Compute the robustness changepoint

robustness_bound() computes the value of the sensitivity parameter M at which the robustness bounds change from excluding to including an ATT of 0.

Usage

robustness_bound(object, level = 0.95)

Arguments

object

an apm_est object; the output of a call to apm_est(). M must have been set to a nonzero value to use robustness_bound().

level

the desired confidence level. Set to 0 to ignore sampling variation in computing the interval bounds. Default is .95.

Value

A single number corresponding to the changepoint value of M. If there is no positive value of M for which the interval bounds cross 0, NA will be returned.

See also

summary.apm_est() for examining the ATT and bounds for a given value of M; uniroot() for the function that finds the changepoint value of M.

Examples

data("ptpdata")

# Combination of 4 models: 2 time trends, 2 lags
models <- apm_mod(list(crude_rate ~ 1),
                  lag = 0:1,
                  time_trend = 0:1)
models
#> - Model 1: baseline mean
#> crude_rate ~ 1
#> family: gaussian(link = "identity")
#> outcome lag: none
#> outcome diff: none
#> log outcome: no
#> time trend: none
#> unit fixed effects: no
#> 
#> - Model 2: AR(1)
#> crude_rate ~ 1
#> family: gaussian(link = "identity")
#> outcome lag: 1
#> outcome diff: none
#> log outcome: no
#> time trend: none
#> unit fixed effects: no
#> 
#> - Model 3: linear trend
#> crude_rate ~ 1
#> family: gaussian(link = "identity")
#> outcome lag: none
#> outcome diff: none
#> log outcome: no
#> time trend: linear
#> unit fixed effects: no
#> 
#> - Model 4: linear trend + AR(1)
#> crude_rate ~ 1
#> family: gaussian(link = "identity")
#> outcome lag: 1
#> outcome diff: none
#> log outcome: no
#> time trend: linear
#> unit fixed effects: no

# Fit the models to data; unit_var must be supplied for
# fixed effects
fits <- apm_pre(models,
                data = ptpdata,
                group_var = "group",
                time_var = "year",
                val_times = 2004:2007,
                unit_var = "state",
                nsim = 100,
                verbose = FALSE)

est <- apm_est(fits,
               post_time = 2008,
               M = 1,
               R = 20,
               verbose = FALSE)

est
#> An `apm_est` object
#> 
#>  - grouping variable: group
#>  - unit variable: state
#>  - time variable: year
#>    - validation times: 
#>    - post-treatment time: 2008
#>  - sensitivity parameter (M): 1
#>  - bootstrap replications: 20
#> 
#> Use `summary()` or `plot()` to examine estimates and uncertainty bounds.

# ATT estimate and bounds for M = 1
summary(est)
#>       Estimate Std. Error  CI low CI high z_value Pr(>|z|)    
#> ATT     1.0217     0.1495  0.7286  1.3148   6.832 8.35e-12 ***
#> M = 1        .          . -0.1756  2.4973       .        .    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#Changepoint value of M ignoring estimation uncertainty
(M <- robustness_bound(est, level = 0))
#> [1] 1.463209

summary(est, level = 0, M = M)
#>          Estimate Std. Error CI low CI high z_value Pr(>|z|)    
#> ATT        1.0217     0.1495 1.0217  1.0217   6.832 8.35e-12 ***
#> M = 1.46        .          . 0.0000  2.0435       .        .    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#Changepoint value of M accounting for estimation uncertainty
(M <- robustness_bound(est, level = .95))
#> [1] 0.8521963

summary(est, level = .95, M = M)
#>          Estimate Std. Error CI low CI high z_value Pr(>|z|)    
#> ATT        1.0217     0.1495 0.7286  1.3148   6.832 8.35e-12 ***
#> M = 0.85        .          . 0.0000  2.3130       .        .    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1