3 is cat. variable with : 1,2 & 3, where 1 is reference category. Now I want to estimate parameters with stratified bootstrap including CIs, but could not find any relevant function
data <- data.frame (x = c(1,1,2,3,1,1,1,3,1,2,3),
y = c(100,130,33,45,98,145,45,29,200,104,89),
w = c(16,19,34,19,11,34,17,43,100,34,10))
df$x <- as.factor(df$x)
df$x <- relevel(df$x,ref = "1")
fit <- lm(y ~ x*w, data = data)
Related
I want to calculate a linear mixed model in which:
y = frequency of a correct response (in column "answers_correct" = "True")
x = condition benevolent (in column "condition_benevolent" = "True")
True in x means that the experimental condition was benevolent and false means that the experimental conditions were either malignant or random. The graph may help to understand the data.
I appreciate any help!! In the following my tries....
#Linear mixed model benevolent
#data_with_id$condition_benevolent_numeric <- recode(data_with_id$condition_benevolent, "False" = 0, "True" = 1)
#n <- 480
x <- c(data_with_id$condition_benevolent)
data_with_id$condition_benevolent <- as.numeric(data_with_id$condition_benevolent == "A")
view(data_with_id$condition_benevolent)
x <- model.matrix(~x -1, data = data_with_id, drop.unused.levels = TRUE)[,-1] #dummycodierung, True=1
#frequ <- häufigkeit_richtig_df_benev
y <- data_with_id$answers_correct
model_H1.1_benevolent <- lmer(y ~ x + (1|trial), data=data_with_id)
summary(model_H1.1_benevolent)
length(y)
length(x)
length(data_with_id$trial)
view(y)
view(x)
nrow(data_with_id)
nrow(data_with_id$condition_benevolent)
nrow(data_with_id$trial)
I know variations of this question have been asked before but I haven't yet seen an answer on how to implement the multinomial Poisson transformation with multilevel models.
I decided to make a fake dataset and follow the method outlined here, also consulting the notes the poster mentions as well as the Baker paper on MP transformation.
In order to check if I'm doing the coding correctly, I decided to create a binary outcome variable as a first step; because glmer can handle binary response variables, this will let me check I'm correctly recasting the logit regression as multiple Poissons.
The context of this problem is running multilevel regressions with survey data where the outcome variable is response to a question and the possible predictors are demographic variables. As I mentioned above, I wanted to see if I could properly code the binary outcome variable as a Poisson regression before moving on to multi-level outcome variables.
library(dplyr)
library(lme4)
key <- expand.grid(sex = c('Male', 'Female'),
age = c('18-34', '35-64', '45-64'))
set.seed(256)
probs <- runif(nrow(key))
# Make a fake dataset with 1000 responses
n <- 1000
df <- data.frame(sex = sample(c('Male', 'Female'), n, replace = TRUE),
age = sample(c('18-34', '35-64', '45-64'), n, replace = TRUE),
obs = seq_len(n), stringsAsFactors = FALSE)
age <- model.matrix(~ age, data = df)[, -1]
sex <- model.matrix(~ sex, data = df)[, -1]
beta_age <- matrix(c(0, 1), nrow = 2, ncol = 1)
beta_sex <- matrix(1, nrow = 1, ncol = 1)
# Create class probabilities as a function of age and sex
probs <- plogis(
-0.5 +
age %*% beta_age +
sex %*% beta_sex +
rnorm(n)
)
id <- ifelse(probs > 0.5, 1, 0)
df$y1 <- id
df$y2 <- 1 - df$y1
# First run the regular hierarchical logit, just with a varying intercept for age
glm_out <- glmer(y1 ~ (1|age), family = 'binomial', data = df)
summary(glm_out)
#Next, two Poisson regressions
glm_1 <- glmer(y1 ~ (1|obs) + (1|age), data = df, family = 'poisson')
glm_2 <- glmer(y2 ~ (1|obs) + (1|age), data = df, family = 'poisson')
coef(glm_1)$age - coef(glm_2)$age
coef(glm_out)$age
The outputs for the last two lines are:
> coef(glm_1)$age - coef(glm_2)$age
(Intercept)
18-34 0.14718933
35-64 0.03718271
45-64 1.67755129
> coef(glm_out)$age
(Intercept)
18-34 0.13517758
35-64 0.02190587
45-64 1.70852847
These estimates seem close but they are not exactly the same. I'm thinking I've specified an equation wrong with the intercept.
