1. Hidden Markov models (HMMs) that include individual-level random effects have recently been promoted for inferring animal movement behaviour from biotelemetry data. These ‘mixed HMMs’ come at significant cost in terms of implementation and computation, and discrete random effects have been advocated as a practical alternative to more computationally intensive continuous random effects. However, the performance of mixed HMMs has not yet been sufficiently explored to justify their widespread adoption, and there is currently little guidance for practitioners weighing the costs and benefits of mixed HMMs for a particular research objective.
2. I performed an extensive simulation study comparing the performance of a suite of fixed and random effect models for individual heterogeneity in the hidden state process of a two-state HMM. I focused on sampling scenarios more typical of telemetry studies, which often consist of relatively long time series (30–250 observations per animal) for relatively few individuals (5–100 animals).
3. I generally found mixed HMMs did not improve state assignment relative to standard HMMs. Reliable estimation of random effects required larger sample sizes than are often feasible in telemetry studies. Continuous random effect models performed reasonably well with data generated under discrete random effects, but not vice versa. Random effects accounting for unexplained individual variation can improve estimation of state transition probabilities and measurable covariate effects, but discrete random effects can be a relatively poor (and potentially misleading) approximation for continuous variation.
4. When weighing the costs and benefits of mixed HMMs, three important considerations are study objectives, sample size and model complexity. HMM applications often focus on state assignment with little emphasis on heterogeneity in state transition probabilities, in which case random effects in the hidden state process simply may not be worth the additional effort. However, if explaining variation in state transition probabilities is a primary objective and sufficient explanatory covariates are not available, then random effects are worth pursuing as a more parsimonious alternative to individual fixed effects.
5. To help put my findings in context and illustrate some potential challenges that practitioners may encounter when applying mixed HMMs, I revisit a previous analysis of long-finned pilot whale biotelemetry data.

中文翻译：

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值得努力？动物遥测数据隐马尔可夫模型随机效应的实际检验

1. 包含个体水平随机效应的隐马尔可夫模型 (HMM) 最近被推广用于从生物遥测数据推断动物运动行为。这些“混合 HMM”在实现和计算方面的成本很高，并且离散随机效应已被提倡作为计算密集型连续随机效应的实用替代方案。然而，混合 HMM 的性能尚未得到充分探索以证明其广泛采用的合理性，并且目前几乎没有指导从业者权衡混合 HMM 用于特定研究目标的成本和收益。
2. 我进行了广泛的模拟研究，比较了一套固定和随机效应模型在两态 HMM 的隐藏状态过程中个体异质性的性能。我专注于更典型的遥测研究的抽样场景，这些场景通常由相对较长的时间序列（每只动物 30-250 次观察）组成，用于相对较少的个体（5-100 只动物）。
3. 我通常发现混合 HMM 并没有改善相对于标准 HMM 的状态分配。随机效应的可靠估计需要比遥测研究中通常可行的更大的样本量。连续随机效应模型在离散随机效应下生成的数据表现相当不错，但反之则不然。解释无法解释的个体变异的随机效应可以改进状态转移概率和可测量协变量效应的估计，但离散随机效应可能是连续变异的相对较差（并且可能具有误导性）的近似值。
4. 在权衡混合 HMM 的成本和收益时，三个重要的考虑因素是研究目标、样本大小和模型复杂性。HMM 应用程序通常专注于状态分配，很少强调状态转换概率的异质性，在这种情况下，隐藏状态过程中的随机效应可能根本不值得额外的努力。然而，如果解释状态转移概率的变化是一个主要目标，并且没有足够的解释性协变量，那么随机效应作为个体固定效应的更简洁的替代方案值得追求。
5. 为了帮助将我的发现放在上下文中，并说明从业者在应用混合 HMM 时可能遇到的一些潜在挑战，我回顾了之前对长鳍领航鲸生物遥测数据的分析。