We propose a spatiotemporal generalized von Bertalanffy (vonB) growth model that also includes between-individual (BI) variation and male/female correlation. The generalized vonB model includes the effect of maturation on growth. The model and the methodology are applied to a long time-series of survey observations of age and length for American plaice on the Grand Bank off the northeast coast of Canada. The bias in age-length data due to size selectivity of the survey gear is accounted for. The survey design includes length-stratified age sampling which is a type of response selective sampling design for growth model estimation. We propose and implement a conditional empirical proportion likelihood approach for these data. Neglecting this sampling scheme can lead to seriously biased estimation results. We found that a 6-parameter growth model is necessary for capturing the biphasic growth patterns of the American plaice on the Grand Bank, and the survey gear selectivity and BI variation are important for a good model fit. We proposed an empirically optimal BI variation model for this data. Our estimation results indicate that there are substantial differences in size-at-age for male and female American plaice, and this changes over time and between regions.

中文翻译：

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通过长度分层抽样收集​​数据的时空Richards-Schnute增长模型及其估计

我们提出了一个时空广义冯·贝塔朗菲（von B）生长模型，该模型还包括个体间（BI）变异和男性/女性相关性。广义的vonB模型包括成熟对生长的影响。该模型和方法适用于加拿大东北沿海大银行对美国的年龄和长度的长期调查观察。考虑到由于测量齿轮的尺寸选择性而导致的年龄长度数据的偏差。调查设计包括按年龄分层的年龄抽样，这是一种用于生长模型估计的响应选择性抽样设计。我们针对这些数据提出并实施了条件经验比例似然法。忽略这种采样方案可能导致估计结果严重偏差。我们发现6参数生长模型对于在Grand Bank上捕获美国的双相生长模式是必要的，并且调查齿轮的选择性和BI变异对于良好的模型拟合非常重要。我们针对该数据提出了一个经验最优的BI变化模型。我们的估计结果表明，雌雄male在年龄上的大小存在很大差异，并且随着时间的推移以及地区之间的差异而变化。