How to correlate between time series of unequal frequencies

Question

I measured the room temperature every minute for 36 minutes and the skin temperature 32 times per second over the same period of time. I have 35 repetitions of an experiment with a tag (ID). I need to be able to look at the correlation, but the samples have unequal sizes.

Data:

I have data.frame df1with room temperature measured every minute, and another data.frame df2with skin temperature measured 32 times per second. I have data in 36 minutes. In addition, there is another column called ID that shows the experiment number (1-35), but I do not know how to present this in the following data examples. So technically I'm looking for a correlation for every SkinTemp vs RoomTemp based on ID.

    df1 <- data.frame(
        roomTemp = rnorm(1*36),
    )

   df2 <- data.frame(
        skinTemp = rnorm(32*60*36),
        )

I tried to do:

Data <- data.frame(
  Y=c(df1,df2),
  Variable =factor(rep(c("RoomTemp", "SkinTemp"), times=c(length(df1), length(df2))))
)

cor(Data$Y~Data$Variable)

.

Answer 1

roomTemp , skinTemp . . , .

UPDATE:

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library(data.table)
library(reshape2)
library(dplyr)
library(purrr)
library(ggplot2)
theme_set(theme_classic(base_size=16))

:

set.seed(395)
df1 <- data.frame(roomTemp = c(cumsum(rnorm(1*36)), cumsum(rnorm(1*36))),
                  ID = rep(c("A","B"), each=36))
df2 <- data.frame(skinTemp = c(cumsum(rnorm(32*60*36,0,0.01)),
                               cumsum(rnorm(32*60*36,0,0.01))),
                  ID = rep(c("A","B"), each=32*60*36))

, df1, df1 df2, .

# Add time column
df1$time = rep(0:(0.5*nrow(df1)-1)*60 + 0.0438,2)
df2$time = rep(0:(0.5*nrow(df2)-1)/32, 2)

. ID time, ID.

# Convert data frames to data tables
setDT(df1)
setDT(df2)

# Make time a key column in both data frames (for joining)
setkey(df1, ID, time)
setkey(df2, ID, time)

# Rolling join roomTemp to nearest time value of skinTemp
df2 = df1[df2, roll="nearest"]

# Rename rolling joined room temperature column
names(df2)[grep("roomTemp", names(df2))] = "roomTempRoll"

roomTemp ID, map_df purrr. map_df ID. approx . approxfun , . map_df , y, roomTemp, dplyr roomTempInterp df2.

# Add interpolated room temperature by ID
df2$roomTempInterp = unique(df2$ID) %>% 
  map_df(~ approx(df1$time[df1$ID==.x], df1$roomTemp[df1$ID==.x], 
                  xout=df2$time[df2$ID==.x]), .id="ID") %>% .$y

ID, ID.

# Plot so we can see what the rolling joined room temperature and 
#  interpolated room temperature look like
ggplot(melt(df2, id.var=c("ID", "time")), aes(time, value, colour=variable)) +
  geom_line(size=0.7) +
  geom_point(data=df1, aes(time, roomTemp), colour="black") +
  facet_grid(ID ~ .)

ID:

df2 %>% group_by(ID) %>%
  summarise(r_interp = cor(skinTemp, roomTempInterp, use="pairwise.complete.obs"),
            r_roll = cor(skinTemp, roomTempRoll, use="pairwise.complete.obs"))

      ID    r_interp      r_roll
1      A -0.04853998 -0.02993207
2      B -0.53993960 -0.53092150

-, , , .

library(data.table)
library(reshape2)
library(dplyr)
library(ggplot2)
theme_set(theme_classic(base_size=16))

# Fake data with autocorrelation
set.seed(395)
df1 <- data.frame(roomTemp = cumsum(rnorm(1*36)))
df2 <- data.frame(skinTemp = cumsum(rnorm(32*60*36,0,0.01)))

. datetime, , .

# Add time column
df1$time = 0:(nrow(df1)-1)*60
df2$time = 0:(nrow(df2)-1)/32

, , . approxfun . splinefun .

# Function to interpolate room temperature between measurements
roomTempInterp = approxfun(df1$time, df1$roomTemp)

, data.table .

