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This is an R package designed to aid in the analysis of panel data, designs in which the same group of respondents/entities are contacted/measured multiple times. panelr provides some useful infrastructure, like a panel_data object class, as well as automating some emerging methods for analyses of these data.

wbm() automates the “within-between” (also known as “between-within” and “hybrid”) specification that combines the desirable aspects of both fixed effects and random effects econometric models and fits them using the lme4 package in the backend. Bayesian estimation of these models is supported by interfacing with the brms package (wbm_stan()) and GEE estimation via geepack (wbgee()).

It also automates the fairly new “asymmetric effects” specification described by Allison (2019) and supports estimation via GLS for linear asymmetric effects models (asym()) and via GEE for non-Gaussian models (asym_gee()).


panelr is now available via CRAN.


panel_data frames

While not strictly required, the best way to start is to declare your data as panel data. I’ll load the example data WageData to demonstrate.

 [1] "exp"   "wks"   "occ"   "ind"   "south" "smsa"  "ms"    "fem"  
 [9] "union" "ed"    "blk"   "lwage" "t"     "id"   

The two key variables here are t and id. t is the wave of the survey the row of the data refers to while id is the survey respondent. This is a perfectly balanced data set, so there are 7 observations for each of the 595 respondents. We will use those two pieces of information to create a panel_data object.

wages <- panel_data(WageData, id = id, wave = t)
# Panel data:    4,165 x 14
# entities:      id [595]
# wave variable: t [1, 2, 3, ... (7 waves)]
   id        t   exp   wks   occ   ind south  smsa    ms   fem union    ed
   <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
 1 1         1     3    32     0     0     1     0     1     0     0     9
 2 1         2     4    43     0     0     1     0     1     0     0     9
 3 1         3     5    40     0     0     1     0     1     0     0     9
 4 1         4     6    39     0     0     1     0     1     0     0     9
 5 1         5     7    42     0     1     1     0     1     0     0     9
 6 1         6     8    35     0     1     1     0     1     0     0     9
 7 1         7     9    32     0     1     1     0     1     0     0     9
 8 2         1    30    34     1     0     0     0     1     0     0    11
 9 2         2    31    27     1     0     0     0     1     0     0    11
10 2         3    32    33     1     1     0     0     1     0     1    11
# ... with 4,155 more rows, and 2 more variables: blk <dbl>, lwage <dbl>

We have to tell panel_data() which column refers to the unique identifiers for respondents/entities (the latter when you have something like countries or companies instead of people) and which column refers to the period/wave of data collection.

Note that the resulting panel_data object will remember which of the columns is the ID column and which is the wave column. It will also fight you a bit when you do things that might have the side effect of dropping those columns or putting them out of time order. panel_data frames are modified tibbles (tibble package) that are grouped by entity (i.e., the ID column).

panel_data frames are meant to play nice with the tidyverse. Here’s a quick sample of how a tidy workflow with panelr can work:

# Create `panel_data` object
wages <- panel_data(WageData, id = id, wave = t) %>%
  # Pass to mutate, which will calculate statistics groupwise when appropriate
    wage = exp(lwage), # reverse transform the log wage variable
    mean_wage_individual = mean(wage), # means calculated separately by entity
    lag_wage = lag(wage) # mutate() will calculate lagged values correctly
  ) %>%
  # Use `panelr`'s complete_data() to filter for entities that have
  # enough observations
  complete_data(wage, union, min.waves = 5) %>% # drop if there aren't 5 completions
  # You can use unpanel() if you need to do rowwise or columnwise operations
  unpanel() %>%
    mean_wage_grand = mean(wage)
  ) %>%
  # You'll need to convert back to panel_data if you want to keep using panelr functions
  panel_data(id = id, wave = t)

wbm() — the within-between model

Anyone can fit a within-between model without the use of this package as it is just a particular specification of a multilevel model. With that said, it’s something that will require some programming and could be rather prone to error. In the best case, it is cumbersome and inefficient to create the necessary variables.

wbm() is the primary model-fitting function that you’ll use from this package and it fits within-between models for you, utilizing lme4 as a backend for estimation.

