Summarize a TMB Mixed-Effects Demand Model Fit
Arguments
- object
An object of class
beezdemand_tmb.- report_space
Character. Reporting space for core demand parameters. One of
"internal","natural","log10".estimate/std.errorare reported on this scale;statistic/p.valueare always computed on the estimation scale (the Wald test is defined there and is not recomputed after back-transforming, so on the natural scalestatistic != estimate/std.error, by design).- ...
Additional arguments (currently unused).
Value
An object of class summary.beezdemand_tmb (also inherits
from beezdemand_summary). The variance_components element
reports the Q0 and alpha random-effect SDs on the log10 scale:
the random effects are estimated on the natural-log scale internally and
divided by log(10) for reporting, so they are directly comparable
with nlme::VarCorr() on a fit_demand_mixed() fit using the
default param_space = "log10". The residual SD is reported on the
model's likelihood scale (equation-dependent) and the random-effect
correlations are scale-invariant; neither is rescaled.
Examples
# \donttest{
data(apt)
fit <- fit_demand_tmb(apt, equation = "exponential", verbose = 0)
#> equation='exponential': Dropped 14 zero-consumption observations (146 remaining).
summary(fit)
#>
#> TMB Mixed-Effects Demand Model Summary
#> ==================================================
#>
#> Equation: exponential
#> Backend: TMB_mixed
#> Convergence: Yes
#> Subjects: 10 Observations: 146
#>
#> --- Fixed Effects ---
#> term estimate std.error statistic p.value
#> Q0:(Intercept) 6.5120 0.8097 15.0689 < 2e-16
#> alpha:(Intercept) 0.0030 0.0017 -10.3606 < 2e-16
#> log_k 0.8955 0.4838 1.8509 0.064184
#> logsigma -0.9528 0.2292 -4.1564 3.23e-05
#> logsigma -0.7798 0.2302 -3.3879 0.000704
#> logsigma_e -1.9498 0.0631 -30.9183 < 2e-16
#> rho_raw -0.4675 0.3292 -1.4202 0.155547
#>
#> --- Variance Components ---
#> (Q0/alpha RE SDs on log10 scale; residual SD on likelihood scale)
#> Component Estimate
#> sigma_b (Q0 RE SD) 0.1675
#> sigma_c (alpha RE SD) 0.1991
#> sigma_e (Residual SD) 0.1423
#>
#> --- RE Correlations ---
#> Component Estimate
#> rho_bc (Q0-alpha correlation) -0.4362
#>
#> --- Fit Statistics ---
#> Log-likelihood: 40.65
#> AIC: -67.3
#> BIC: -46.41
#>
#> --- Population Demand Metrics ---
#> Pmax: 11.2377 Omax: 23.8941 Method: analytic_lambert_w
#>
#> --- Individual Parameter Summaries ---
#> Q0: Min=2.8370 Med=6.2483 Mean=6.9793 Max=10.2274
#> alpha: Min=0.0016 Med=0.0034 Mean=0.0034 Max=0.0062
#> Pmax: Min=5.7902 Med=11.6341 Mean=12.1608 Max=21.1473
#> Omax: Min=11.7465 Med=21.2007 Mean=26.1542 Max=44.1357
#>
#> Notes:
#> * 14 zero-consumption observations dropped for equation='exponential'.
summary(fit, report_space = "log10")
#>
#> TMB Mixed-Effects Demand Model Summary
#> ==================================================
#>
#> Equation: exponential
#> Backend: TMB_mixed
#> Convergence: Yes
#> Subjects: 10 Observations: 146
#>
#> --- Fixed Effects ---
#> term estimate std.error statistic p.value
#> Q0:(Intercept) 0.8137 0.0540 15.0689 < 2e-16
#> alpha:(Intercept) -2.5194 0.2432 -10.3606 < 2e-16
#> log_k 0.8955 0.4838 1.8509 0.064184
#> logsigma -0.9528 0.2292 -4.1564 3.23e-05
#> logsigma -0.7798 0.2302 -3.3879 0.000704
#> logsigma_e -1.9498 0.0631 -30.9183 < 2e-16
#> rho_raw -0.4675 0.3292 -1.4202 0.155547
#>
#> --- Variance Components ---
#> (Q0/alpha RE SDs on log10 scale; residual SD on likelihood scale)
#> Component Estimate
#> sigma_b (Q0 RE SD) 0.1675
#> sigma_c (alpha RE SD) 0.1991
#> sigma_e (Residual SD) 0.1423
#>
#> --- RE Correlations ---
#> Component Estimate
#> rho_bc (Q0-alpha correlation) -0.4362
#>
#> --- Fit Statistics ---
#> Log-likelihood: 40.65
#> AIC: -67.3
#> BIC: -46.41
#>
#> --- Population Demand Metrics ---
#> Pmax: 11.2377 Omax: 23.8941 Method: analytic_lambert_w
#>
#> --- Individual Parameter Summaries ---
#> Q0: Min=2.8370 Med=6.2483 Mean=6.9793 Max=10.2274
#> alpha: Min=0.0016 Med=0.0034 Mean=0.0034 Max=0.0062
#> Pmax: Min=5.7902 Med=11.6341 Mean=12.1608 Max=21.1473
#> Omax: Min=11.7465 Med=21.2007 Mean=26.1542 Max=44.1357
#>
#> Notes:
#> * 14 zero-consumption observations dropped for equation='exponential'.
# }