Visualise the relation between two variables in panel data

问题

I am familiar with R, but not very much with plotting. I have panel data as follows:

library(plm)
library(dplyr)
data("EmplUK", package="plm")
EmplUK <- EmplUK %>%
group_by(firm, year) %>%
mutate(Vote = sample(c(0,1),1) ,
     Vote_won = ifelse(Vote==1, sample(c(0,1),1),0))

# EDIT: 

EmplUK <- pdata.frame(EmplUK , index=c("firm", "year"), drop.index = FALSE)

# A tibble: 1,031 x 9
# Groups:   firm, year [1,031]
    firm  year sector   emp  wage capital output  Vote Vote_won
   <dbl> <dbl>  <dbl> <dbl> <dbl>   <dbl>  <dbl> <dbl>    <dbl>
 1     1  1977      7  5.04  13.2   0.589   95.7     1        0
 2     1  1978      7  5.60  12.3   0.632   97.4     0        0
 3     1  1979      7  5.01  12.8   0.677   99.6     1        1
 4     1  1980      7  4.72  13.8   0.617  101.      1        1
 5     1  1981      7  4.09  14.3   0.508   99.6     0        0
 6     1  1982      7  3.17  14.9   0.423   98.6     0        0
 7     1  1983      7  2.94  13.8   0.392  100.      0        0
 8     2  1977      7 71.3   14.8  16.9     95.7     1        0
 9     2  1978      7 70.6   14.1  17.2     97.4     1        1
10     2  1979      7 70.9   15.0  17.5     99.6     1        1

toplot <- plm(output ~ wage, data=EmplUK, model="within")

Coefficients:
     Estimate Std. Error t-value   Pr(>|t|)    
wage   -0.707      0.143   -4.94 0.00000095 ***

I would like to evaluate what the best relation between two variables in panel data are (linear, quadratic, polynomial) by visualising the relation between output and wage (and perhaps fitting such linear, quadratic, polynomial). I am however super unfamiliar with plotting.

I am looking for something like this (source) (where I get the formula for the fitted line):

I tried starting out as follows:

plot(EmplUK$output,EmplUK$wage,type='l',col='red',main='Linear relationship')

But that gives me this:

In all honesty I have very little idea what I am doing here. Is there anyone who could get me in the right direction?

回答1:

I would probably do it with the de-meaned data.

demeaned_data <- EmplUK %>% 
  group_by(firm) %>% 
  mutate(across(c(output, wage), function(x)x-mean(x)))

ggplot(demeaned_data, aes(x=wage, y=output)) + 
  geom_point() + 
  geom_smooth(aes(colour="linear", fill="linear"), 
              method="lm", 
              formula=y ~ x, ) + 
  geom_smooth(aes(colour="quadratic", fill="quadratic"), 
              method="lm", 
              formula=y ~ x + I(x^2)) + 
  geom_smooth(aes(colour="cubic", fill="cubic"), 
              method="lm", 
              formula=y ~ x + I(x^2) + I(x^3)) + 
  scale_fill_brewer(palette="Set1") + 
  scale_colour_brewer(palette="Set1") + 
  theme_classic() + 
  labs(colour="Functional Form", fill="Functional Form")

An alternative would be to estimate the model with OLS and firm dummy variables and then you could get predictions for each firm and plot them separately.

library(ggeffects)
data("EmplUK", package="plm")
EmplUK <- EmplUK %>% mutate(firm = as.factor(firm))
m1 <- lm(output ~ wage + firm, data=EmplUK )
m2 <- lm(output ~ wage + I(wage^2) + firm, data=EmplUK )
m3 <- lm(output ~ wage + I(wage^2) + I(wage^3) + firm, data=EmplUK )

p1 <- ggpredict(m1, terms=c("wage", "firm")) %>% 
  mutate(form="linear") %>% 
  rename("wage" = "x", 
         "firm" = "group", 
         "output" = "predicted")
p2 <- ggpredict(m2, terms=c("wage", "firm")) %>% 
  mutate(form="quadratic") %>% 
  rename("wage" = "x", 
         "firm" = "group", 
         "output" = "predicted")
p3 <- ggpredict(m3, terms=c("wage", "firm")) %>% 
  mutate(form="cubic") %>% 
  rename("wage" = "x", 
         "firm" = "group", 
         "output" = "predicted")

ggplot() + 
  geom_line(data=p1, aes(x=wage, y=output, colour="linear")) + 
  geom_line(data=p2, aes(x=wage, y=output, colour="quadratic")) + 
  geom_line(data=p3, aes(x=wage, y=output, colour="cubic")) + 
  geom_point(data=EmplUK, aes(x=wage, y=output)) + 
  facet_wrap(~firm) + 
  theme_bw() + 
  labs(colour="Functional\nForm")

回答2:

Maybe something like this using ggplot2 :

library(ggplot2)

ggplot(EmplUK, aes(output, wage)) + 
  geom_line(color = 'red') + 
  geom_smooth(size = 2) + 
  ggtitle('Linear relationship') + 
  theme_bw()

回答3:

plm has a built-in plot method plm:::plot.plm which also shows the fixed effects. For the polynomial analysis you could use the yhat of a loess modell and colorize by firm. So both plots together can give you an idea of the data situation.

EmplUK <- transform(EmplUK, yhat=predict(loess(output ~ wage)))

op <- par(mfrow=c(1, 2), mar=c(4.5, 4, 3, 1))
plot(toplot)  ## from `plm:::plot.plm`
plot(output ~ wage, EmplUK, type="p", pch=20, cex=.5, col=firm, ylim=range(EmplUK$yhat))
invisible(sapply(unique(EmplUK$firm), function(x)
       lines(yhat ~ wage, EmplUK[EmplUK$firm == x, ], col=x, lwd=1)))
par(op)

Of course loess can't use factor variables; on Cross Validated they suggest a Semiparametric Nonlinear Mixed Effects model using the nlme package to apply LOESS on mixed models.

来源：https://stackoverflow.com/questions/65537179/visualise-the-relation-between-two-variables-in-panel-data

标签

ggplot2

plot

panel