# Get started with coresynth

coresynth provides six causal-inference estimators for panel data behind a single formula interface, with the computational core (QP solving, SVD, Kalman filtering) written in C++ via RcppArmadillo. This vignette walks through the basics: fitting a model, comparing methods, and pulling results out with `broom` and `plot()`.

    library(coresynth)

## The unified formula

Every estimator is reached through `scm_fit()` with the same formula syntax:

    outcome ~ treatment | unit_id + time_id

The data must be a long-format balanced panel (one row per unit–time), and `treatment` is a 0/1 indicator that switches on for treated units in post-treatment periods. `method =` selects the estimator.

## A toy panel

We simulate a balanced panel of 10 units over 20 periods. Unit `u1` is treated from period 11 onward with a true ATT of 2.0.

    set.seed(42)
    N <- 10; TT <- 20; T_pre <- 10
    f   <- cumsum(rnorm(TT, 0, 0.5))     # common factor
    lam <- rnorm(N, 1, 0.3)              # unit loadings
    dat <- expand.grid(time = seq_len(TT), id = paste0("u", seq_len(N)))
    dat$y <- as.vector(outer(f, lam)) + rnorm(nrow(dat), 0, 0.3)
    dat$d <- as.integer(dat$id == "u1" & dat$time > T_pre)
    dat$y[dat$d == 1] <- dat$y[dat$d == 1] + 2.0   # inject the treatment effect

    head(dat)
    #>   time id         y d
    #> 1    1 u1 0.7590559 0
    #> 2    2 u1 0.5774968 0
    #> 3    3 u1 0.8414384 0
    #> 4    4 u1 0.6355518 0
    #> 5    5 u1 1.1532557 0
    #> 6    6 u1 0.4384856 0

## Fitting one method

    fit <- scm_fit(y ~ d | id + time, data = dat, method = "scm")
    fit
    #> === coresynth fit ===
    #> Method : SCM
    #> Estimate (ATT): 2.2711
    #> Pre-treatment periods: 10

The estimated ATT lives in `fit$estimate`:

    fit$estimate
    #> [1] 2.271125

## Comparing all six methods

Because the interface is shared, swapping estimators is a one-word change. Here we run all six on the same data (true ATT = 2.0).

    methods <- c("scm", "sdid", "gsc", "mc", "tasc", "si")
    fits    <- lapply(methods, function(m) scm_fit(y ~ d | id + time, data = dat, method = m))
    names(fits) <- methods

    data.frame(
      method   = methods,
      estimate = round(sapply(fits, `[[`, "estimate"), 3)
    )
    #>      method estimate
    #> scm     scm    2.271
    #> sdid   sdid    2.150
    #> gsc     gsc    2.255
    #> mc       mc    2.696
    #> tasc   tasc    1.154
    #> si       si    2.346

Method | Reference
--- | ---
`scm` | Abadie, Diamond & Hainmueller (2010)
`sdid` | Arkhangelsky et al. (2021)
`gsc` | Xu (2017)
`mc` | Athey et al. (2021)
`tasc` | Rho et al. (2026)
`si` | Agarwal et al. (2025)

## Visualizing a fit

`plot.coresynth()` offers three views via `type =`.

    plot(fits$sdid, type = "trend")   # observed vs. synthetic

    plot(fits$scm, type = "gap")      # treatment effect over time

    plot(fits$scm, type = "weights")  # donor weights

## tidy / glance / augment

coresynth integrates with `broom`, so results drop straight into tidy workflows and paper tables.

    library(broom)

    tidy(fits$scm)     # donor weights as a data frame
    #>   term   estimate        type
    #> 1   u2 0.24752069 unit_weight
    #> 2   u3 0.00000000 unit_weight
    #> 3   u4 0.07055224 unit_weight
    #> 4   u5 0.00000000 unit_weight
    #> 5   u6 0.14767482 unit_weight
    #> 6   u7 0.32770301 unit_weight
    #> 7   u8 0.00000000 unit_weight
    #> 8   u9 0.00000000 unit_weight
    #> 9  u10 0.20654924 unit_weight
    glance(fits$scm)   # one-row model summary
    #>   method estimate n_controls n_treated T_pre T_post staggered multi_arm
    #> 1    scm 2.271125          9         1    10     10     FALSE     FALSE

For custom plots or diagnostics, the accessor generics return the underlying series from any fit under a uniform interface, whatever the estimation method:

    head(treated_outcomes(fits$scm))    # observed treated series
    #> [1] 0.7590559 0.5774968 0.8414384 0.6355518 1.1532557 0.4384856
    head(synthetic_outcomes(fits$scm))  # estimated counterfactual
    #> [1] 0.5549202 0.2098675 0.7254600 0.8242011 0.9246564 0.6843428
    dim(donor_outcomes(fits$scm))       # T x N_co donor outcome matrix
    #> [1] 20  9

`export_json()` writes a fit to disk as JSON for reproducibility or downstream (e.g. AI) workflows:

    export_json(fits$scm, file = "scm_result.json")

## Where to next

- Estimators — covariates, predictors, and method-specific options for all six estimators plus the experimental-design variant.
- Inference — placebo, bootstrap, jackknife, parametric, and conformal inference.
- Staggered adoption — cohort-based estimation when units adopt treatment at different times.