I need to plot a set of smoothed trajectories for individuals in a longitudinal (person-period) dataset. I can plot the individual trajectories across days using OLS regression but I would like to know how to plot the trajectories using a non-parametric smoother.
Sample data below. Same outcome variable measured five times for each individual at ages eleven, twelve, thirteen, fourteen and fifteen. Exposure is a predictor variable but we are not interested in it for this exercise.
id <- c(9, 45, 268, 314, 442, 514, 569, 624, 723, 918, 949, 978, 1105, 1542, 1552, 1653)
eleven <- c(2.23, 1.12, 1.45, 1.22, 1.45, 1.34, 1.79, 1.12, 1.22, 1.00, 1.99, 1.22, 1.34, 1.22, 1.00, 1.11)
twelve <- c(2.23, 1.12, 1.45, 1.22, 1.45, 1.34, 1.79, 1.12, 1.22, 1.00, 1.99, 1.22, 1.34, 1.22, 1.00, 1.11)
thirteen <- c(1.90, 1.45, 1.99, 1.55, 1.45, 2.23, 1.90, 1.22, 1.12, 1.22, 1.12, 2.12, 1.99, 1.99, 2.23, 1.34)
fourteen <- c(2.12, 1.45, 1.79, 1.12, 1.67, 2.12, 1.99, 1.12, 1.00, 1.99, 1.45, 3.46, 1.90, 1.79, 1.55, 1.55)
fifteen <- c(2.66, 1.99, 1.34, 1.12, 1.90, 2.44, 1.99, 1.22, 1.12, 1.22, 1.55, 3.32, 2.12, 2.12, 1.55, 2.12)
exposure <- c(1.54, 1.16, 0.90, 0.81, 1.13, 0.90, 1.99, 0.98, 0.81, 1.21, 0.93, 1.59, 1.38, 1.44, 1.04, 1.25)
df <- data.frame(id, eleven, twelve, thirteen, fourteen, fifteen, exposure)
Now we convert the person-level dataset to a person-period (i.e. long) dataframe and add a time variable
library(reshape2)
library(plyr)
dfPP <- melt(df, measure.vars = c("eleven", "twelve", "thirteen", "fourteen", "fifteen"), var = "age", value.name = "score")
dfPP <- dfPP[order(dfPP$id), ]
dfPP$time <- rep(0:4, 16)
We can plot the raw data using an interaction plot
interaction.plot(dfPP$age, dfPP$id, dfPP$score)
but what we really want are lines of best fit for each individual
fit <- by(dfPP, dfPP$id, function (bydata) fitted.values(lm(score ~ time, data = bydata)))
fit <- unlist(fit)
interaction.plot(dfPP$age, dfPP$id, fit, xlab = "age", ylab = "score")
It would also be good to plot the average change trajectory across subjects
ints <- by(dfPP, df$id, function (data) coefficients(lm(score ~ time, data = data))[[1]])
ints1 <- unlist(ints)
slopes <- by(dfPP, dfPP$id, function (data) coefficients(lm(score ~ time, data = data))[[2]])
slopes1 <- unlist(slopes)
so to plot the mean trajectory we use an abline, superimposed over the existing graph
abline(a = mean(ints1), b = mean(slopes1), lwd = 2, col = "red")
Now this is all fine but does anyone know how to achieve a similar result except using a non-parametric smoother? Also with an average trajectory line superimposed. Using some kind of loess function perhaps?
Related
I am trying to run a simulation in R, but I am having trouble writing the proper for loop.
The iteration I am trying to perform is
i=1
distance<-NULL
for(i in 1:48)
{
sample<-coordinates[sample(.N, i)]
meand = (dist(cbind(sample$x,sample$y)))
ppp<-sample
table<-as.matrix(dist(ppp))
table[table == 0] <- 1000
maxmin<-apply(table, 1, FUN=min)
distance.1<-mean(maxmin)
distance<-rbind(distance,distance.1)
}
The result give a 48 row dataframe of results ,where i = 1:48
What I would like to do is run about 1000 iteration for each i in the for loop. Then I would like to store the average of the 1000 results, and store them for each i.
I am thinking that replicate() function might be the solution, but I am having trouble using them.
So the expected output is somewhat
i=1 a (average of 1000 iteration)
i=2 b (average of 1000 iteration)
i=3 c (average of 1000 iteration)
.
.
.
i=48 d (average of 1000 iteration)
How should I rewrite my code to perform a fast iteration? I would sincerely appreciate some help.
