Lag in multiindex time series panel data on R - r

Question

I have a dataset with hundreds of rows structured like this
User Date Value1 Value2
A 2012-01-01 4 3
A 2012-01-02 5 7
A 2012-01-03 6 1
A 2012-01-04 7 4
B 2012-01-01 2 4
B 2012-01-02 3 2
B 2012-01-03 4 9
B 2012-01-04 5 3
As the panel data has two indices (User=k, Date=t), I struggle to run a regression on R where the dependent variable (Value 1) is lagged only on the time index. the regression should be performed as follows:
Value1(k,t+1) ~ Value2(k,t)
or
Value1(k,t) ~ Value2(k,t-1)
Any suggestions?

Answer 1

For every user, you can do:
> df <- data.frame(User = c(rep("A", 4), rep("B", 4)),
+ Date = rep(seq.Date(as.Date("2012-01-01"), as.Date("2012-01-04"), by = "day"), 2),
+ Value1 = c(4, 5, 6, 7, 2, 3, 4, 5),
+ Value2 = c(3, 7, 1, 4, 4, 2, 9, 3))
>
> df_A <- df[df$User == "A", c("Value1", "Value2")]
> ts_A <- ts(df_A, start = c(2012, 1, 1), frequency = 365)
> ts_A <- ts.intersect(ts_A, lag(ts_A, -1))
> colnames(ts_A) <- c("Value1", "Value2", "Value1_t_1", "Value2_t_1")
>
> lm(Value1 ~ Value2_t_1, ts_A)
Call:
lm(formula = Value1 ~ Value2_t_1, data = ts_A)
Coefficients:
(Intercept) Value2_t_1
6.3929 -0.1071
>
Hope it helps.

Answer 2

Here's a solution using the dplyr package, you may notice in the code below I explicitly reference the lag function from dplyr as opposed to base R (stats). This is because the lag function from dplyr does not require a time series input.
I would also note that the two formulas you list may produce different regression results as you will be running them over different sets of data i.e.
Value1(k,t+1) ~ Value2(k,t) : run on the time period of 1-01-2012 to 1-03-2012
Value1(k,t) ~ Value2(k,t-1) : run on the time period of 1-02-2012 to 1-04-2012
library("tidyverse")
df <- data.frame(User = c(rep("A", 4), rep("B", 4)),
Date = rep(seq.Date(as.Date("2012-01-01"), as.Date("2012-01-04"), by = "day"), 2),
Value1 = c(4, 5, 6, 7, 2, 3, 4, 5),
Value2 = c(3, 7, 1, 4, 4, 2, 9, 3))
df2 <- df %>% arrange(User,Date) %>%
group_by(User) %>%
mutate(lag_v2 = dplyr::lag(Value2),
lead_v1 = dplyr::lead(Value1))
df3<-df2[!is.na(df2$lag_v2),]
df4<-df2[!is.na(df2$lead_v1),]
summary(lm(Value1~lag_v2,data=df3))
summary(lm(lead_v1~Value2,data=df4))