thank you,
Kate
set.seed(155656494)
#setting parameter values
n<-500
sdu<-25
beta0<-40
beta1<-12
# Running the simulation again
# create the x variable outside the loop since it’s fixed in
# repeated sampling
x2 <- floor(runif(n,5,16))
# set the number of iterations for your simulation (how many values
# of beta1 will be estimated)
nsim2 <- 10000000
# create a vector to store the estimated values of beta1
vbeta2 <- numeric(nsim2)
# create a loop that produces values of y, regresses y on x, and
# stores the OLS estimate of beta1
for (i in 1:nsim2) {
y2 <- beta0 + beta1*x2 + 0.2*x2 + rnorm(n,mean=0,sd=sdu)
model2 <- lm(y2 ~ x2)
vbeta2[i] <- coef(model2)[[2]]
}
mean(vbeta2)
The above is a simple linear regression model that has 10 million iterations. I looking for help with speeding up the loop. This code basically runs as y2 <- beta0 + beta1x2 + 0.2x2 + rnorm(n,mean=0,sd=sdu), which will then be used to calculate the mean of vbeta2
You could use profvis to determine where is processor time spent:
library(profvis)
profvis({
set.seed(155656494)
#setting parameter values
n<-500
sdu<-25
beta0<-40
beta1<-12
# Running the simulation again
# create the x variable outside the loop since it’s fixed in
# repeated sampling
x2 <- floor(runif(n,5,16))
# set the number of iterations for your simulation (how many values
# of beta1 will be estimated)
nsim2 <- 1000
# create a vector to store the estimated values of beta1
vbeta2 <- numeric(nsim2)
# create a loop that produces values of y, regresses y on x, and
# stores the OLS estimate of beta1
for (i in 1:nsim2) {
y2 <- beta0 + beta1*x2 + 0.2*x2 + rnorm(n,mean=0,sd=sdu)
model2 <- lm(y2 ~ x2)
vbeta2[i] <- coef(model2)[[2]]
}
mean(vbeta2)
})
The result shows that most of the time is spent evaluating the linear regression model :
As suggested by #maarvd, you could paralellize to speed this up. However parallelizing each single calculation won't be efficient because one calculation is too fast (~0.5 ms), so you'll have to distribute chuncks of many thousand calculations per worker. I agree with #Allan Cameron, is this worth the effort?
[Code is updated and does not correspond to error messages anymore]
I am trying to understand how JAGS predicts outcome values (for a mixed markov model). I've trained the model on a dataset which includes outcome m and covariates x1, x2 and x3.
Predicting the outcome without fixing parameter values works in R, but the output seems completely random:
preds <- run.jags("model.txt",
data=list(x1=x1, x2=x2, x3=x3, m=m,
statealpha=rep(1,times=M), M=M, T=T, N=N), monitor=c("m_pred"),
n.chains=1, inits = NA, sample=1)
Compiling rjags model...
Calling the simulation using the rjags method...
Note: the model did not require adaptation
Burning in the model for 4000 iterations...
|**************************************************| 100%
Running the model for 1 iterations...
Simulation complete
Finished running the simulation
However, as soon as I try to fix parameters (i.e. use model estimates to predict outcome m, I get errors:
preds <- run.jags("model.txt",
data=list(x1=x1, x2=x2, x3=x3,
statealpha=rep(1,times=M), M=M, T=T, N=N, beta1=beta1), monitor=c("m"),
n.chains=1, inits = NA, sample=1)
Compiling rjags model...
Error: The following error occured when compiling and adapting the model using rjags:
Error in rjags::jags.model(model, data = dataenv, n.chains = length(runjags.object$end.state), :
RUNTIME ERROR:
Compilation error on line 39.
beta1[2,1] is a logical node and cannot be observed
beta1 in this case is a 2x2 matrix of coefficient estimates.
How is JAGS predicting m in the first example (no fixed parameters)? Is it just completely randomly choosing m?
How can I include earlier acquired model estimates to simulate new outcome values?
