Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study

The Poisson distribution is commonly assumed as the error structure for count data; however, empirical data may exhibit greater variability than expected based on a given statistical model. Greater variability could point to model misspecification, such as missing crucial information about the epidemiology of the disease or changes in population behavior. When the mechanism producing the apparent overdispersion is unknown, it is typically assumed that the variance in the data exceeds the mean (by some scaling factor). Thus, a probability distribution that allows for overdispersion (negative binomial, for example) may better represent the data. Here, we utilize simulation studies to assess how misspecifying the error structure affects parameter estimation results, specifically bias and uncertainty, as a function of the level of random noise in the data. We compare results for two parameter estimation methods: nonlinear least squares and maximum likelihood estimation with Poisson error structure. We analyze two phenomenological models the generalized growth model and generalized logistic growth model to assess how results of parameter estimation are affected by the level of overdispersion underlying in the data. We use simulation to obtain confidence intervals and mean squared error of parameter estimates. We also analyze the impact of the amount of data, or ascending phase length, on the results of the generalized growth model for increasing levels of overdispersion. The results show a clear pattern of increasing uncertainty, or confidence interval width, as the overdispersion in the data increases. While maximum likelihood estimation consistently yields narrower confidence intervals and smaller mean squared error, differences between the two methods were minimal and not practically significant. At moderate levels of overdispersion, both estimation methods yielded similar performance. Importantly, it is shown that issues of parameter uncertainty and bias in the presence of overdispersion can be mitigated with the inclusion of more data. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Kimberlyn Roosa [verfasserIn] Ruiyan Luo [verfasserIn] Gerardo Chowell [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	parameter uncertainty overdispersion phenomenological models generalized growth model epidemiological models parameter estimation

Übergeordnetes Werk:	In: Mathematical Biosciences and Engineering - AIMS Press, 2020, 16(2019), 5, Seite 4299-4313
Übergeordnetes Werk:	volume:16 ; year:2019 ; number:5 ; pages:4299-4313

