In this paper, we consider the analysis of unequally spaced longitudinal data using transition regression models with random effects. Diffusion as well as stabilization processes will be discussed, but our main focus will be on the latter. The initial conditions problem, which usually arises in transition models with random effects, is addressed. The usefulness of the proposed model is assessed on a large database of longitudinal haemoglobin values collected from blood donations by a Dutch private organization.
AitkinMAlfoM (2003) Longitudinal analysis of repeated binary data using autoregressive and random effect modelling. Statistical Modelling, 3, 291–303.
2.
Arellano-ValleRBBolfarineHLachosVH (2007) Bayesian inference for skew-normal linear mixed models. Journal of Applied Statistics, 34, 663–82.
3.
BaartAMDe KortWLAtsmaFMoonsKGMVergouweY (in press) Development and validation of a prediction model for low haemoglobin deferral in a large cohort of whole blood donors. Transfusion.
4.
BaartAMDe KortWLMoonsKGMVergouweY (2011) Prediction of low haemoglobin levels in whole blood donors. Vox Sanguinis, 100, 204–11.
5.
CrouchleyRDaviesRB (2001) A comparison of GEE and random effects models for distinguishing heterogeneity, nonstationarity and state dependence in a collection of short binary event series. Statistical Modelling: An International Journal, 1, 271–85.
6.
DigglePHeagertyPLiangKYZegerS (2002) Analysis of longitudinal data, 2nd edition.New York: Oxford University Press.
7.
HausmanJATaylorWE (1981) Panel data and unobservable individual effects. Econometrica, 49, 1377–98.
HeckmanJJ (1991) Identifying the hand of past: distinguishing state dependence from heterogeneity. The American Economic Review, 81, 75–79.
10.
HsiaoC (2002) Analysis of panel data, 2nd edition. Cambridge University Press.
11.
JonesRHBoadi-BoatengF (1991) Unequally spaced longitudinal data with AR(1) serial correlation. Biometrics, 47, 161–75.
12.
KazemiICrouchleyR (2006) Modelling the initial conditions in dynamic regression models of panel data with random effects. In BaltagiBH (ed). Panel data econometrics, theoretical contributions and empirical applications. Amsterdam, Netherlands: Elsevier, 91–117.
13.
KazemiIDaviesRB (2002) The asymptotic bias of MLEs for dynamic panel data models. In StasinopoulosMTouloumiG (eds), Statistical modelling in society, Proceedings of the 17th IWSM, Chania, Greece, 391–95.
14.
LesaffreELawsonA (2012) Bayesian methods in biostatistics. New York: John Wiley.
15.
LunnDSpiegelhalterDThomasABestN (2009) The BUGS project: evolution, critique and future directions (with discussion). Statistics in Medicine, 28, 3049–82.
16.
NerloveM (1999) Likelihood inference for dynamic panel models. Annales d conomie et de Statistique, 55-56, 369–410.
17.
OraveczZTuerlinckxF (2011) The linear mixed model and the hierarchical Ornstein Uhlenbeck model: some equivalences and differences. British Journal of Mathematical and Statistical Psychology, 64, 134–60.
18.
PindyckRRubinfeldD (2008) Microeconomics, 7th edition.Upper Saddle River, US: Prentice Hall.
19.
SchmidCH (2001) Marginal and dynamic regression models for longitudinal data. Statistics in Medicine, 20, 3295–311.
20.
SevestrePTrognonA (1996) Dynamic linear models. In MatyasSevestre (ed.), The econometrics of panel data: a handbook of the theory with applications, 2nd revised edition. Dordrecht: Kluwer Academic Publishers, 120–44.
21.
SpiegelhalterDJBestNGCarlinBPvan der LindeA (2002) Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society: Series B, 64, 583–39.
22.
VerbekeGFieuwsS (2007) The effect of miss-specified baseline characteristics on inference for longitudinal trends in linear mixed models. Biostatistics, 8, 772–83.
23.
VerbekeGFieuwsSLesaffreEKatoBSForemanMDBroosPLOMilisenK (2006) A comparison of procedures to correct for baseline differences in the analysis of continuous longitudinal data: a case study. Applied Statistics, 55, 93–102.
24.
VerbekeGMolenberghsG (2000) Linear mixed models for longitudinal data. New York: Springer.
25.
WooldridgeJM (2005) Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity. Journal of Applied Econometrics, 20, 39–54.
