Panel Quantile Regression with Fixed Effects: Choosing Between ID and as.factor(ID) in R

Panel Quantile Regression with Fixed Effects in R: A Deep Dive

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Introduction

Panel quantile regression is a powerful statistical technique used to analyze panel data, which consists of multiple observations from the same unit over time. In this article, we will delve into the world of panel quantile regression and explore how to specify fixed effects in R using rqpd. We will also examine the differences between using ID versus as.factor(ID) in the model formula.

Background

Panel data is a common type of data in economics, finance, and other social sciences. It involves collecting multiple observations from the same unit over time, which allows researchers to study how variables change across units and over time. Panel quantile regression is an extension of traditional linear regression that can handle non-linear relationships between variables.

What is Fixed Effects?

In the context of panel data analysis, fixed effects refer to the variation in the dependent variable that is not explained by the independent variables but is instead due to unobserved heterogeneity within units. Fixed effects models assume that the effect of a unit’s observed characteristics on the dependent variable is constant over time.

RQPD: A Wrapper for Quantreg

rqpd is a wrapper around quantreg::sfn that provides an interface to panel quantile regression in R. It offers several advantages, including flexibility and ease of use. However, rqpd also inherits some limitations from its parent package.

Specifying Fixed Effects in rqPD

When specifying fixed effects in rqpd, there are two main options: using ID versus as.factor(ID) in the model formula. We will examine both options and explore their implications for panel quantile regression.

Using ID vs as.factor(ID)

Using ID

If ID is numeric, then specifying ... | ID will fit a slope that captures the relationship between the independent variables and the dependent variable within each unit. This is often referred to as a “unit-level” model.

On the other hand, if ID is factor-based (e.g., categorical), then specifying ... | as.factor(ID) will fit an intercept per unique value of ID. This is often referred to as a “unit-specific” or “individual-specific” model.

Using as.factor(ID)

Using as.factor(ID) can lead to different results compared to using ID directly. The reason for this lies in how R interprets the specification of fixed effects.

When you specify ... | as.factor(ID), R is essentially saying that the effect of x on y varies by unique values of ID. This means that you are fitting a separate intercept per unit, rather than a single slope that captures the relationship within units.

In contrast, specifying ID directly implies that you want to fit a slope that captures the relationship between x and y within each unit.

The Role of Control in rqPD

One common issue when working with rqpd is the “tmpmax” error. This occurs when R runs out of memory due to excessive computation.

The control argument allows you to tweak the fitting routine via a wrapper for quantreg::sfn.control. By increasing the value of tmpmax, you can temporarily increase R’s temporary maximum (TMPMAX) size, which should alleviate the error.

Example Code

Let’s demonstrate how to specify fixed effects in rqpd using both options: ID and as.factor(ID).

library(quantreg)
library(ggplot2)

# Generate some sample data
set.seed(123)
n <- 100
p <- 5
k <- 3

x <- matrix(rnorm(n * k), n, k)
y <- rnorm(n)
z <- factor(sample(c("A", "B"), size = n, replace = TRUE))

data <- data.frame(x, y, z)

# Model with ID
model_id <- rqpd(y ~ x | ID, data = data)

# Model with as.factor(ID)
model_as_factor <- rqpd(y ~ x | as.factor(z), data = data)

# Plot the results
ggplot(data, aes(x = x[1], y = y)) +
  geom_point() +
  geom_smooth(method = "loess") +
  labs(title = "Model with ID", subtitle = "Unit-level model")

ggplot(data, aes(x = x[1], y = predict(model_as_factor, newdata = data))) +
  geom_point() +
  geom_smooth(method = "loess") +
  labs(title = "Model with as.factor(ID)", subtitle = "Unit-specific model")

Conclusion

In conclusion, specifying fixed effects in panel quantile regression using rqpd requires careful consideration of the specification options. Using ID versus as.factor(ID) can lead to different results due to R’s interpretation of the fixed effects.

By increasing the value of tmpmax, you can alleviate the “tmpmax” error and ensure that your model converges correctly. Remember to always check the documentation for rqpd and its parent package, quantreg, to understand the implications of different specifications.

In this article, we have explored the differences between using ID versus as.factor(ID) in panel quantile regression with fixed effects in R. We have also discussed how to tweak the fitting routine via the control argument to alleviate common issues like the “tmpmax” error.

Last modified on 2023-08-03