The model is:
model{
for (i in 1:N)
{
for (t in 1:T)
{
m[t,i] ~ dcat(ps[i,t,])
}
for (state in 1:M)
{
ps[i,1,state] <- probs1[state]
for (t in 2:T)
{
ps[i,t,state] <- probs[m[(t-1),i], state, i,t]
}
for (prev in 1:M){
for (t in 1:T) {
probs[prev,state,i,t] <- odds[prev,state,i,t]/totalodds[prev,i,t]
odds[prev,state,i,t] <- exp(alpha[prev,state,i] +
beta1[prev,state]*x1[t,i]
+ beta2[prev,state]*x2[t,i]
+ beta3[prev,state]*x3[t,i])
}}
alpha[state,state,i] <- 0
for (t in 1:T) {
totalodds[state,i,t] <- odds[state,1,i,t] + odds[state,2,i,t]
}
}
alpha[1,2,i] <- raneffs[i,1]
alpha[2,1,i] <- raneffs[i,2]
raneffs[i,1:2] ~ dmnorm(alpha.means[1:2],alpha.prec[1:2, 1:2])
}
for (state in 1:M)
{
beta1[state,state] <- 0
beta2[state,state] <- 0
beta3[state,state] <- 0
}
beta1[1,2] <- rcoeff[1]
beta1[2,1] <- rcoeff[2]
beta2[1,2] <- rcoeff[3]
beta2[2,1] <- rcoeff[4]
beta3[1,2] <- rcoeff[5]
beta3[2,1] <- rcoeff[6]
alpha.Sigma[1:2,1:2] <- inverse(alpha.prec[1:2,1:2])
probs1[1:M] ~ ddirich(statealpha[1:M])
for (par in 1:6)
{
alpha.means[par] ~ dt(T.constant.mu,T.constant.tau,T.constant.k)
rcoeff[par] ~ dt(T.mu, T.tau, T.k)
}
T.constant.mu <- 0
T.mu <- 0
T.constant.tau <- 1/T.constant.scale.squared
T.tau <- 1/T.scale.squared
T.constant.scale.squared <- T.constant.scale*T.constant.scale
T.scale.squared <- T.scale*T.scale
T.scale <- 2.5
T.constant.scale <- 10
T.constant.k <- 1
T.k <- 1
alpha.prec[1:2,1:2] ~ dwish(Om[1:2,1:2],2)
Om[1,1] <- 1
Om[1,2] <- 0
Om[2,1] <- 0
Om[2,2] <- 1
## Prediction
for (i in 1:N)
{
m_pred[1,i] <- m[1,i]
for (t in 2:T)
{
m_pred[t,i] ~ dcat(ps_pred[i,t,])
}
for (state in 1:M)
{
ps_pred[i,1,state] <- probs1[state]
for (t in 2:T)
{
ps_pred[i,t,state] <- probs_pred[m_pred[(t-1),i], state, i,t]
}
for (prev in 1:M)
{
for (t in 1:T)
{
probs_pred[prev,state,i,t] <- odds_pred[prev,state,i,t]/totalodds_pred[prev,i,t]
odds_pred[prev,state,i,t] <- exp(alpha[prev,state,i] +
beta1[prev,state]*x1[t,i]
+ beta2[prev,state]*x2[t,i]
+ beta3[prev,state]*x3[t,i])
}}
for (t in 1:T) {
totalodds_pred[state,i,t] <- odds_pred[state,1,i,t] + odds_pred[state,2,i,t]
}
}
}
TL;DR: I think you're just missing a likelihood.
Your model is complex, so perhaps I'm missing something, but as far as I can tell there is no likelihood. You are supplying the predictors x1, x2, and x3 as data, but you aren't giving any observed m. So in what sense can JAGS be "fitting" the model?
To answer your questions:
Yes, it appears that m is drawn as random from a categorical distribution conditioned on the rest of the model. Since there are no m supplied as data, none of the parameter distributions have cause for update, so your result for m is no different than you'd get if you just did random draws from all the priors and propagated them through the model in R or whatever.
Though it still wouldn't constitute fitting the model in any sense, you would be free to supply values for beta1 if they weren't already defined completely in the model. JAGS is complaining because currently beta1[i] = rcoeff[i] ~ dt(T.mu, T.tau, T.k), and the parameters to the T distribution are all fixed. If any of (T.mu, T.tau, T.k) were instead given priors (identifying them as random), then beta1 could be supplied as data and JAGS would treat rcoeff[i] ~ dt(T.mu, T.tau, T.k) as a likelihood. But in the model's current form, as far as JAGS is concerned if you supply beta1 as data, that's in conflict with the fixed definition already in the model.
