China
Africa
Explore chapters and articles related to this topic
The Golem of Prague
Published in Richard McElreath, Statistical Rethinking, 2020
Partial pooling is the key technology, and the contexts in which it is appropriate are diverse. Here are four commonplace examples.To adjust estimates for repeat sampling. When more than one observation arises from the same individual, location, or time, then traditional, single-level models may mislead us.To adjust estimates for imbalance in sampling. When some individuals, locations, or times are sampled more than others, we may also be misled by single-level models.To study variation. If our research questions include variation among individuals or other groups within the data, then multilevel models are a big help, because they model variation explicitly.To avoid averaging. Pre-averaging data to construct variables can be dangerous. Averaging removes variation, manufacturing false confidence. Multilevel models preserve the uncertainty in the original, pre-averaged values, while still using the average to make predictions.
Analyzing data streams for social scientists
Published in Uwe Engel, Anabel Quan-Haase, Sunny Xun Liu, Lars Lyberg, Handbook of Computational Social Science, Volume 2, 2021
Lianne Ippel, Maurits Kaptein, Jeroen K. Vermunt
In this section, we focus on the online estimation with dependent observations. Commonly, dependent observations are analyzed with multilevel models. For the online estimation of these models, we introduce the streaming expectation maximization approximation (SEMA) algorithm, an online learning algorithm based on the EM algorithm (Ippel et al., 2019, 2016b). Multilevel models have several advantages, such as better out-of-sample predictions, over models that assume a fixed effect; they are also easier to interpret as the models only exist of three types of parameters (i.e., regression coefficients, variance parameters, and residual variance) (Raudenbush & Bryk, 2002; Skrondal & Rabe-Hesketh, 2004). However, the downside of these models is that they rely on iterations to fit the model, similar to the logistic regression. When data are either large (i.e., long) or augmented with new observations, the estimation time of such a multilevel model quickly becomes infeasible, as does the required computational power to do the series of matrix inversions necessary to estimate the model parameters. While we assume data to enter over time, using SEMA for model estimation can still be beneficial in the case of stationary data. While in a data stream, SEMA will not revisit previously seen observations; that is not to say that it is impossible. In a stationary data set, SEMA can be used to iterate over the data set more efficiently than the offline method, using fewer iterations in order to converge (Ippel et al., 2016b). In this section, we first detail the multilevel model and highlight one of the commonly used estimation algorithms to fit the model, that is, EM algorithm. We then continue with the discussion of SEMA.
Study on the socioeconomic and climatic effects of forest fire incidence in the Changbai Mountain area based on a cross-classified multilevel model
Published in Geomatics, Natural Hazards and Risk, 2023
Shuo Zhen, Hang Zhao, Zhengxiang Zhang, Yiwei Yin, Xin Wang
The multilevel model has different names, such as the multilevel linear model, mixed effects model, random coefficient regression model, random effects model and hierarchical linear model, in different research fields, for example, sociology, biostatistics and econometrics (Guo 2002; Liu et al. 2012; Peng and Knaap 2021). The multilevel model examines the influence of group-level and individual-level covariates on individual-level results by analyzing hierarchical data (Diez-Roux 2000; Leyland and Groenewegen 2003). This method solves the problem of data nesting (Matsueda and Drakulich 2016). Thus, multilevel models can link dependent variables (wildfire incidence) with predictive variables (social and climatic factors) at multiple geographical levels (Srholec 2010). In this study, multilevel models were implemented using hierarchical linear and nonlinear modelling (HLM, version 7.0).
The time courses of runners’ recovery-stress responses after a mountain ultra-marathon: Do appraisals matter?
Published in European Journal of Sport Science, 2019
Marvin Gaudino, Guillaume Martinent, Guillaume Y Millet, Michel Nicolas
Multilevel models extend multiple regressions to data that are hierarchically structured (nested data). In the present study, repeated measurements (Level 1 units of analysis) were nested within runners (Level 2 units of analysis) because several observations were gathered for each runner. Although the assumption of multiple regression models that all observations are independent may not be the case with nested data, multilevel models provide unbiased estimates of the parameters by taking into account the hierarchical structure of the data (Singer & Willett, 2003). Thus, multilevel models are a flexible approach that can be applied to evaluate inter-individual differences in intra-individual changes of recovery and stress since each runner has his own curve (Doron & Martinent, 2016).
Childhood football play and practice in relation to self-regulation and national team selection; a study of Norwegian elite youth players
Published in Journal of Sports Sciences, 2018
Martin K. Erikstad, Rune Høigaard, Bjørn Tore Johansen, Ngianga-Bakwin Kandala, Tommy Haugen
With some exceptions (e.g., Haugaasen et al., 2014a), studies on athletes` training histories have typically analysed the data using approaches such as ANOVA or independent t-tests (e.g., Forsman et al., 2016; Hornig et al., 2016). The present study applied a random intercept mixed model, which allowed us to account for the longitudinal and hierarchical nature of the practice histories (practice histories are nested within players and between players) and quantified the correlations among observations in the same cluster on the different time points (see e.g., Diggle et al., 2002). Another advantage of multilevel models is the handling of missing data, as observations can be included in the analysis even with the presence of missing data (Diggle et al., 2002; Quené & van den Bergh, 2004). While the present study is, to our knowledge, the first to use random intercept mixed models to analyse athlete`s practice histories, this statistical approach has been applied in other areas of research with similar types of design (see Diggle et al., 2002; Everitt & Rabe-Hesketh, 2006). However, the present study has identified differences in practice histories between players at distinct performance levels and levels of self-regulation, and not whether the conducted practice caused these differences. Also, further investigation of the psychometric properties of the reduced measure of self-regulation is needed to ensure reliable and valid measurement of self-regulation in football.