I am working through a class problem to test if the central limit theorem applies to medians as well. I've written the code, and as far as I can tell, it is working just fine. But my dnorm stat to plot the normal distribution is not showing up. It just creates a flat line when it should create a bell curve. Here is the code:
set.seed(14)
median_clt <- rnorm(1000, mean = 10, sd = 2)
many_sample_medians <- function(vec, n, reps) {
rep_vec <- replicate(reps, sample(vec, n), simplify = "vector")
median_vec <- apply(rep_vec, 2, median)
return(median_vec)
}
median_clt_test <- many_sample_medians(median_clt, 500, 1000)
median_clt_test_df <- data.frame(median_clt_test)
bw_clt <- 2 * IQR(median_clt_test_df$median_clt_test) / length(median_clt_test_df$median_clt_test)^(1/3)
ggplot(median_clt_test_df, aes(x = median_clt_test)) +
geom_histogram(binwidth = bw_clt, aes(y = ..density..), fill = "hotpink1", col = "white") +
stat_function(fun = ~dnorm(.x, mean = 10, sd = 2), col = "darkorchid1", lwd = 2) +
theme_classic()
As far as I can tell, the rest of the code is working properly - it just doesn't plot the dnorm stat function correctly. The exact same stat line worked for me before, so I'm not sure what's gone wrong.
The line isn't quite flat; it's just very stretched out compared to the histogram. We can see this more clearly if we zoom out on the x axis and zoom in on the y axis:
ggplot(median_clt_test_df, aes(x = median_clt_test)) +
geom_histogram(binwidth = bw_clt, aes(y = ..density..),
fill = "hotpink1", col = "white") +
stat_function(fun = ~dnorm(.x, mean = 10, sd = 2),
col = "darkorchid1",
lwd = 2) +
xlim(c(5, 15)) +
coord_cartesian(xlim = c(5, 15), ylim = c(0, 1)) +
theme_classic()
But why is this?
It's because you are using dnorm to plot the distribution of the random variable from which the medians were drawn, but your histogram is a sample of the medians themselves. So you are plotting the wrong dnorm curve. The sd should not be the standard deviation of the random variable, but the standard deviation of the sample medians:
ggplot(median_clt_test_df, aes(x = median_clt_test)) +
geom_histogram(binwidth = bw_clt, aes(y = ..density..),
fill = "hotpink1", col = "white") +
stat_function(fun = ~dnorm(.x,
mean = mean(median_clt_test),
sd = sd(median_clt_test)),
col = "darkorchid1",
lwd = 2)
theme_classic()
If you prefer you could use the theoretical standard error of the mean instead of the measured standard deviation of your medians - these will be very similar.
# Theoretical SEM
2/sqrt(500)
#> [1] 0.08944272
# SD of medians
sd(median_clt_test)
#> [1] 0.08850221
Related
I have the following code:
plot <- ggplot(data = df_sm)+
geom_histogram(aes(x=simul_means, y=..density..), binwidth = 0.20, fill="slategray3", col="black", show.legend = TRUE)
plot <- plot + labs(title="Density of 40 Means from Exponential Distribution", x="Mean of 40 Exponential Distributions", y="Density")
plot <- plot + geom_vline(xintercept=sampl_mean,size=1.0, color="black", show.legend = TRUE)
plot <- plot + stat_function(fun=dnorm,args=list(mean=sampl_mean, sd=sampl_sd),color = "dodgerblue4", size = 1.0)
plot <- plot+ geom_vline(xintercept=th_mean,size=1.0,color="indianred4",linetype = "longdash")
plot <- plot + stat_function(fun=dnorm,args=list(mean=th_mean, sd=th_mean_sd),color = "darkmagenta", size = 1.0)
plot
I want to show the legends of each layer, I tried show.legend = TRUE but it does nothing.
All my data frame is means from exponential distribution simulations, also I have some theoretical values from the distribution (mean and standard deviation) which I describe as th_mean and th_mean_sd.