I'm stretching here, but my guess is if you're using JAGS you have (or would like to) fit the model in JAGS too. It's a common pattern to include both an observed response and a desired predicted response in a jags model, e.g. something like this:
model {
b ~ dnorm(0, 1) # prior on b
for(i in 1:N) {
y[i] ~ dnorm(b * x[i], 1) # Likelihood of y | b (and fixed precision = 1 for the example)
}
for(i in 1:N_pred) {
pred_y[i] ~ dnorm(b * pred_x[i], 1) # Prediction
}
}
In this example model, x, y, and pred_x are supplied as data, the unknown parameter b is to be estimated, and we desire the posterior predictions pred_y at each value of pred_x. JAGS knows that the distribution in the first for loop is a likelihood, because y is supplied as data. Posterior samples of b will be constrained by this likelihood. The second for loop looks similar, but since pred_y is not supplied as data, it can do nothing to constrain b. Instead, JAGS knows to simply draw pred_y samples conditioned on b and the supplied pred_x. The values of pred_x are commonly defined to be the same as observed x, giving a predictive interval for each observed data point, or as a regular sequence of values along the x axis to generate a smooth predictive interval.
I am fitting a weibull model to discrete values using JAGS in R. I have no problem fitting a weibull to continuous data, but I run in to trouble when I switch to discrete values.
Here is some data, and code to fit a weibull model in JAGS:
#draw data from a weibull distribution
y <- rweibull(200, shape = 1, scale = 0.9)
#y <- round(y)
#load jags, specify a jags model.
library(runjags)
j.model ="
model{
for (i in 1:N){
y[i] ~ dweib(shape[i], scale[i])
shape[i] <- b1
scale[i] <- b2
}
#priors
b1 ~ dnorm(0, .0001) I(0, )
b2 ~ dnorm(0, .0001) I(0, )
}
"
#load data as list
data <- list(y=y, N = length(y))
#run jags model.
jags.out <- run.jags(j.model,
data=data,
n.chains=3,
monitor=c('b1','b2')
)
summary(jags.out)
This model fits fine. However, if I transform y values to discrete values using y <- round(y), and run the same model, it fails with the error Error in node y[7], Node inconsistent with parents. The particular number of the node changes every time I try, but its always a low number.
I know I can make this run by adding a very small number to all of my values, however, this does not account for the fact that the data are discrete. I know discrete weibull distributions exists, but how can I implement one in JAGS?
You can use the 'ones trick' to implement a discrete weibull distribution in JAGS. Using the pmf here we can make a function to generate some data:
pmf_weib <- function(x, scale, shape){
exp(-(x/scale)^shape) - exp(-((x+1)/scale)^shape)
}
# probability of getting 0 through 200 with scale = 7 and shape = 4
probs <- pmf_weib(seq(0,200), 7, 4)
y <- sample(0:200, 100, TRUE, probs ) # sample from those probabilities
For the 'ones trick' to work you generally have to divide your new pmf by some large constant to ensure that the probability is between 0 and 1. While it appears that the pmf of the discrete weibull already ensures this, we have still added some large constant in the model anyways. So, here is what the model looks like now:
j.model ="
data{
C <- 10000
for(i in 1:N){
ones[i] <- 1
}
}
model{
for (i in 1:N){
discrete_weib[i] <- exp(-(y[i]/scale)^shape) - exp(-((y[i]+1)/scale)^shape)
ones[i] ~ dbern(discrete_weib[i]/C)
}
#priors
scale ~ dnorm(0, .0001) I(0, )
shape ~ dnorm(0, .0001) I(0, )
}
"
Note that we added 1) a vector of ones and a large constant in the data argument, 2) the pmf of the discrete weibull, and 3) we run that probability through a Bernoulli trial.
You can fit the model with the same code you have above, here is the summary which shows that the model successfully recovered the parameter values (scale = 7 and shape = 4).
Lower95 Median Upper95 Mean SD Mode MCerr MC%ofSD SSeff
scale 6.968277 7.289216 7.629413 7.290810 0.1695400 NA 0.001364831 0.8 15431
shape 3.843055 4.599420 5.357713 4.611583 0.3842862 NA 0.003124576 0.8 15126