The joint growth model on SSM coordinates as an engine's formulas

Return the package's fixed joint growth model in the formula pieces one mixed-model engine takes. The model reads the long table ssm_growth_data() builds: one intercept and one linear time slope per coordinate (e, x, y), a person-level random intercept per coordinate with the three intercepts free to correlate, and a separate residual variance per coordinate. Printing the object shows the complete fit call for the engine and, below it, the lines that keep the fixed effects and their covariance from the fit, or the posterior draws for brms. Those are the inputs of the recipe's next step, the trajectory.

Usage

ssm_growth_formula(
  engine = c("glmmTMB", "nlme", "brms"),
  time = "wave",
  id = "person"
)

# S3 method for class 'circumplex_growth_formula'
print(x, ...)

Arguments

engine: Optional. One of "glmmTMB" (default), "nlme" or "brms". The engine is named only; it is not loaded or called.
time: Optional. The name of the time column in the long table (default "wave"), the same time given to ssm_growth_data().
id: Optional. The name of the person column in the long table (default "person"), the same id given to ssm_growth_data(). time and id must each be one non-empty name, different from each other and from dv and value, the columns the long table reserves. A name that is not syntactic, such as "my wave", is backticked in the formulas, so every name reads as one column and never as formula syntax.
x: An object of class "circumplex_growth_formula".
...: Ignored (S3 consistency).

Value

A list of class "circumplex_growth_formula" with attributes engine, time and id. Its elements are formula objects, one per argument or formula part the engine's fit call takes. For "glmmTMB": formula, value ~ 0 + dv + dv:<time> + us(0 + dv | <id>), and dispformula, ~ 0 + dv. For "nlme": fixed, value ~ 0 + dv + dv:<time>, random, ~ 0 + dv | <id>, and weights, ~ 1 | dv, the form that nlme::varIdent() takes. For "brms": formula, value ~ 0 + dv + dv:<time> + (0 + dv | <id>), and sigma, sigma ~ 0 + dv, the two parts of a brms::bf() call.

Details

The model has no options. Adding a covariate, a quadratic time term or another random-effects structure changes the model whose interval coverage the package validated, so the pieces are built for the user to paste and, if they choose, to edit by hand with that in mind. That validation ran the frequentist REML fit. The brms dialect fits the same likelihood under brms's default priors, and its posterior intervals were not part of it. The nlme call sets na.action = na.omit, since nlme::lme() otherwise stops on a row whose value is NA; glmmTMB and brms drop such rows by default.

Examples

ssm_growth_formula("glmmTMB", time = "wave", id = "person")
#> Joint growth model on SSM coordinates, glmmTMB dialect.
#> Fit on the long table from ssm_growth_data(), then keep the fixed effects:
#> 
#> fit <- glmmTMB::glmmTMB(
#>   value ~ 0 + dv + dv:wave + us(0 + dv | person),
#>   dispformula = ~ 0 + dv,
#>   data = long,
#>   REML = TRUE
#> )
#> coef <- glmmTMB::fixef(fit)$cond
#> vcov <- as.matrix(vcov(fit)$cond)
ssm_growth_formula("nlme")
#> Joint growth model on SSM coordinates, nlme dialect.
#> Fit on the long table from ssm_growth_data(), then keep the fixed effects:
#> 
#> fit <- nlme::lme(
#>   fixed = value ~ 0 + dv + dv:wave,
#>   random = ~ 0 + dv | person,
#>   weights = nlme::varIdent(form = ~ 1 | dv),
#>   data = long,
#>   na.action = na.omit,
#>   method = "REML"
#> )
#> coef <- nlme::fixef(fit)
#> vcov <- as.matrix(vcov(fit))
ssm_growth_formula("brms")
#> Joint growth model on SSM coordinates, brms dialect.
#> Fit on the long table from ssm_growth_data(), then keep the draws:
#> 
#> fit <- brms::brm(
#>   brms::bf(
#>     value ~ 0 + dv + dv:wave + (0 + dv | person),
#>     sigma ~ 0 + dv
#>   ),
#>   data = long
#> )
#> draws <- as.matrix(fit)