Factorial Designs

2021 ◽  
pp. 139-160
Author(s):  
Andy Hector

This chapter moves on from simple ‘one-way’ designs to more complex factorial designs. It extends the simple linear model to include interactions as well as average main effects. Interactions are assessed relative to a null additive expectation where the treatments have no effect on each other. Interactions can be positive, when effects are more than additive, or negative, when they are less than expected. The chapter considers in detail the analysis of an example data set concerning the mechanisms of loss of plant diversity following fertilizer treatment.

1995 ◽  
Vol 22 (3) ◽  
pp. 207-208 ◽  
Author(s):  
Michael J. Strube ◽  
Miriam D. Goldstein

This article describes a QuickBASIC program for demonstrating the difference between main effects and interactions in factorial designs. The program guides the student through the construction of data patterns corresponding to different combinations of the main effects and the interaction in a 2 times 2 design. Program feedback provides tailored guidance to help students produce the requested patterns of means. The program also generates ideal solutions for comparison. To simulate actual experience, the program generates a data set (N = 80) for each constructed pattern of means and calculates the tests of significance for the main effects and interaction. The program can be used in conjunction with a traditional lecture on factorial designs to improve student understanding of main effects and interactions and to develop student skill in recognizing main effects and interactions from graphical displays.


2021 ◽  
pp. 096228022110028
Author(s):  
T Baghfalaki ◽  
M Ganjali

Joint modeling of zero-inflated count and time-to-event data is usually performed by applying the shared random effect model. This kind of joint modeling can be considered as a latent Gaussian model. In this paper, the approach of integrated nested Laplace approximation (INLA) is used to perform approximate Bayesian approach for the joint modeling. We propose a zero-inflated hurdle model under Poisson or negative binomial distributional assumption as sub-model for count data. Also, a Weibull model is used as survival time sub-model. In addition to the usual joint linear model, a joint partially linear model is also considered to take into account the non-linear effect of time on the longitudinal count response. The performance of the method is investigated using some simulation studies and its achievement is compared with the usual approach via the Bayesian paradigm of Monte Carlo Markov Chain (MCMC). Also, we apply the proposed method to analyze two real data sets. The first one is the data about a longitudinal study of pregnancy and the second one is a data set obtained of a HIV study.


2021 ◽  
Author(s):  
Kevin Bellinguer ◽  
Robin Girard ◽  
Guillaume Bontron ◽  
Georges Kariniotakis

<div> <p>In recent years, the share of photovoltaic (PV) power in Europe has grown: the installed capacity increased from around 10 GW in 2008 to nearly 119 GW in 2018 [1]. Due to the intermittent nature of PV generation, new challenges arise regarding economic profitability and the safe operation of the power network. To overcome these issues, a special effort is made to develop efficient PV generation forecasting tools.</p> <p> </p> <p>For short-term PV production forecasting, past production observations are typically the main drivers. In addition, spatio-temporal (ST) inputs such as Satellite-Derived Surface Irradiance (SDSI) provide relevant information regarding the weather situation in the vicinity of the farm. Moreover, the literature shows us that Numerical Weather Predictions (NWPs) provide relevant information regarding weather trends.</p> <p> </p> <p>NWPs can be integrated in the forecasting process in two different ways. The most straightforward approach considers NWPs as explanatory input variables to the forecasting models. Thus, the atmosphere dynamics are directly carried by the NWPs. The alternative considers NWPs as state variables: weather information is used to filter the training data set to obtain a coherent subset of PV production observations measured under similar weather conditions as the PV production to be predicted. This approach is based on analog methods and makes the weather dynamics to be implicitly contained in the PV production observations. This conditioned learning approach permits to perform local regressions and is adaptive in the sense that the model training is conditioned to the weather situation.</p> <p>The specialized literature focuses on spot NWPs which permits to find situations that evolve in the same way but does not preserve ST patterns. In this context, the addition of SDSI features cannot make the most of the conditioning process. Ref. [3] proposes to use geopotential fields, which are wind drivers, as analog predictors.</p> <p> </p> <p>In this work, we propose the following contributions to the state of the art:</p> <p>We investigate the influence of spot NWPs on the performances of an auto-regressive (AR) and a random forest models according to the two above-mentioned approaches: either as additional explanatory features and/or as analog features. The analogy score proposed by [2] is used to find similar weather situations, then the model is trained over the associated PV production observations. The results highlight that the linear model performs better with the conditioned approach while the non-linear model obtains better performances when fed with explanatory features.</p> <p>Then, the similarity score is extended to gridded NWPs data through the use of a principal component analysis. This method allows to condition the learning to large-scale weather information. A comparison between spot and gridded NWPs conditioned approaches applied with AR model highlights that gridded NWPs improves the influence of SDSI over forecasting performances.</p> <p> </p> <p>The proposed approaches are evaluated using 9 PV plants in France and for a testing period of 12 months.</p> <p> </p> <strong>References</strong> <p>[1]      IRENA - https://www.irena.org/Statistics/Download-Data</p> <p>[2]      Alessandrini, Delle Monache, et al. An analog ensemble for short-term probabilistic solar power forecast. Applied Energy, 2015. https://doi.org/10.1016/j.apenergy.2015.08.011</p> <p>[3]      Bellinguer, Girard, Bontron, Kariniotakis. Short-term Forecasting of Photovoltaic Generation based on Conditioned Learning of Geopotential Fields. 2020, UPEC. https://doi.org/10.1109/UPEC49904.2020.9209858</p> </div>


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