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3934/mbe.2019214

Katalog-ID:	DOAJ064464342

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allfields	10.3934/mbe.2019214 doi (DE-627)DOAJ064464342 (DE-599)DOAJ8f5f8970b4cf4546b8ef5e6c7c9d4d6d DE-627 ger DE-627 rakwb eng TP248.13-248.65 QA1-939 Kimberlyn Roosa verfasserin aut Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The Poisson distribution is commonly assumed as the error structure for count data; however, empirical data may exhibit greater variability than expected based on a given statistical model. Greater variability could point to model misspecification, such as missing crucial information about the epidemiology of the disease or changes in population behavior. When the mechanism producing the apparent overdispersion is unknown, it is typically assumed that the variance in the data exceeds the mean (by some scaling factor). Thus, a probability distribution that allows for overdispersion (negative binomial, for example) may better represent the data. Here, we utilize simulation studies to assess how misspecifying the error structure affects parameter estimation results, specifically bias and uncertainty, as a function of the level of random noise in the data. We compare results for two parameter estimation methods: nonlinear least squares and maximum likelihood estimation with Poisson error structure. We analyze two phenomenological models the generalized growth model and generalized logistic growth model to assess how results of parameter estimation are affected by the level of overdispersion underlying in the data. We use simulation to obtain confidence intervals and mean squared error of parameter estimates. We also analyze the impact of the amount of data, or ascending phase length, on the results of the generalized growth model for increasing levels of overdispersion. The results show a clear pattern of increasing uncertainty, or confidence interval width, as the overdispersion in the data increases. While maximum likelihood estimation consistently yields narrower confidence intervals and smaller mean squared error, differences between the two methods were minimal and not practically significant. At moderate levels of overdispersion, both estimation methods yielded similar performance. Importantly, it is shown that issues of parameter uncertainty and bias in the presence of overdispersion can be mitigated with the inclusion of more data. parameter uncertainty overdispersion phenomenological models generalized growth model epidemiological models parameter estimation Biotechnology Mathematics Ruiyan Luo verfasserin aut Gerardo Chowell verfasserin aut In Mathematical Biosciences and Engineering AIMS Press, 2020 16(2019), 5, Seite 4299-4313 (DE-627)522894844 (DE-600)2265126-3 15510018 nnns volume:16 year:2019 number:5 pages:4299-4313 https://doi.org/10.3934/mbe.2019214 kostenfrei https://doaj.org/article/8f5f8970b4cf4546b8ef5e6c7c9d4d6d kostenfrei https://www.aimspress.com/article/doi/10.3934/mbe.2019214?viewType=HTML kostenfrei https://doaj.org/toc/1551-0018 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 16 2019 5 4299-4313
spelling	10.3934/mbe.2019214 doi (DE-627)DOAJ064464342 (DE-599)DOAJ8f5f8970b4cf4546b8ef5e6c7c9d4d6d DE-627 ger DE-627 rakwb eng TP248.13-248.65 QA1-939 Kimberlyn Roosa verfasserin aut Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The Poisson distribution is commonly assumed as the error structure for count data; however, empirical data may exhibit greater variability than expected based on a given statistical model. Greater variability could point to model misspecification, such as missing crucial information about the epidemiology of the disease or changes in population behavior. When the mechanism producing the apparent overdispersion is unknown, it is typically assumed that the variance in the data exceeds the mean (by some scaling factor). Thus, a probability distribution that allows for overdispersion (negative binomial, for example) may better represent the data. Here, we utilize simulation studies to assess how misspecifying the error structure affects parameter estimation results, specifically bias and uncertainty, as a function of the level of random noise in the data. We compare results for two parameter estimation methods: nonlinear least squares and maximum likelihood estimation with Poisson error structure. We analyze two phenomenological models the generalized growth model and generalized logistic growth model to assess how results of parameter estimation are affected by the level of overdispersion underlying in the data. We use simulation to obtain confidence intervals and mean squared error of parameter estimates. We also analyze the impact of the amount of data, or ascending phase length, on the results of the generalized growth model for increasing levels of overdispersion. The results show a clear pattern of increasing uncertainty, or confidence interval width, as the overdispersion in the data increases. While maximum likelihood estimation consistently yields narrower confidence intervals and smaller mean squared error, differences between the two methods were minimal and not practically significant. At moderate levels of overdispersion, both estimation methods yielded similar performance. Importantly, it is shown that issues of parameter uncertainty and bias in the presence of overdispersion can be mitigated with the inclusion of more data. parameter uncertainty overdispersion phenomenological models generalized growth model epidemiological models parameter estimation Biotechnology Mathematics Ruiyan Luo verfasserin aut Gerardo Chowell verfasserin aut In Mathematical Biosciences and Engineering AIMS Press, 2020 16(2019), 5, Seite 4299-4313 (DE-627)522894844 (DE-600)2265126-3 15510018 nnns volume:16 year:2019 number:5 pages:4299-4313 https://doi.org/10.3934/mbe.2019214 kostenfrei https://doaj.org/article/8f5f8970b4cf4546b8ef5e6c7c9d4d6d kostenfrei https://www.aimspress.com/article/doi/10.3934/mbe.2019214?viewType=HTML kostenfrei https://doaj.org/toc/1551-0018 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 16 2019 5 4299-4313