The code for my simulation is the following:
lambda <- 0.2
th_mean <- 1/lambda
th_sd <- 1/lambda
th_var <- th_sd^2
n <- 40
th_mean_sd <- th_sd/sqrt(n)
th_mean_var <- th_var/sqrt(n)
simul <- 1000
simul_means <- NULL
for(i in 1:simul) {
simul_means <- c(simul_means, mean(rexp(n, lambda)))
}
sampl_mean <- mean(simul_means)
sampl_sd <- sd(simul_means)
df_sm<-data.frame(simul_means)
If you want to get a legend you have to map on aesthetics instead of setting the color, fill, ... as parameter, i.e. move color=... inside aes(...) and make use of scale_color/fill_manual to set the color values. Personally I find it helpful to make use of some meaningful labels, e.g. in case of your histogram I map the label "hist" on the fill but you could whatever label you like:
set.seed(123)
lambda <- 0.2
th_mean <- 1 / lambda
th_sd <- 1 / lambda
th_var <- th_sd^2
n <- 40
th_mean_sd <- th_sd / sqrt(n)
th_mean_var <- th_var / sqrt(n)
simul <- 1000
simul_means <- NULL
for (i in 1:simul) {
simul_means <- c(simul_means, mean(rexp(n, lambda)))
}
sampl_mean <- mean(simul_means)
sampl_sd <- sd(simul_means)
df_sm <- data.frame(simul_means)
library(ggplot2)
ggplot(data = df_sm) +
geom_histogram(aes(x = simul_means, y = ..density.., fill = "hist"), binwidth = 0.20, col = "black") +
labs(title = "Density of 40 Means from Exponential Distribution", x = "Mean of 40 Exponential Distributions", y = "Density") +
stat_function(fun = dnorm, args = list(mean = sampl_mean, sd = sampl_sd), aes(color = "sampl_mean"), size = 1.0) +
stat_function(fun = dnorm, args = list(mean = th_mean, sd = th_mean_sd), aes(color = "th_dens"), size = 1.0) +
geom_vline(size = 1.0, aes(xintercept = sampl_mean, color = "sampl_mean")) +
geom_vline(size = 1.0, aes(xintercept = th_mean, color = "th_mean"), linetype = "longdash") +
scale_fill_manual(values = c(hist = "slategray3")) +
scale_color_manual(values = c(sampl_dens = "dodgerblue4", th_dens = "darkmagenta", th_mean = "indianred4", sampl_mean = "black"))
While completing a project for understanding central limit theorem for exponential distribution, I ran into an annoying error message when plotting simulated vs theoretical distributions. When I run the code below, I get an error: 'mapping' is not used by stat_function().
By mapping I assume the error is referring to the aes parameter, which I later map to color red using scale_color_manual in order to show it in a legend.
My question is two-fold: why is this error happening? and is there a more efficient way to create a legend without using scale_color_manual?
Thank you!
lambda <- 0.2
n_sims <- 1000
set.seed(100100)
total_exp <- rexp(40 * n_sims, rate = lambda)
exp_data <- data.frame(
Mean = apply(matrix(total_exp, n_sims), 1, mean),
Vars = apply(matrix(total_exp, n_sims), 1, var)
)
g <- ggplot(data = exp_data, aes(x = Mean))
g +
geom_histogram(binwidth = .3, color = 'black', aes(y=..density..), fill = 'steelblue') +
geom_density(size=.5, aes(color = 'Simulation'))+
stat_function(fun = dnorm, mapping = aes(color='Theoretical'), args = list(mean = 1/lambda, sd = 1/lambda/sqrt(40)), size=.5, inherit.aes = F, show.legend = T)+
geom_text(x = 5.6, y = 0.1, label = "Theoretical and Sample Mean", size = 2, color = 'red') +
scale_color_manual("Legend", values = c('Theoretical' = 'red', 'Simulation' = 'blue')) +
geom_vline(aes(xintercept = 1/lambda), lwd = 1.5, color = 'grey') +