A three-part model syntax is used that goes like this:

dv ~ varying_variables | invariant_variables | cross_level_interactions/random effects

It works like a typical formula otherwise. The bars just tell panelr how to treat the variables. Note also that you can specify random slopes using lme4-style syntax in the third part of the formula as well. A random intercept for the ID variable is included by default and doesn’t need to be specified in the formula.

Lagged variables are supported as well through the lag() function. Unlike base R, panelr lags the variables correctly — wave 1 observations will have NA values for the lagged variable rather than taking the final wave value of the previous entity.

Here we will specify a model using the wages data. We will predict logged wages (lwage) using two time-varying variables — lagged union membership (union) and contemporaneous weeks worked (wks) — along with a time-invariant predictor, a binary indicator for black race (blk). For demonstrative purposes, we’ll fit a random slope for lag(union) and a cross-level interaction between blk and wks.

model <- wbm(lwage ~ lag(union) + wks | blk | blk * wks + (lag(union) | id), data = wages)
Entities: 595
Time periods: 2-7
Dependent variable: lwage
Model type: Linear mixed effects
Specification: within-between

AIC = 1427.04, BIC = 1495.03
Pseudo-R² (fixed effects) = 0.05
Pseudo-R² (total) = 0.75
Entity ICC = 0.73

                    Est.   S.E.   t val.      d.f.      p
---------------- ------- ------ -------- --------- ------
lag(union)          0.04   0.04     1.24     88.17   0.22
wks                -0.00   0.00    -1.51   2948.04   0.13

                           Est.   S.E.   t val.     d.f.      p
----------------------- ------- ------ -------- -------- ------
(Intercept)                6.20   0.24    25.89   571.97   0.00
imean(lag(union))          0.03   0.04     0.72   593.27   0.47
imean(wks)                 0.01   0.01     2.30   571.29   0.02
blk                       -0.35   0.06    -5.65   591.87   0.00

                 Est.   S.E.   t val.      d.f.      p
------------- ------- ------ -------- --------- ------
wks:blk         -0.00   0.00    -1.06   2956.56   0.29

p values calculated using Satterthwaite d.f.
  Group      Parameter     Std. Dev. 
---------- -------------- -----------
    id      (Intercept)     0.3785   
    id       lag(union)      0.24    
 Residual                   0.2291   

Note that imean() is an internal function that calculates the individual-level mean, which represents the between-subjects effects of the time-varying predictors. The within effects are the time-varying predictors at the occasion level with the individual-level mean subtracted. If you want the model specified such that the occasion level predictors do not have the mean subtracted, use the model = "contextual" argument. The “contextual” label refers to the way these terms are normally interpreted when it is specified that way.

You may also use model = "between" to fit what econometricians call the random effects model, which does not disaggregate the within- and between-entity variation.

widen_panel() and long_panel()

Two functions that should cover your bases for the tricky business of reshaping panel data are included. Sometimes, like for doing SEM-based analyses, you need your data in wide format — i.e., one row per entity. widen_panel() makes that easy and should require minimal trial and error or thinking.

Perhaps more often, your raw data are already in wide format and you need to get it into long format to do cool stuff like use wbm(). That can be very tricky, but long_panel() (I didn’t think lengthen_panel() or longen_panel() quite worked as names) should cover most situations. You tell it what the labels for periods are (e.g., does it range from 1 to 5, "A" to "E", or something else?), where they are located (before or after the variable’s name?), and what kinds of formatting go before/after it. Check out the vignette for more details and some worked examples.


I’m happy to receive bug reports, suggestions, questions, and (most of all) contributions to fix problems and add features. I prefer you use the Github issues system over trying to reach out to me in other ways. Pull requests for contributions are encouraged.

Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.


The source code of this package is licensed under the MIT License.