Package 'dpm'

Dynamic panel models fit with maximum likelihood

Description

Estimate dynamic panel models with fixed effects via maximum likelihood estimation.

Usage

dpm(
  formula,
  data,
  error.inv = FALSE,
  const.inv = FALSE,
  alpha.free = FALSE,
  y.lag = 1,
  y.free = FALSE,
  x.free = FALSE,
  fixed.effects = TRUE,
  partial.pre = FALSE,
  print.only = FALSE,
  id = NULL,
  wave = NULL,
  err.inv = NULL,
  weights = NULL,
  ...
)

Arguments

formula	Model formula. See details for instructions on specifying parameters properly.
data	Data frame in "long" format. Prefers a "panel_data" object.
error.inv	Constrain the error variance to be equal across waves. Default is FALSE.
const.inv	Constrain the dependent variable's variance to be equal across waves (or makes its intercept equal across waves). This removes cross-sectional dependence. Default is FALSE.
alpha.free	Estimate each wave of the dependent variable's loading on the alpha latent variable. Default is FALSE, meaning each wave has a loading of 1.
y.lag	Which lag(s) of the dependent variable to include in the regression. Default is 1, but any number or vector of numbers can be used.
y.free	If TRUE, allows the regression coefficient(s) for the lagged dependent variable to vary over time. Default is FALSE. You may alternately provide a number or vector of numbers corresponding to which lags should vary freely.
x.free	If TRUE, allows the regressions coefficient(s) for the predictor(s) to vary over time. Default is FALSE. If TRUE, the predictor regression coefficient(s) can vary over time. Alternately, you may provide a character vector of predictors to allow to vary if you only want a subset of predictors to vary.
fixed.effects	Fit a fixed effects model? Default is TRUE. If FALSE, you get a random effects specification instead.
partial.pre	Make lagged, predetermined predictors (i.e., they are surrounded by pre() in the model formula) correlated with the contemporaneous error term, as discussed in Allison (2022)? Default is FALSE.
print.only	Instead of estimating the model, print the lavaan model string to the console instead.
id	Name of the data column that identifies which individual the observation is. Not needed if data is a "panel_data" object.
wave	Name of the data column that identifies which wave the observation is from. Not needed if data is a "panel_data" object.
err.inv	Deprecated, same purpose as error.inv.
weights	Equivalent to the argument to lm, presumably the unquoted name of a variable in the data that represents the weight. It is passed to lavaan()'s sampling.weights argument.
...	Extra parameters to pass to sem. Examples could be missing = "fiml" for missing data or estimator = "MLM" for robust estimation.

Details

The right-hand side of the formula has two parts, separated by a bar (|). The first part should include the time-varying predictors. The second part, then, is for the time-invariant variables. If you put a time-varying variable in the second part of the formula, by default the first wave's value of that variable is treated as the constant.

You must include time-varying predictors. If you do not include a bar in the formula, all variables are treated as time-varying.

If you would like to include an interaction between time-varying and time-invariant predictors, you can add a third part to the formula to specify that term.

Predetermined variables:

To set a variable as predetermined, or weakly exogenous, surround the variable with a pre function. For instance, if you want the variable union to be predetermined, you could specify the formula like this: wks ~ pre(union) + lwage | ed, where wks is the dependent variable, lwage is a strictly exogenous time-varying predictor, and ed is a strictly exogenous time-invariant predictor.

To lag a predictor, surround the variable with a lag function in the same way. Note that the lag function used is specific to this package, so it does not work the same way as the built-in lag function (i.e., it understands that you can only lag values within entities).

Note: CFI and TLI model fit measures for these models should not be used. They are anti-conservative compared to other implementations and we have not yet figured out how to get more plausible values.

Value

An object of class dpm which has its own summary method.

The dpm object is an extension of the lavaan class and has all the capabilities of lavaan objects, with some extras.

It contains extra slots for:

• mod_string, the character object used to specify the model to lavaan. This is helpful if you want to fit the model yourself or wish to check that the specification is correct.

• wide_data, the widened data frame necessary to fit the SEM.

Author(s)

Jacob A. Long, in consultation with Richard A. Williams and Paul D. Allison. All errors are Jacob's.

References

Allison, P. D., Williams, R., & Moral-Benito, E. (2017). Maximum likelihood for cross-lagged panel models with fixed effects. Socius, 3, 1–17. http://journals.sagepub.com/doi/10.1177/2378023117710578

Examples

# Load example data
data("WageData", package = "panelr")
# Convert data to panel_data format for ease of use
wages <- panel_data(WageData, id = id, wave = t)

# Replicates Allison, Williams, & Moral-Benito (2017) analysis
fit <- dpm(wks ~ pre(lag(union)) + lag(lwage) | ed, data = wages,
            error.inv = TRUE, information = "observed")
# Note: information = "observed" only needed to match Stata/SAS standard errors
summary(fit)

---

Dynamic Panel Model (dpm) class

Description

Models fit using dpm() return values of this class, which inherits from lavaan-class.

Slots

call_info

A list of metadata about the arguments used.

call

The actual function call.

mod_string

The model formula passed to lavaan.

wide_data

The data provided to the data argument in the function

formula

The Formula::Formula() object provided to dpm(). call.

---

Retrieve lavaan model syntax from fitted dpm model

Description

This helper function provides a simple way to retrieve the lavaan model syntax from a fitted dpm() object.

Usage

get_syntax(model, print = TRUE)

Arguments

model	A dpm object.
print	Print the syntax to the console so it is formatted properly? Default is TRUE.