EDIT
dput(coordinates)
structure(list(x = c(0.24, 0.72, 1.2, 3.675, 4.155, 4.635, 5.115,
5.595, 6.075, 8.55, 9.03, 9.51, 9.99, 10.47, 10.95, 13.425, 13.905,
14.385, 14.865, 15.345, 15.825, 18.3, 18.78, 19.26, 19.26, 18.78,
18.3, 15.825, 15.345, 14.865, 14.385, 13.905, 13.425, 10.95,
10.47, 9.99, 9.51, 9.03, 8.55, 6.075, 5.595, 5.115, 4.635, 4.155,
3.675, 1.2, 0.72, 0.24), y = c(0.24, 0.24, 0.24, 0.24, 0.24,
0.24, 0.24, 0.24, 0.24, 0.24, 0.24, 0.24, 0.24, 0.24, 0.24, 0.24,
0.24, 0.24, 0.24, 0.24, 0.24, 0.24, 0.24, 0.24, 2.88, 2.88, 2.88,
2.88, 2.88, 2.88, 2.88, 2.88, 2.88, 2.88, 2.88, 2.88, 2.88, 2.88,
2.88, 2.88, 2.88, 2.88, 2.88, 2.88, 2.88, 2.88, 2.88, 2.88)), row.names = c(NA,
-48L), class = c("data.table", "data.frame"), .internal.selfref = <pointer: 0x0000027c2a7f1ef0>)
If I understood correctly your question, apply functions might work just fine to solve your problem. Below, I'm just a nesting a sapply to do the 1000 additional replicates within each i.
sapply(1:48, function(i){
mean(sapply(1:1000, function(x){
sample<-coordinates[sample(.N, i)]
meand = (dist(cbind(sample$x,sample$y)))
ppp<-sample
table<-as.matrix(dist(ppp))
table[table == 0] <- 1000
maxmin<-apply(table, 1, FUN=min)
mean(maxmin)
}))
})
I'd be easier with a sample of your data. Good luck!
I'm trying to use prophet library to predict y using Group and Regressors. My code and the errors received are below.
In Model1:
I've received this error: Error in setup_dataframe(object, df) :
Regressor "x1" missing from dataframe
In Model2:
Model2 runs. But I'm unable to figure it out how to add regressors x1
and x2.
library(prophet)
library(dplyr)
df <- data.frame(ds = rep(c("2020-01-01", "2020-01-02", "2020-01-03", "2020-01-04", "2020-01-05",
"2020-01-06", "2020-01-07", "2020-01-08", "2020-01-09", "2020-01-10", "2020-01-11", "2020-01-12",
"2020-01-13", "2020-01-14", "2020-01-15"), 2),
group = rep(c("A", "B"), each = 15),
y = c(8.15, 1.74, 2.97, 2.36, 0.94, 1.84, 3.17, 12.51, 0.63, 6.92, 5.51,
7.50, -2.47, 4.38, 6.28, 7.69, 2.89, 3.77, 7.27, -1.19, 4.64, 9.49, 5.43, 0.36, 14.12,
8.77, -3.05, -0.72, 10.99, 10.33),
x1 = c(3.11, 2.16, 0.91, 2.78, 0.06, 1.12, 1.73, 3.95, 1.43, 3.40, 2.37, 1.80, 0.95,
1.66, 3.06, -0.23, 3.11, 3.07, -0.39, 0.13, 4.38, 2.15, 1.61, 1.54, 5.50, 2.21,
0.89, 3.24, 4.27, 2.55),
x2 = c(2.52, -0.21, 1.03, -0.21, 0.44, 0.36 , 0.72, 4.28, -0.40, 1.76, 1.57,
2.85, -1.71, 1.36, 1.61, 3.96, -0.11 , 0.35, 3.83, -0.66, 0.13, 3.67, 1.91, -0.59, 4.31,
3.28, -1.97, -1.98, 3.36, 3.89))
df$ds <- as.Date(df$ds)
# Model 1
Model1 <- function(df) {
m <- prophet(seasonality.mode = 'multiplicative')
m <- add_regressor(m, 'x1')
m <- add_regressor(m, 'x2')
m <- fit.prophet(m, df)
future <- make_future_dataframe(m, periods = 5, freq = 'day')
mod1 <- predict(m, future)
return(mod1)
}
mod1 <-df %>%
group_by(group) %>%
do(Model1(.)) %>%
dplyr::select(ds, group, yhat)
# Model 2
library(prophet)
library(dplyr)
library(purrr)
library(tidyr)
Model2 <- df %>%
nest(-group) %>%
mutate(m = map(data, prophet)) %>%
mutate(future = map(m, make_future_dataframe, period = 5)) %>%
mutate(forecast = map2(m, future, predict))
I would like to plot a threshold model with smooth 95% confidence interval lines between line segments. You would think this would be on the simple side but I have not been able to find an answer!
