Figures & data
Fig. 1 Location-scale transformation model. The transformation (left) and cumulative distribution function (right) are shown for the baseline configuration (i.e., and
) and different values of the location parameter
and of the scale parameter
.
![Fig. 1 Location-scale transformation model. The transformation (left) and cumulative distribution function (right) are shown for the baseline configuration (i.e., μ(x)=0 and σ(x)=1) and different values of the location parameter μ(x) and of the scale parameter σ(x).](/cms/asset/c00429c8-5f0f-43d5-ba15-f52254b5a805/utas_a_2203177_f0001_c.jpg)
Fig. 2 Stratification. Distribution (top) and density (bottom) of postpartum blood loss conditional on delivery mode estimated by the stratified transformation model (left) and location-scale transformation model (right). In addition, the empirical cumulative distribution function is shown in the top row, in-sample log-likelihoods are given in the bottom row.
![Fig. 2 Stratification. Distribution (top) and density (bottom) of postpartum blood loss conditional on delivery mode estimated by the stratified transformation model (left) and location-scale transformation model (right). In addition, the empirical cumulative distribution function is shown in the top row, in-sample log-likelihoods are given in the bottom row.](/cms/asset/42574f01-d611-44c2-be59-05231d5976dc/utas_a_2203177_f0002_c.jpg)
Fig. 3 Crossing hazards. The survivor functions of the two groups estimated by the nonparametric Kaplan-Meier method (step function) are shown along the estimates from the location-scale Weibull model (left) and the distribution-free location-scale transformation model (right).
![Fig. 3 Crossing hazards. The survivor functions of the two groups estimated by the nonparametric Kaplan-Meier method (step function) are shown along the estimates from the location-scale Weibull model (left) and the distribution-free location-scale transformation model (right).](/cms/asset/8126ac95-83a2-49e1-a3b0-dd0b709c37cb/utas_a_2203177_f0003_c.jpg)
Fig. 4 Partial proportional hazards. Three annual quantile functions (0.25, 0.50, and 0.75th quantile) for DVCs (for a hypothetical Monday in 2002) estimated by three transformation models of increasing complexity. The in-sample log-likelihoods of the corresponding models are given in the panels.
![Fig. 4 Partial proportional hazards. Three annual quantile functions (0.25, 0.50, and 0.75th quantile) for DVCs (for a hypothetical Monday in 2002) estimated by three transformation models of increasing complexity. The in-sample log-likelihoods of the corresponding models are given in the panels.](/cms/asset/227a189b-b5dc-421c-9928-468ab0550d0b/utas_a_2203177_f0004_b.jpg)
Table 1 Partial proportional hazards.
Fig. 5 Location-scale transformation tree. Female orgasm frequency in heterosexual relationships as a function of questionnaire variables reported by the female respondent.
![Fig. 5 Location-scale transformation tree. Female orgasm frequency in heterosexual relationships as a function of questionnaire variables reported by the female respondent.](/cms/asset/d8aabf7a-dcd1-4e1f-9419-cda2b7b9d3b8/utas_a_2203177_f0005_b.jpg)
Fig. 6 Transformation additive models for location and scale (TAMLS). Conditional quantiles of head circumference along age estimated by the Box-Cox-t GAMLSS (BCT GAMLSS, top panel) and the TAMLS (bottom panel). The former model comprises four and the latter model two smooth terms.
![Fig. 6 Transformation additive models for location and scale (TAMLS). Conditional quantiles of head circumference along age estimated by the Box-Cox-t GAMLSS (BCT GAMLSS, top panel) and the TAMLS (bottom panel). The former model comprises four and the latter model two smooth terms.](/cms/asset/4ce8fab4-7212-4852-bbba-2e0f07c067da/utas_a_2203177_f0006_b.jpg)
Table 2 Model selection.