A short note on quantifying and visualizing yearly variation in online monitored temperature data

The paper demonstrates how seasonal variation in sequentially arriving temperature data can be visualized by the specification of landmarks and subsequent time warping. We exemplify the idea with water temperature data from the river Wupper in northwestern Germany and with air temperature data from Berlin, Germany. Landmarks are thereby based on temperature thresholds. The method allows to assess whether the seasonal variation is running ahead or behind the average

Female wage profiles: An additive mixed model approach to employment breaks due to childcare

The paper investigates female wage profiles in West-Germany between 1984 and 2008 using data from the German Socio Economic Panel. The empirical study focuses on the short-run wageloss due to childcare and the long-run wage-profile in post-birth employment, respectivly. This is compared with wage profiles from females who are not mothers. As statistical analysis tool Additive Mixed Models are employed and estimated seperatetly for different levels of educational achievements. The models are dynamic in that main covariate effects are allowed to vary smoothly with working experience. The intention of the paper is to demonstrate with state of the art statistical models how wages are affected by labour market experience, employment interruptions and other covariates. The educational level of the mother and the time off the job influence the amount of wageloss and the wage profile afterwards. Labour market experience, as one major determinant of human capital, influences wages heavily and follows a dynamic patter. --Additive Mixed Models,Dynamic Effects,Maternity Leave,Panel Data,Employment Interruption,Wage Profiles,Female Labour Supply

Bootstrapping for penalized spline regression.

We describe and contrast several different bootstrapping procedures for penalized spline smoothers. The bootstrapping procedures considered are variations on existing methods, developed under two different probabilistic frameworks. Under the first framework, penalized spline regression is considered an estimation technique to find an unknown smooth function. The smooth function is represented in a high dimensional spline basis, with spline coefficients estimated in a penalized form. Under the second framework, the unknown function is treated as a realization of a set of random spline coefficients, which are then predicted in a linear mixed model. We describe how bootstrapping methods can be implemented under both frameworks, and we show in theory and through simulations and examples that bootstrapping provides valid inference in both cases. We compare the inference obtained under both frameworks, and conclude that the latter generally produces better results than the former. The bootstrapping ideas are extended to hypothesis testing, where parametric components in a model are tested against nonparametric alternatives.Methods; Framework; Regression; Linear mixed model; Mixed model; Model; Theory; Simulation; Hypothesis testing;

Modeling longitudinal data with ordinal response by varying coefficients

The paper presents a smooth regression model for ordinal data with longitudinal dependence structure. A marginal model with cumulative logit link (McCullagh 1980) is applied to cope for the ordinal scale and the main and covariate effects in the model are allowed to vary with time. Local fitting is pursued and asymptotic properties of the estimates are discussed. A data example demonstrates the exploratory flavor of the smooth model. In a second step, the longitudinal dependence of the observations is considered. Cumulative log odds ratios are fitted locally which provides insight how the dependence of the ordinal observations changes with time

Edge Preserving Smoothing by Local Mixture Modelling

Smooth models became more and more popular over the last couple of years. Standard smoothing methods however can not cope with discontinuities in a function or its first derivative. In particular, this implies that structural changes in data may be hidden in smooth estimates. Recently, Chu, Glad, Godtliebsen & Marron (1998) suggest local M estimation as edge preserving smoother. The basic idea behind local M estimation is that observations beyond a jump are considered as outliers and down-weighted or neglected in the estimation. We pursue a different, but related idea here and treat observations beyond a jump as tracing from a different population which differs from the current one by a shift in the mean. This means we impose locally a mixture model where mixing takes place due to different mean values. For fitting we apply a local version of the EM algorithm. The advantage of our approach shows in its general formulation. In particular, it easily extends to non Gaussian data. The procedure is applied in two examples, the first concerning the analysis of structural changes in the duration of unemployment, the second focusing on disease mapping