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Derive trait-varying sensitivities (alpha_i, beta_i) and abiotic slope (theta, gamma_i)

Source: R/derive_sensitivities.R
derive_sensitivities.Rd

From an auxiliary GLMM on standardized predictors, extract fixed-effect systems for r_z, C_z, and S_z, evaluate them at invader trait coordinates, and (optionally) test whether the abiotic slope on r_z should vary with traits (tr1, tr2). Biotic terms are enforced as nonnegative penalties on invasion fitness.

Usage

derive_sensitivities(fit_coeffs, Q_inv, inv_ids, lrt = TRUE)

Arguments

fit_coeffs

A fitted glmmTMB model on (r_z + C_z + S_z) × (tr1 + tr2).

Q_inv

Data frame with invader trait coordinates tr1, tr2 (rownames = invader IDs).

inv_ids

Character vector of invader IDs specifying the output order.

lrt

Logical or character. If logical:

  • TRUE → Wald test; FALSE → no test. If character, one of "wald", "lrt", or "none". Default is equivalent to "wald" for TRUE and "none" for FALSE.

Value

A list with components:

alpha_i, beta_i

Nonnegative penalties for C_z and S_z.

alpha_signed_i, beta_signed_i

Signed (pre-clamp) slopes.

theta0

Intercept for r_z slope system.

theta_i

Trait-varying r_z slope evaluated at invader traits.

gamma_i

Either theta_i (if test is significant) or a constant vector equal to theta0 (if not).

a0,a1,a2; b0,b1,b2

Coefficient components for C_z and S_z systems: main effect and interactions with tr1,tr2.

df

Per-invader tidy data frame with traits, signed slopes, clamping flags, and theta_i/gamma_i.

clamp_summary

Counts and proportions of clamped \(\alpha\) and \(\beta\).

use_theta

Logical; TRUE if the chosen test was significant.

lrt

Back-compat alias of test_tab (data frame with test result).

test_tab

Data frame with test statistic, df, and p-value (or NULL).

test_type

One of "wald", "lrt", or "none".

prior_note

Reminder of the nonnegative-penalty prior.

Details

Biotic penalties (prior/constraint). Invasion fitness is modeled as $$\lambda_{is} = \Gamma_{is} \, r^{(z)}_{is} \;-\; \alpha_i \, C^{(z)}_{is} \;-\; \beta_i \, S^{(z)}_{is}.$$ We therefore set \(\alpha_i = \max(0, -\text{slope}_{C,i})\) and \(\beta_i = \max(0, -\text{slope}_{S,i})\), where \(\text{slope}_{C,i}\) and \(\text{slope}_{S,i}\) are the fitted (possibly trait-varying) slopes for C_z and S_z. Signed versions (before clamping) are returned for diagnostics.

Testing trait-varying abiotic slope. The argument lrt controls whether and how to test the joint null \(H_0: r_z:tr1 = r_z:tr2 = 0\).

  • For backward compatibility, lrt = TRUE performs a Wald joint χ² test using the fixed-effects variance–covariance (no refit).

  • lrt = FALSE performs no test.

  • Alternatively, pass a character string: "wald", "lrt", or "none".

    • "lrt" refits a reduced model (dropping both interactions) and runs a likelihood-ratio test (anova(..., test = "Chisq")).

If the chosen test is significant at \(\alpha = 0.05\), the function uses the trait-varying theta_i; otherwise a constant theta0 is used for gamma_i.

See also

glmmTMB::glmmTMB(), stats::anova()