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) 6.5533 0.8122 15.1690 < 2e-16
#> alpha:(Intercept) 0.0038 0.0006 -37.7147 < 2e-16
#> logsigma -0.9506 0.2294 -4.1441 3.41e-05
#> logsigma -0.7772 0.2304 -3.3733 0.000743
#> logsigma_e -1.9469 0.0629 -30.9396 < 2e-16
#> rho_raw -0.4593 0.3292 -1.3951 0.162994
#>
#> --- Variance Components ---
#> (Q0/alpha RE SDs on log10 scale; residual SD on likelihood scale)
#> Component Estimate
#> sigma_b (Q0 RE SD) 0.1679
#> sigma_c (alpha RE SD) 0.1996
#> sigma_e (Residual SD) 0.1427
#>
#> --- RE Correlations ---
#> Component Estimate
#> rho_bc (Q0-alpha correlation) -0.4295
#>
#> --- Fit Statistics ---
#> Log-likelihood: 40.53
#> AIC: -69.07
#> BIC: -51.17
#>
#> --- Population Demand Metrics ---
#> Pmax: 11.6482 Omax: 23.9232 Method: analytic_lambert_w
#>
#> --- Individual Parameter Summaries ---
#> Q0: Min=2.8583 Med=6.2762 Mean=7.0238 Max=10.2728
#> alpha: Min=0.0021 Med=0.0043 Mean=0.0042 Max=0.0078
#> Pmax: Min=5.9675 Med=12.0725 Mean=12.6217 Max=22.1596
#> Omax: Min=11.6871 Med=21.2953 Mean=26.1968 Max=44.1029
#>
#> 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) 0.8165 0.0538 15.1690 < 2e-16
#> alpha:(Intercept) -2.4199 0.0642 -37.7147 < 2e-16
#> logsigma -0.9506 0.2294 -4.1441 3.41e-05
#> logsigma -0.7772 0.2304 -3.3733 0.000743
#> logsigma_e -1.9469 0.0629 -30.9396 < 2e-16
#> rho_raw -0.4593 0.3292 -1.3951 0.162994
#>
#> --- Variance Components ---
#> (Q0/alpha RE SDs on log10 scale; residual SD on likelihood scale)
#> Component Estimate
#> sigma_b (Q0 RE SD) 0.1679
#> sigma_c (alpha RE SD) 0.1996
#> sigma_e (Residual SD) 0.1427
#>
#> --- RE Correlations ---
#> Component Estimate
#> rho_bc (Q0-alpha correlation) -0.4295
#>
#> --- Fit Statistics ---
#> Log-likelihood: 40.53
#> AIC: -69.07
#> BIC: -51.17
#>
#> --- Population Demand Metrics ---
#> Pmax: 11.6482 Omax: 23.9232 Method: analytic_lambert_w
#>
#> --- Individual Parameter Summaries ---
#> Q0: Min=2.8583 Med=6.2762 Mean=7.0238 Max=10.2728
#> alpha: Min=0.0021 Med=0.0043 Mean=0.0042 Max=0.0078
#> Pmax: Min=5.9675 Med=12.0725 Mean=12.6217 Max=22.1596
#> Omax: Min=11.6871 Med=21.2953 Mean=26.1968 Max=44.1029
#>
#> Notes:
#> * 14 zero-consumption observations dropped for equation='exponential'.
# }