labs(x = 'Exponential Distribution Simulations Average Values') +
ggtitle('Sample Mean vs Theoretical Mean of the Averages of the Exponential Distribution')+
theme_classic(base_size = 10)
It's not an error, it's a warning:
library(ggplot2)
lambda <- 0.2
n_sims <- 1000
set.seed(100100)
total_exp <- rexp(40 * n_sims, rate = lambda)
exp_data <- data.frame(
Mean = apply(matrix(total_exp, n_sims), 1, mean),
Vars = apply(matrix(total_exp, n_sims), 1, var)
)
g <- ggplot(data = exp_data, aes(x = Mean))
g +
geom_histogram(binwidth = .3, color = 'black', aes(y=..density..), fill = 'steelblue') +
geom_density(size=.5, aes(color = 'Simulation'))+
stat_function(fun = dnorm, mapping = aes(color='Theoretical'), args = list(mean = 1/lambda, sd = 1/lambda/sqrt(40)), size=.5, inherit.aes = F, show.legend = T)+
geom_text(x = 5.6, y = 0.1, label = "Theoretical and Sample Mean", size = 2, color = 'red') +
scale_color_manual("Legend", values = c('Theoretical' = 'red', 'Simulation' = 'blue')) +
geom_vline(aes(xintercept = 1/lambda), lwd = 1.5, color = 'grey') +
labs(x = 'Exponential Distribution Simulations Average Values') +
ggtitle('Sample Mean vs Theoretical Mean of the Averages of the Exponential Distribution')+
theme_classic(base_size = 10)
#> Warning: `mapping` is not used by stat_function()
Created on 2020-05-01 by the reprex package (v0.3.0)
You can suppress the warning by calling geom_line(stat = "function") rather than stat_function():
library(ggplot2)
lambda <- 0.2
n_sims <- 1000
set.seed(100100)
total_exp <- rexp(40 * n_sims, rate = lambda)
exp_data <- data.frame(
Mean = apply(matrix(total_exp, n_sims), 1, mean),
Vars = apply(matrix(total_exp, n_sims), 1, var)
)
g <- ggplot(data = exp_data, aes(x = Mean))
g +
geom_histogram(binwidth = .3, color = 'black', aes(y=..density..), fill = 'steelblue') +
geom_density(size=.5, aes(color = 'Simulation'))+
geom_line(stat = "function", fun = dnorm, mapping = aes(color='Theoretical'), args = list(mean = 1/lambda, sd = 1/lambda/sqrt(40)), size=.5, inherit.aes = F, show.legend = T)+
geom_text(x = 5.6, y = 0.1, label = "Theoretical and Sample Mean", size = 2, color = 'red') +
scale_color_manual("Legend", values = c('Theoretical' = 'red', 'Simulation' = 'blue')) +
geom_vline(aes(xintercept = 1/lambda), lwd = 1.5, color = 'grey') +
labs(x = 'Exponential Distribution Simulations Average Values') +
ggtitle('Sample Mean vs Theoretical Mean of the Averages of the Exponential Distribution')+
theme_classic(base_size = 10)
Created on 2020-05-01 by the reprex package (v0.3.0)
In my opinion, the warning is erroneous, and an issue has been filed about this problem: https://github.com/tidyverse/ggplot2/issues/3611
However, it's not that easy to solve, and therefore as of now the warning is there.
I'm unable to recreate your issue -- when I run your code a plot is generated (below), which suggests the issue is likely to do you with your environment. A general 'solution' is to clear your workspace using the menu dropdown or similar: Session -> Clear workspace..., then re-run your code.
For refactoring the color issue, you can simplify scale_color_manual to
scale_color_manual("Legend", values = c('blue','red')), but how it is now, is a bit better in my view. Anything beyond that has more to do with changing the data structure and mapping.
Apologies, I don't have the rep to make a comment.
