# State-space models and random effects

Illustration of the benefits of state-space models over log-linear regression for estimating survival (Maunder et al. 2015)

Research Summary

Mark has done extensive research into applying state-space models in stock assessment and other population dynamics applications focusing on the use of random effects to model process variation. Mark was an early advocate of the equivalence of state-space models and modelling process error through random effects. With Rick Deriso, Mark developed a general non-Bayesian approach to integrating over the process variation with an application based on recruitment deviates (Maunder and Deriso, 2003). In collaboration with George Watters, Mark developed a general approach to integrate covariates for population processes in population dynamics models that included process error and showed that hypothesis tests were biased if the unexplained process variation was not modelled (Maunder and Watters 2003). Maunder and Deriso (2011) extended this approach to include missing covariate data as random effects, while Deriso et al. (2007) explained the need for estimating the random effects variance and variances of the likelihoods. As the covariates explain additional process variation the variance parameter of the random effect (the unexplained process variation) should decrease, illustrating the need to estimate the variance of the random effect when including covariates to explain process variation.

Mark has also published a series of papers on state-space models that attempt to explain their development and some of the issues involved (e.g. Maunder and Deriso, 2011; Maunder et al., 2015). In particular, the simplified explanations in Maunder et al. (2015) are useful for illustrating the concepts of state-space models.

Mark has developed state-space models in other contexts including modelling temporal variation in capture probability and survival in mark-recapture studies (Maunder et al. 2008), Bayesian analysis (e.g. Hoyle and Maunder, 2004; Maunder et al. 2006), and wildlife modelling (e.g. Hoyle and Maunder 2004). Of particular interest is the illustration of how fisheries modelling methods, including using random effects to model process variation, can be used to model wildlife population and the implementation of population viability analysis (Maunder, 2004).

Mark developed the penalized likelihood approach to include recruitment variation in forward projections to reduce computational demands (run time) on integrated models and illustrated how the lognormal bias correction factor causes bias in years where there is no data (i.e. the projections; Maunder et al. 2006), which is related to the bias correction factor for years with incomplete data.

Mark's (Maunder et al. 2015) paper explaining the use of state-space population dynamics models in hypothesis testing and the associated advantages over simple log-linear regressions for modeling survival, is a great resource for teaching this topic.

Relevant Papers

Maunder, M.N., Deriso, R.B., and Hanson, C.H. 2015. Use of state-space population dynamics models in hypothesis testing: advantages over simple log-linear regressions for modeling survival, illustrated with application to longfin smelt (Spirinchus thaleichthys). Fisheries Research, 164: 102–111. https://www.sciencedirect.com/science/article/pii/S0165783614003105

Maunder, M.N. and Deriso, R.B. 2011. A state–space multistage life cycle model to evaluate population impacts in the presence of density dependence: illustrated with application to delta smelt (Hyposmesus transpacificus) Can. J. Fish. Aquat. Sci. 68: 1285–1306. https://www.nrcresearchpress.com/doi/full/10.1139/f2011-071#.Xp4TTchKjD4

Maunder, M.N. and Deriso, R.B. 2010. Dealing with missing covariate data in fishery stock assessment models. Fisheries Research 101: 80-86. https://www.sciencedirect.com/science/article/abs/pii/S0165783609002537

Maunder, M.N., Skaug, H.J., Fournier, D.A., and Hoyle, S.D. 2008. Comparison of estimators for mark-recapture models: random effects, hierarchical Bayes, and AD Model Builder. In: Modeling Demographic Processes in Marked Populations. Eds. Thomson, D.L., Cooch, E.G., and Conroy, M.J. Environmental and Ecological Statistics 3: 917-948. https://www.springerprofessional.de/en/comparison-of-fixed-effect-random-effect-and-hierarchical-bayes-/1510090

Maunder M.N., Harley, S.J., and Hampton, J. 2006. Including parameter uncertainty in forward projections of computationally intensive statistical population dynamic models. ICES Journal of Marine Science 63: 969-979. https://academic.oup.com/icesjms/article/63/6/969/618044

Hoyle, S. D. and Maunder, M.N. 2004. A Bayesian integrated population dynamics model to analyze data for protected species. EURING proceedings. Animal Biodiversity and Conservation, 27(1): 247-266. https://www.raco.cat/index.php/abc/article/view/57163

Maunder M.N. 2004. Population Viability Analysis, Based on Combining Integrated, Bayesian, and Hierarchical Analyses. Acta Oecologica 26: 85-94. Special issue for the Extinction Working Group of the National Center for Ecological Synthesis and Analysis. https://www.sciencedirect.com/science/article/abs/pii/S1146609X04000566

Maunder, M.N. and Deriso, R.B. 2003. Estimation of recruitment in catch-at-age models. Can. J. Fish. Aquat. Sci. 60: 1204-1216. https://www.nrcresearchpress.com/doi/abs/10.1139/f03-104#.Xp40ZshKjD4

Maunder, M.N. and Watters, G.M. 2003. A general framework for integrating environmental time series into stock assessment models: model description, simulation testing, and example. Fishery Bulletin, 101: 89-99. http://aquaticcommons.org/15108/

Deriso, R.B., Maunder, M.N., and Skalski, J.R. 2007. Variance estimation in integrated assessment models and its importance for hypothesis testing. Can. J. Fish. Aquat. Sci. 64: 187-197. https://www.nrcresearchpress.com/doi/abs/10.1139/f06-178#.Xp4nR8hKjD4