# Convert data frames to data tables
setDT(df1)
setDT(df2)

# Make time a key column in both data frames (for joining)
setkey(df1, time)
setkey(df2, time)

.

# Rolling join roomTemp to nearest time value of skinTemp
df2 = df1[df2, roll="nearest"]

# Rename rolling joined room temperature column
names(df2)[grep("roomTemp", names(df2))] = "roomTempRoll"

roomTemp df1 df2.

df2 = df1[df2, ]  # Equivalent to dplyr: df2 = left_join(df2, df1)

, .

# Add interpolated room temperature
df2$roomTempInterp = roomTempInterp(df2$time)

, , roomTemp . 10 df2, df2 roomTempRoll roomTempInterp roomTemp df1. roomTemp skinTemp.

    roomTemp    time roomTempRoll     skinTemp roomTempInterp
 1: -1.21529 0.00000     -1.21529 -0.006511475      -1.215290
 2:       NA 0.03125     -1.21529 -0.014058076      -1.215531
 3:       NA 0.06250     -1.21529 -0.017741690      -1.215773
 4:       NA 0.09375     -1.21529 -0.030211177      -1.216014
 5:       NA 0.12500     -1.21529 -0.027105225      -1.216255
 6:       NA 0.15625     -1.21529 -0.035784295      -1.216497
 7:       NA 0.18750     -1.21529 -0.031319748      -1.216738
 8:       NA 0.21875     -1.21529 -0.033758959      -1.216979
 9:       NA 0.25000     -1.21529 -0.040667384      -1.217220
10:       NA 0.28125     -1.21529 -0.026291442      -1.217462

, , . roomTemp.

ggplot(melt(df2 %>% select(-roomTemp), id.var="time"), aes(time, value, colour=variable)) +
  geom_line(size=1) +
  geom_point(data=df2, aes(time, roomTemp), colour="black")

Answer 2

, .

, , , ( "" ) . ( ) . , 36 * 60 * 32 , 36 * 60 * 32 1. , [36 * 60 * 32, 36 * 60 * 32 * 2] "2" ..

library(lubridate)
library(dplyr)

# create the times of our observations
time.room.temp <- seq.POSIXt(from = as.POSIXct('02/20/2017', format = '%m/%d/%Y'), to = as.POSIXct('02/21/2017', format = '%m/%d/%Y'), by = 36*60)
time.skin.temp <- seq.POSIXt(from = as.POSIXct('02/20/2017', format = '%m/%d/%Y'), to = as.POSIXct('02/21/2017', format = '%m/%d/%Y'), by = 1/32)

n.obs.room.temp <- length(room.temp)
n.obs.skin.temp <- length(skin.temp)

# create some "actual" temperature data
obs.room.temp <- rnorm(n.obs.room.temp, mean = 60, sd = 10)
obs.skin.temp <- rnorm(n.obs.skin.temp, mean = 95, sd = 5)

room.temp.df <- data.frame('room temp' = obs.room.temp, 'time' = time.room.temp)
skin.temp.df <- data.frame('skin temp' = obs.skin.temp, 'time' = time.skin.temp)

# Every 32 indices, seconds is incremented by one.. So our modulus calculuation should be every
# time the index evenly divides 36*60*32... there are 69120 skin-temp observations for every room-temp observation
# So we can effectively "bin" the different seconds for which we observed skin temperatures in order to create a mean temperature by bin,
# i.e. a mean skin temperature for every time at which room temp was recorded
bins <- cut(1:n.obs.skin.temp, seq(0, n.obs.skin.temp, 36*60*32), labels = 1:40)
skin.temp.df$bins <- bins

# Now, we can effectively group skin temperature observations by room temperature observations, and get the average (or median, if you like)
# temperature for each bin
shorter.skin.temp.df <- skin.temp.df %>%
  group_by(bins) %>%
  summarise(average.skin.temp = mean(skin.temp))

# Now we can get the correlation between the two types of temperatures!
cor(room.temp.df$room.temp, shorter.skin.temp.df$average.skin.temp)

: "" :

> print(length(unique(skin.temp.df$bins)))
[1] 41
> print(length(unique(room.temp.df$time)))
[1] 41

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