I have created a graph that overlays a normally distributed density plot on top of a previous density plot using the dnorm() function. However, I am having a difficult time adding a legend. Below is the code to create the plot with one of my attempts at adding a legend.
library(tidyverse)
my.data = rnorm(1000, 3, 10)
ggplot(enframe(my.data), aes(value)) +
geom_density(fill = "mediumseagreen", alpha = 0.1) +
geom_area(stat = "function", fun = function(x) dnorm(x, mean = 0, sd = 5), fill = "red", alpha = .5)+
theme(legend.position="right")+
scale_color_manual("Line.Color", values=c(red="red",green="green"),
labels=paste0("Plot",1:2))
To summarize I am trying to add a legend to this plot that has labels "Plot1" and "Plot2"
There might be better answers. This is what I have achieved with several attemps:
library(tidyverse)
my.data = rnorm(1000, 3, 10)
ggplot(enframe(my.data), aes(value)) +
geom_density(aes(color = "Plot1", fill = "Plot1"), alpha = 0.1) +
geom_area(aes(color = "Plot2", fill = "Plot2"), stat = "function",
fun = function(x) dnorm(x, mean = 0, sd = 5), alpha = .5)+
theme(legend.position="right") +
scale_color_manual(" ", values=c(Plot1="green", Plot2="red")) +
scale_fill_manual(" ", values=c(Plot1 ="green", Plot2="red"))
I plot a density curve using ggplot2. After I plot the data, I would like to add a normal density plot right on top of it with a fill.
Currently, I am using rnorm() to create the data but this is not efficient and would work poorly on small data sets.
library(tidyverse)
#my data that I want to plot
my.data = rnorm(1000, 3, 10)
#create the normal density plot to overlay the data
overlay.normal = rnorm(1000, 0, 5)
all = tibble(my.data = my.data, overlay.normal = overlay.normal)
all = melt(all)
ggplot(all, aes(value, fill = variable))+geom_density()
The goal would be to plot my data and overlay a normal distribution on top of it (with a fill). Something like:
ggplot(my.data)+geom_density()+add_normal_distribution(mean = 0, sd = 5, fill = "red)
Here's an approach using stat_function to define a normal curve and draw it within the ggplot call.
ggplot(my.data %>% enframe(), aes(value)) +
geom_density(fill = "mediumseagreen", alpha = 0.1) +
stat_function(fun = function(x) dnorm(x, mean = 0, sd = 5),
color = "red", linetype = "dotted", size = 1)
I figured out the solution from mixing Jon's answer and an answer from Hadley.
my.data = rnorm(1000, 3, 10)
ggplot(my.data %>% enframe(), aes(value)) +
geom_density(fill = "mediumseagreen", alpha = 0.1) +
geom_area(stat = "function", fun = function(x) dnorm(x, mean = 0, sd = 5), fill = "red", alpha = .5)
I'm trying to show data of two groups. I am using the ggplot2 package to graph the data and using stat_summary() to obtain a point estimate (mean) and 90% CI within the plot of the data. What I'd like is for the mean and confidence interval be structured off to the right of the points representing the distribution of the data. Currently, stat_summary() will simply impose the mean and CI over top of the distribution.
Here is an example of data that I am working with:
set.seed(9909)
Subjects <- 1:100
values <- c(rnorm(n = 50, mean = 30, sd = 5), rnorm(n = 50, mean = 35, sd = 8))
data <- cbind(Subjects, values)
group1 <- rep("group1", 50)
group2 <- rep("group2", 50)
group <- c(group1, group2)
data <- data.frame(data, group)
data
And this is what my current ggplot2 code looks like (distribution as points with the mean and 90% CI overlaid on top for each group):
ggplot(data, aes(x = group, y = values, group = 1)) +
geom_point() +
stat_summary(fun.y = "mean", color = "red", size = 5, geom = "point") +
stat_summary(fun.data = "mean_cl_normal", color = "red", size = 2, geom = "errorbar", width = 0, fun.args = list(conf.int = 0.9)) + theme_bw()
Is it possible to get the mean and confidence intervals to position_dodge to the right of their respective groups?
You can use position_nudge:
ggplot(data, aes(x = group, y = values, group = 1)) +
geom_point() +
stat_summary(fun.y = "mean", color = "red", size = 5, geom = "point",
position=position_nudge(x = 0.1, y = 0)) +
stat_summary(fun.data = "mean_cl_normal", color = "red", size = 2,
geom = "errorbar", width = 0, fun.args = list(conf.int = 0.9),
position=position_nudge(x = 0.1, y = 0)) +
theme_bw()