In christophergandrud/ecmSim: Simulate and Display Quantities of Interest From Error Correction Models (ECM)

ecmSim

Early stage development version of a possible R package for simulating quantities of interest from Error Correction Models (ECM). This includes interactions [!INCOMPLETE!].

Use the ecm_builder function to simulated the quantities of interest and the ecm_plot function (NOT COMPLETED to plot the results.

Example

Imagine we have a two time series dv and iv. We want to estimate the relationship between these two series using an error correction model.

Our estimation model could look like this (assuming we have already created the change and lag variables and they are each in their own vectors or equal length):

# Simulated data to estimate the model from
iv <- rnorm(10)
lag_iv <- c(NA, iv[-length(iv)])
d_iv <-  iv - lag_iv

b0 = 2
b1 = -0.2
b2 = 1.1
b3 = 2.2
starting_d_dv <- -4.1
eps <- rnorm(iv, sd = 0.2)

dv <- vector()
d_dv <- vector()
lag_dv <- vector()
for (i in 2:length(lag_iv)) {
    if (i == 2) {
        dv_start <- b0 + b2*lag_iv[i] + b3*d_iv[i] + eps[i]
                          lag_dv[3] <- dv_start + starting_d_dv
    }
    else if (i == 3) {
        d_dv[i] <- b0 + b1*lag_dv[i] + b2*lag_iv[i] + b3*d_iv[i] + eps[i]
    }
    else if (i > 3) {
        lag_dv[i] <- lag_dv[i-1] + d_dv[i-1]
        d_dv[i] <- b0 + b1*lag_dv[i] + b2*lag_iv[i] + b3*d_iv[i] + eps[i]
    }
}

# Estimate error correction model
m1 <- lm(d_dv ~ lag_dv + lag_iv + d_iv)

We then create a data frame of fitted values for the baseline scenario to simulate.

baseline_scen <- data.frame(lag_dv = mean(lag_dv, na.rm = TRUE),
                            lag_iv = mean(lag_iv, na.rm = TRUE))

We also specify the "shock" to iv, the effects of which we want to compare to the baseline.

iv_shock <- sd(d_iv, na.rm = TRUE)

We now have all of the information we need to simulate the effects estimated in the ECM over 20 periods:

library(ecmSim)

m1_sims <- ecm_builder(obj = m1, lag_iv = 'lag_iv', d_iv = 'd_iv',
                       iv_shock = sd(d_iv, na.rm = TRUE),
                       baseline_df = baseline_scen, t_extent = 20)

# Show a sample of the simulation output
head(m1_sims)

The simulated quantity of interest is the change in the value of dv. We could alternatively supply qi_d_dv = FALSE to ecm_builder to return the dependent variable at each time point (i.e. lagged dv + the change in dv from the previous period).

We can plot the results (note, in the future there will be a ecm_plot function to simplify this process):

library(ggplot2)

ggplot(m1_sims, aes(time__, qi_median, group = is_shocked,
                    colour == is_shocked, fill = is_shocked)) +
    geom_line(aes(color = is_shocked)) +
    geom_ribbon(aes(ymin = qi_min, ymax = qi_max), alpha = 0.2) +
    xlab('\nSimulation Time') + ylab('Predicted dv Change\n') +
    theme_bw()

To-do

• [ ] Create ecm_plot function.

• [ ] Interaction example.

See Also

• See Warner (2016) for details.

• King, Gary, Michael Tomz, and Jason Wittenberg. 2000. "Making the Most of Statistical Analyses: Improving Interpretation and Presentation." American Journal of Political Science 44(2): 341-55.

christophergandrud/ecmSim documentation built on May 13, 2019, 7:02 p.m.