My threshold/breakpoints are known, it would be great if there were a way to visualize this data. I have tried the segmented package which produces the following plot:
The plot shows a threshold model with a breakpoint at 5.4. However, the confidence intervals are not smooth between regression lines.
If anyone knows of any way to produce smooth (i.e. without the jump between line segments) CI lines between segmented regression lines (ideally in ggplot) that would be amazing. Thank you so much.
I have included sample data and the code I have tried below:
x <- c(2.26, 1.95, 1.59, 1.81, 2.01, 1.63, 1.62, 1.19, 1.41, 1.35, 1.32, 1.52, 1.10, 1.12, 1.11, 1.14, 1.23, 1.05, 0.95, 1.30, 0.79,
0.81, 1.15, 1.10, 1.29, 0.97, 1.05, 1.05, 0.84, 0.64, 0.80, 0.81, 0.61, 0.71, 0.75, 0.30, 0.30, 0.49, 1.13, 0.55, 0.77, 0.51,
0.67, 0.43, 1.11, 0.29, 0.36, 0.57, 0.02, 0.22, 3.18, 3.79, 2.49, 2.44, 2.12, 2.45, 3.22, 3.44, 3.86, 3.53, 3.13)
y <- c(22.37, 18.93, 16.99, 15.65, 14.62, 13.79, 13.09, 12.49, 11.95, 11.48, 11.05, 10.66, 10.30, 9.96, 9.65, 9.35, 9.07, 8.81,
8.56, 8.32, 8.09, 7.87, 7.65, 7.45, 7.25, 7.05, 6.86, 6.68, 6.50, 6.32, 6.15, 5.97, 5.80, 5.63, 5.47, 5.30,
5.13, 4.96, 4.80, 4.63, 4.45, 4.28, 4.09, 3.90, 3.71, 3.50, 3.27, 3.01, 2.70, 2.28, 22.37, 16.99, 11.05, 8.81,
8.56, 8.32, 7.25, 7.05, 6.50, 6.15, 5.63)
lin.mod <- lm(y ~ x)
segmented.mod <- segmented(lin.mod, seg.Z = ~x, psi=2)
plot(x, y)
plot(segmented.mod, add=TRUE, conf.level = 0.95)
which produces the following plot (and associated jumps in 95% confidence intervals):
segmented plot
Background: The non-smoothness in existing change point packages are due to the fact that frequentist packages operate with a fixed change point value. But as with all inferred parameters, this is wrong because there is indeed uncertainty concerning the location of the change.
Solution: AFAIK, only Bayesian methods can quantify that and the mcp package fills this space.
library(mcp)
model = list(
y ~ 1 + x, # Segment 1: Intercept and slope
~ 0 + x # Segment 2: Joined slope (no intercept change)
)
fit = mcp(model, data = data.frame(x, y))
Default plot (plot.mcpfit() returns a ggplot object):
plot(fit) + ggtitle("Default plot")
Each line represents a possible model that generated the data. The posterior for the change point is shown as a blue density. You can add a credible interval on top using plot(fit, q_fit = TRUE) or plot it alone:
plot(fit, lines = 0, q_fit = c(0.025, 0.975), cp_dens = FALSE) + ggtitle("Credible interval only")
If your change point is indeed known and if you want to model different residual scales for each segment (i.e., quasi-emulate segmented), you can do:
model2 = list(
y ~ 1 + x,
~ 0 + x + sigma(1) # Add intercept change in residual scale
)
fit = mcp(model2, df, prior = list(cp_1 = 1.9)) # Note: prior is a fixed value - not a distribution.
plot(fit, q_fit = TRUE, cp_dens = FALSE)
Notice that the CI does not "jump" around the change point as in segmented. I believe that this is the correct behavior. Disclosure: I am the author of mcp.
I have following file :
file 1
structure(list(Total_Gene_Symbol = c("5S_rRNA", "7SK", "A1BG-AS1"
), Test = c("1.02, 1.12, 1.11, 1.18, 1.12, 1.19, 1.25, 1.24, 1.24, 1.02",
"1.97, 2.27, 2.14, 1.15", "1.3, 1.01, 1.36, 1.42, 1.38, 1.01, 1.31, 1.34,
1.29, 1.34, 2.02, 1.12, 1.01, 1.31, 1.22"
)), .Names = c("Total_Gene_Symbol", "Test"), row.names = c(NA,
3L), class = "data.frame")
file 1 column test is number separated by ",".
