Bayesian information criterion accounting for the number of covariance parameters in mixed effects models

Heo, Junoh; Lee, Jung Yeon; Kim, Wonkuk

doi:10.29220/csam.2020.27.3.301

Cited by 4 publications

(7 citation statements)

References 22 publications

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“…Third, the study used the Akaike Information Criterion (AIC) to complement the evaluation of how well the regression models fit the data they are generated from [69][70][71]. According to the AIC, the best-fit model is the one that explains the highest amount of disparity using the fewest possible independent variables [ibid].…”

Section: Plos Sustainability and Transformationmentioning

confidence: 99%

“…So if two models explain the same amount of disparity, the one with fewer parameters will have a lower AIC score and will be the better-fit of the PLOS SUSTAINABILITY AND TRANSFORMATION model. The basic formula for AIC, is defined as in Eq 11 [69].…”

Section: Plos Sustainability and Transformationmentioning

confidence: 99%

“…This is usually obtained from statistical output. For small sample sizes, n K <� 40 À � , the second-order AIC is used (Eq 12) [69].…”

Section: Plos Sustainability and Transformationmentioning

confidence: 99%

“…According to Heo et al [69], an alternative formula for least squares regression type analyses for normally distributed errors is given in Eq 13, where n is the sample size, and K as defined previously in Eq 11.…”

Section: Plos Sustainability and Transformationmentioning

confidence: 99%

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Trade, GDP value adding activities and income inequality in the East African community

Kadigi

2022

PLOS Sustain Transform

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This paper investigates the extent to which the East African Community (EAC) countries have developed economically over time and whether income inequality decreases with economic growth. The relationship between trade and GDP per capita amongst EAC member countries is evaluated using the World Bank’s meta-data of development indicators and the EAC Secretariat’s data spanning from 2000–2019. Convergence in GDP per capita and inequality are tested using Coefficient of variation (CV) and weighted beta. The results show that agriculture, manufacturing, trade and repair, construction, and transport and storage constituted the top five GDP value adding activities, contributing about 38 percent to total annual GDP. The EAC GDP per capita were diverging in the long run but converging in short to medium terms, implying increase and decrease in the regional income inequality respectively. Agriculture, electricity and gas, transport and storage, real estate activities, public administration, and education were income inequality-increasing sectors. Together with finance and insurance, these sectors were also positively associated with GDP per capita. The exports of EAC member countries were found to be highly concentrated in few sectors and destination markets, implying limited diversification of products and markets. In their quest to diversify, these countries should choose the right mixes of export goods and services keeping in view of the prevailing market factors in importing countries, such as, changing taste and demands.

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Section: Plos Sustainability and Transformationmentioning

confidence: 99%

Section: Plos Sustainability and Transformationmentioning

confidence: 99%

“…This is usually obtained from statistical output. For small sample sizes, n K <� 40 À � , the second-order AIC is used (Eq 12) [69].…”

Section: Plos Sustainability and Transformationmentioning

confidence: 99%

Section: Plos Sustainability and Transformationmentioning

confidence: 99%

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Trade, GDP value adding activities and income inequality in the East African community

Kadigi

2022

PLOS Sustain Transform

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“…Although this sheds light on the importance of using the appropriate effective sample size for the level‐specific fixed effects, its results are not extended to more general situations (e.g., models with random slopes). In an unpublished paper, Shen and González (2021) advocated for the use of the sum of all entries of the inverse correlation matrix of the parameter estimates as the effective sample size. However, a proof of this was not provided.…”

Section: Introductionmentioning

confidence: 99%

The effective sample size in Bayesian information criterion for level‐specific fixed and random‐effect selection in a two‐level nested model

Cho,

Wu,

Naveiras

2023

Brit J Math & Statis

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Popular statistical software provides the Bayesian information criterion (BIC) for multi‐level models or linear mixed models. However, it has been observed that the combination of statistical literature and software documentation has led to discrepancies in the formulas of the BIC and uncertainties as to the proper use of the BIC in selecting a multi‐level model with respect to level‐specific fixed and random effects. These discrepancies and uncertainties result from different specifications of sample size in the BIC's penalty term for multi‐level models. In this study, we derive the BIC's penalty term for level‐specific fixed‐ and random‐effect selection in a two‐level nested design. In this new version of BIC, called , this penalty term is decomposed into two parts if the random‐effect variance–covariance matrix has full rank: (a) a term with the log of average sample size per cluster and (b) the total number of parameters times the log of the total number of clusters. Furthermore, we derive the new version of BIC, called , in the presence of redundant random effects. We show that the derived formulae, and , adhere to empirical values via numerical demonstration and that ( indicating either or ) is the best global selection criterion, as it performs at least as well as BIC with the total sample size and BIC with the number of clusters across various multi‐level conditions through a simulation study. In addition, the use of is illustrated with a textbook example dataset.

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Genetic association analysis in sugarcane (Saccharum spp.) for sucrose accumulation in humid environments in Colombia

Saavedra-Díaz,

Trujillo-Montenegro,

Jaimes

et al. 2024

BMC Plant Biol

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Background Sucrose accumulation in sugarcane is affected by several environmental and genetic factors, with plant moisture being of critical importance for its role in the synthesis and transport of sugars within the cane stalks, affecting the sucrose concentration. In general, rainfall and high soil humidity during the ripening stage promote plant growth, increasing the fresh weight and decreasing the sucrose yield in the humid region of Colombia. Therefore, this study aimed to identify markers associated with sucrose accumulation or production in the humid environment of Colombia through a genome-wide association study (GWAS). Results Sucrose concentration measurements were taken in 220 genotypes from the Cenicaña’s diverse panel at 10 (early maturity) and 13 (normal maturity) months after planting. For early maturity data was collected during plant cane and first ratoon, while at normal maturity it was during plant cane, first, and second ratoon. A total of 137,890 SNPs were selected after sequencing the 220 genotypes through GBS, RADSeq, and whole-genome sequencing. After GWAS analysis, a total of 77 markers were significantly associated with sucrose concentration at both ages, but only 39 were close to candidate genes previously reported for sucrose accumulation and/or production. Among the candidate genes, 18 were highlighted because they were involved in sucrose hydrolysis (SUS6, CIN3, CINV1, CINV2), sugar transport (i.e., MST1, MST2, PLT5, SUT4, ERD6 like), phosphorylation processes (TPS genes), glycolysis (PFP-ALPHA, HXK3, PHI1), and transcription factors (ERF12, ERF112). Similarly, 64 genes were associated with glycosyltransferases, glycosidases, and hormones. Conclusions These results provide new insights into the molecular mechanisms involved in sucrose accumulation in sugarcane and contribute with important genomic resources for future research in the humid environments of Colombia. Similarly, the markers identified will be validated for their potential application within Cenicaña’s breeding program to assist the development of breeding populations.

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Bayesian information criterion accounting for the number of covariance parameters in mixed effects models

Cited by 4 publications

References 22 publications

Trade, GDP value adding activities and income inequality in the East African community

Trade, GDP value adding activities and income inequality in the East African community

The effective sample size in Bayesian information criterion for level‐specific fixed and random‐effect selection in a two‐level nested model

Genetic association analysis in sugarcane (Saccharum spp.) for sucrose accumulation in humid environments in Colombia

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