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)
For my thesis I have to fit some glm models with MLEs that R doesn't have, I was going ok for the models with close form but now I have to use de Gausian CDF, so i decide to fit a simple probit model.
this is the code:
Data:
set.seed(123)
x <-matrix( rnorm(50,2,4),50,1)
m <- matrix(runif(50,2,4),50,1)
t <- matrix(rpois(50,0.5),50,1)
z <- (1+exp(-((x-mean(x)/sd(x)))))^-1 + runif(50)
y <- ifelse(z < 1.186228, 0, 1)
data1 <- as.data.frame(cbind(y,x,m,t))
myprobit <- function (formula, data)
{
mf <- model.frame(formula, data)
y <- model.response(mf, "numeric")
X <- model.matrix(formula, data = data)
if (any(is.na(cbind(y, X))))
stop("Some data are missing.")
loglik <- function(betas, X, y, sigma) { #loglikelihood
p <- length(betas)
beta <- betas[-p]
eta <- X %*% beta
sigma <- 1 #because of identification, sigma must be equal to 1
G <- pnorm(y, mean = eta,sd=sigma)
sum( y*log(G) + (1-y)*log(1-G))
}
ls.reg <- lm(y ~ X - 1)#starting values using ols, indicating that this model already has a constant
start <- coef(ls.reg)
fit <- optim(start, loglik, X = X, y = y, control = list(fnscale = -1), method = "BFGS", hessian = TRUE) #optimizar
if (fit$convergence > 0) {
print(fit)
stop("optim failed to converge!") #verify convergence
}
return(fit)
}
myprobit(y ~ x + m + t,data = data1)
And i get: Error in X %*% beta : non-conformable arguments, if i change start <- coef(ls.reg) with start <- c(coef(ls.reg), 1) i get wrong stimatives comparing with:
probit <- glm(y ~ x + m + t,data = data1 , family = binomial(link = "probit"))
What am I doing wrong?
Is possible to correctly fit this model using pnorm, if no, what algorithm should I use to approximate de gausian CDF. Thanks!!
The line of code responsible for your error is the following:
eta <- X %*% beta
Note that "%*%" is the matrix multiplication operator. By reproducing your code I noticed that X is a matrix with 50 rows and 4 columns. Hence, for matrix multiplication to be possible your "beta" needs to have 4 rows. But when you run "betas[-p]" you subset the betas vector by removing its last element, leaving only three elements instead of the four you need for matrix multiplication to be defined. If you remove [-p] the code will work.
I am trying to understand how to use mixed linear models to analyse my data by simulating a model, but I can't reproduce the input parameters. What am I missing?
I want to start simulating a model with a random intercept for each subject. Here is the formula of what I want to simulate and reproduce:
If beta1 (<11) is small I find gamma00 as the intercept in fixed section, but I am completedly unaable to retrieve the slope (beta1). Also, the linear effect is not significant. Where is my conceptual mistake?
library(lmerTest)
# Generating data set
# General values and variables
numObj <- 20
numSub <- 100
e <- rnorm(numObj * numSub, mean = 0, sd = 0.1)
x <- scale(runif(numObj * numSub, min = -100, max = 100))
y <- c()
index <- 1
# Coefficients
gamma00 <- 18
gamma01 <- 0.5
beta1 <- -100
w <- runif(numSub, min = -3, max = 3)
uo <- rnorm(numSub, mean = 0, sd = 0.1)
meanBeta0 <- mean(gamma00 + gamma01*w + uo) # I should be able to retrieve that parameter.
for(j in 1:numSub){
for(i in 1:numObj){
y[index] <- gamma00 + gamma01*w[j]+ uo[j] + beta1*x[i] + e[index]
index <- index + 1
}
}
dataFrame2 <- data.frame(y = y, x = x, subNo = factor(rep(1:numSub, each = numObj)), objNum = factor(rep(1:numObj, numSub)))
model2 <- lmer(y ~ x +
(1 | subNo), data = dataFrame2)
summary(model2)
anova(model2)
No conceptual mistake here, just a mixed up index value: you should be using index rather than i to index x in your data generation loop.
Basically due to the mix-up you were using the first subject's x values for generating data for all the subjects, but using the individual x values in the model.