Value

Returns a string with the lavaan model syntax for model. If print is TRUE, it is printed to the console as well.

Examples

data("WageData", package = "panelr")
wages <- panel_data(WageData, id = id, wave = t)
fit <- dpm(wks ~ pre(lag(union)) + lag(lwage), data = wages)
get_syntax(fit)

---

Retrieve wide-format data from fitted dpm model

Description

This helper function provides a simple way to retrieve the widened data from a fitted dpm() object.

Usage

get_wide_data(model)

Arguments

model

A dpm object.

Value

A data.frame with input data transformed from "long" to "wide" format, with just one row per person/entity. Internally, this is generated by calling panelr::widen_panel() after some preprocessing.

Examples

data("WageData", package = "panelr")
wages <- panel_data(WageData, id = id, wave = t)
fit <- dpm(wks ~ pre(lag(union)) + lag(lwage), data = wages)
get_wide_data(fit)

---

lavaan-style summary for dpm objects

Description

This is just a quick way to get lavaan's summary instead the more terse summary designed for dpm objects.

Usage

lav_summary(x, ...)

Arguments

x	The dpm object
...	Other arguments to the lavaan function.

Value

Returns a lavaan.summary object which contains various model data described in ⁠?lavaan::summary,lavaan-method⁠.

Examples

# Load example data
data("WageData", package = "panelr")
# Convert data to panel_data format for ease of use
wages <- panel_data(WageData, id = id, wave = t)

fit <- dpm(wks ~ pre(lag(union)) + lag(lwage) | ed, data = wages)
lav_summary(fit)

---

Summarize dpm objects

Description

The summary method is designed to offer similar arguments to lavaan's summary, but with shorter and more domain-specific output.

Usage

## S4 method for signature 'dpm'
summary(
  object,
  standardized = FALSE,
  ci = FALSE,
  se = TRUE,
  zstat = TRUE,
  pvalue = TRUE,
  ci.level = 0.95,
  boot.ci.type = c("perc", "norm", "basic", "bca.simple"),
  digits = getOption("dpm-digits", 3),
  ...
)

Arguments

object	A dpm object.
standardized	Use lavaan's method for standardizing coefficients? Default is FALSE.
ci	Show confidence intervals? Default is FALSE.
se	Show standard errors? Default is TRUE.
zstat	Show the z statistic? Default is TRUE.
pvalue	Show p values? Default is TRUE.
ci.level	How wide should the confidence intervals be? Ignored if ci is FALSE. Default is .95.
boot.ci.type	If the model was fit with bootstrapped standard errors and ci is TRUE, which method should be used for finding the intervals? Default is "perc".
digits	How many digits should be printed in the model summary? Default is 3. You can set a default by setting the option "dpm-digits".
...	Ignored.

Value

Returns a summary.dpm object, which is a list with three elements:

• model: The dpm object.

• coefficients: A data frame containing coefficient estimates, standard errors, p values, and so on.

• fitmeasures: A numeric vector containing model fit information.

The primary function of the object is to be printed to the console.

---

Tidy methods for dpm

Description

dpm objects support the broom package's tidy method.

Usage

## S3 method for class 'dpm'
tidy(x, conf.int = FALSE, conf.level = 0.95, ...)

## S3 method for class 'dpm'
glance(x, ...)

Arguments

x	A dpm object.
conf.int	Logical indicating whether or not to include a confidence interval in the tidy data frame.
conf.level	The confidence level to use for the confidence interval when conf.int is TRUE. Default is .95, corresponding to a 95% confidence interval.
...	Other arguments passed to summary.dpm.

Value

A tibble::tibble() with information about model components. These will be coefficient estimates (for tidy()) or model fit (for glance()), following the naming standards established by the broom package.

Examples

if (requireNamespace("broom")) {
  library(broom)
  # Load example data
  data("WageData", package = "panelr")
  # Convert data to panel_data format for ease of use
  wages <- panel_data(WageData, id = id, wave = t)

  fit <- dpm(wks ~ pre(lag(union)) + lag(lwage) | ed, data = wages)
  tidy(fit)
}

---

Various methods for dpm objects

Description

R likes it when these things have documentation.

Usage

update(object, ...)

## S3 method for class 'dpm'
update(object, formula., ..., evaluate = TRUE)

## S4 method for signature 'dpm'
update(object, formula., ..., evaluate = TRUE)

## S4 method for signature 'dpm'
show(object)

coef(object, ...)

## S3 method for class 'dpm'
coef(object)

## S4 method for signature 'dpm'
coef(object)

## S4 method for signature 'dpm'
formula(x)

Arguments

object	A dpm object
...	Other arguments to update.
formula.	An updated formula (optional)
evaluate	If updating, should the updated model be updated or just return the call? Default is TRUE, re-run the model.
x	A dpm object

Value

update.dpm(): Returns an updated dpm object.

coef.dpm(): Returns a numeric vector of coefficients. If the model was fit with x.free = TRUE and/or y.free = TRUE, the coefficient names will be formatted with an underscore and the wave corresponding to which time period the coefficient is estimated for.

formula.dpm(): Returns the formula used to fit the model as a Formula object. The formula is the input to dpm(), not the lavaan syntax.

show.dpm(): Returns an invisible "NULL" while printing model info to console.

Examples

data("WageData", package = "panelr")
wages <- panel_data(WageData, id = id, wave = t)
fit <- dpm(wks ~ pre(lag(union)) + lag(lwage), data = wages)

# Re-run model without `lag(lwage)` term
update(fit, . ~ . - lag(lwage))

---