I tried
mat <- stri_split_fixed(Down_FC, ',', simplify=T)
mat <- `dim<-`(as.numeric(mat), dim(mat)) # convert to numeric and save dims
rowMeans(mat, na.rm=T)->M
View(M)
but the above code is averaging entire data.
I want output same like below file 2
file 2
structure(list(Total_Gene_Symbol = c("5S_rRNA", "7SK", "A1BG-AS1"
), Test = c("1.02, 1.12, 1.11, 1.18, 1.12, 1.19, 1.25, 1.24, 1.24, 1.02",
"1.97, 2.27, 2.14, 1.15", "1.3, 1.01, 1.36, 1.42, 1.38, 1.01, 1.31, 1.34,
1.29, 1.34, 2.02, 1.12, 1.01, 1.31, 1.22"
), Average = c(11.49, 7.53, 19.44)), .Names = c("Total_Gene_Symbol",
"Test", "Average"), row.names = c(NA, 3L), class = "data.frame")
What you want is the sum not average! The average is something like the mode, median, mean.
library(magrittr)
df1$total_sum<-
df1$Test %>% str_split(.,",\\s+") %>% sapply(function(x) as.numeric(x) %>% sum(na.rm=T))
Using apply
d1$sum <- apply(d1,1,
function(x)(sum(as.numeric(unlist(strsplit(x['Test'],','))),na.rm = TRUE)))
You can use scan :
df$sum <- sapply(df$Test, function(x) sum(scan(text = x, what=numeric(),sep=","), na.rm=TRUE))
df$average <- sapply(df$Test, function(x) mean(scan(text = x, what=numeric(),sep=","), na.rm=TRUE))
# Total_Gene_Symbol Test sum average
# 1 5S_rRNA 1.02, 1.12, 1.11, 1.18, 1.12, 1.19, 1.25, 1.24, 1.24, 1.02 11.49 1.1490
# 2 7SK 1.97, 2.27, 2.14, 1.15 7.53 1.8825
# 3 A1BG-AS1 1.3, 1.01, 1.36, 1.42, 1.38, 1.01, 1.31, 1.34, \n 1.29, 1.34, 2.02, 1.12, 1.01, 1.31, 1.22 19.44 1.2960
I am using auto.arima() from forecast package and am coming into some strange results with the prediction.
library(forecast)
x <- structure(c(1.92, 2.1, 1.73, 1.35, 1.29, 1.35, 1.42, 1.46, 1.6,
1.67, 1.98, 1.78, 1.77, 2.35, 1.93, 1.43, 1.29, 1.26, 1.93, 2.33,
2.22, 2.19, 2.15, 2.25, 3.12, 3.32, 2.72, 2.28, 2.28, 2.16, 2.81,
3.12, 2.85, 2.98, 3.3, 3.06, 3.56, 3.81, 3.48, 2.64, 2.91, 3.35,
3.73, 3.58, 4, 3.94, 3.79, 3.85), .Tsp = c(2012, 2015.91666666667,
12), class = "ts")
fit <- auto.arima(x)
plot(forecast(fit, 12)) #forecast and actual data
f2 <- fitted.values(fit)
lines(f2, col="red") #add predicted values during training
I don't understand how fitted value (red line) is very close to observed value (black) but then there is a such a big jump in the first forecast.
Any ideas why we see this jump? I've seen other posts on Stack Exchange where the xreg option was used but this is not doing that so I haven't been able to track down a similar post.
Generally I tend to believe that auto.arima slightly overfits data. Some quick exploratory analysis with ACF shows that (0,1,2)(0,1,0)[12] is already a decent model. I will use arima0 from R base to fit this model:
fit0 <- arima0(x, order = c(0,1,2), seasonal = c(0,1,0))
Prediction / forecasting is done with predict.arima0:
pred <- predict(fit0, n.ahead = 12, se.fit = FALSE)
Let's plot observed series and forecast together:
ts.plot(x, pred, col = 1:2)
There is still a jump. But the variation is fairly reasonable, compared with the variability of the series.
Nothing wrong. When we forecast x[49] from x[1:48], it will be different from x[48]. Typically, (0,1,2)(0,1,0)[12] has a linear trend plus a seasonal effect. It helps to visualize your time series and prediction season by season:
ts.plot(window(x, 2012, 2012 + 11/12),
window(x, 2013, 2013 + 11/12),
window(x, 2014, 2014 + 11/12),
window(x, 2015, 2015 + 11/12),
pred, col = 1:5)