allfields_unstemmed	10.3934/mbe.2019214 doi (DE-627)DOAJ064464342 (DE-599)DOAJ8f5f8970b4cf4546b8ef5e6c7c9d4d6d DE-627 ger DE-627 rakwb eng TP248.13-248.65 QA1-939 Kimberlyn Roosa verfasserin aut Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The Poisson distribution is commonly assumed as the error structure for count data; however, empirical data may exhibit greater variability than expected based on a given statistical model. Greater variability could point to model misspecification, such as missing crucial information about the epidemiology of the disease or changes in population behavior. When the mechanism producing the apparent overdispersion is unknown, it is typically assumed that the variance in the data exceeds the mean (by some scaling factor). Thus, a probability distribution that allows for overdispersion (negative binomial, for example) may better represent the data. Here, we utilize simulation studies to assess how misspecifying the error structure affects parameter estimation results, specifically bias and uncertainty, as a function of the level of random noise in the data. We compare results for two parameter estimation methods: nonlinear least squares and maximum likelihood estimation with Poisson error structure. We analyze two phenomenological models the generalized growth model and generalized logistic growth model to assess how results of parameter estimation are affected by the level of overdispersion underlying in the data. We use simulation to obtain confidence intervals and mean squared error of parameter estimates. We also analyze the impact of the amount of data, or ascending phase length, on the results of the generalized growth model for increasing levels of overdispersion. The results show a clear pattern of increasing uncertainty, or confidence interval width, as the overdispersion in the data increases. While maximum likelihood estimation consistently yields narrower confidence intervals and smaller mean squared error, differences between the two methods were minimal and not practically significant. At moderate levels of overdispersion, both estimation methods yielded similar performance. Importantly, it is shown that issues of parameter uncertainty and bias in the presence of overdispersion can be mitigated with the inclusion of more data. parameter uncertainty overdispersion phenomenological models generalized growth model epidemiological models parameter estimation Biotechnology Mathematics Ruiyan Luo verfasserin aut Gerardo Chowell verfasserin aut In Mathematical Biosciences and Engineering AIMS Press, 2020 16(2019), 5, Seite 4299-4313 (DE-627)522894844 (DE-600)2265126-3 15510018 nnns volume:16 year:2019 number:5 pages:4299-4313 https://doi.org/10.3934/mbe.2019214 kostenfrei https://doaj.org/article/8f5f8970b4cf4546b8ef5e6c7c9d4d6d kostenfrei https://www.aimspress.com/article/doi/10.3934/mbe.2019214?viewType=HTML kostenfrei https://doaj.org/toc/1551-0018 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 16 2019 5 4299-4313
allfieldsGer	10.3934/mbe.2019214 doi (DE-627)DOAJ064464342 (DE-599)DOAJ8f5f8970b4cf4546b8ef5e6c7c9d4d6d DE-627 ger DE-627 rakwb eng TP248.13-248.65 QA1-939 Kimberlyn Roosa verfasserin aut Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The Poisson distribution is commonly assumed as the error structure for count data; however, empirical data may exhibit greater variability than expected based on a given statistical model. Greater variability could point to model misspecification, such as missing crucial information about the epidemiology of the disease or changes in population behavior. When the mechanism producing the apparent overdispersion is unknown, it is typically assumed that the variance in the data exceeds the mean (by some scaling factor). Thus, a probability distribution that allows for overdispersion (negative binomial, for example) may better represent the data. Here, we utilize simulation studies to assess how misspecifying the error structure affects parameter estimation results, specifically bias and uncertainty, as a function of the level of random noise in the data. We compare results for two parameter estimation methods: nonlinear least squares and maximum likelihood estimation with Poisson error structure. We analyze two phenomenological models the generalized growth model and generalized logistic growth model to assess how results of parameter estimation are affected by the level of overdispersion underlying in the data. We use simulation to obtain confidence intervals and mean squared error of parameter estimates. We also analyze the impact of the amount of data, or ascending phase length, on the results of the generalized growth model for increasing levels of overdispersion. The results show a clear pattern of increasing uncertainty, or confidence interval width, as the overdispersion in the data increases. While maximum likelihood estimation consistently yields narrower confidence intervals and smaller mean squared error, differences between the two methods were minimal and not practically significant. At moderate levels of overdispersion, both estimation methods yielded similar performance. Importantly, it is shown that issues of parameter uncertainty and bias in the presence of overdispersion can be mitigated with the inclusion of more data. parameter uncertainty overdispersion phenomenological models generalized growth model epidemiological models parameter estimation Biotechnology Mathematics Ruiyan Luo verfasserin aut Gerardo Chowell verfasserin aut In Mathematical Biosciences and Engineering AIMS Press, 2020 16(2019), 5, Seite 4299-4313 (DE-627)522894844 (DE-600)2265126-3 15510018 nnns volume:16 year:2019 number:5 pages:4299-4313 https://doi.org/10.3934/mbe.2019214 kostenfrei https://doaj.org/article/8f5f8970b4cf4546b8ef5e6c7c9d4d6d kostenfrei https://www.aimspress.com/article/doi/10.3934/mbe.2019214?viewType=HTML kostenfrei https://doaj.org/toc/1551-0018 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 16 2019 5 4299-4313
allfieldsSound	10.3934/mbe.2019214 doi (DE-627)DOAJ064464342 (DE-599)DOAJ8f5f8970b4cf4546b8ef5e6c7c9d4d6d DE-627 ger DE-627 rakwb eng TP248.13-248.65 QA1-939 Kimberlyn Roosa verfasserin aut Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The Poisson distribution is commonly assumed as the error structure for count data; however, empirical data may exhibit greater variability than expected based on a given statistical model. Greater variability could point to model misspecification, such as missing crucial information about the epidemiology of the disease or changes in population behavior. When the mechanism producing the apparent overdispersion is unknown, it is typically assumed that the variance in the data exceeds the mean (by some scaling factor). Thus, a probability distribution that allows for overdispersion (negative binomial, for example) may better represent the data. Here, we utilize simulation studies to assess how misspecifying the error structure affects parameter estimation results, specifically bias and uncertainty, as a function of the level of random noise in the data. We compare results for two parameter estimation methods: nonlinear least squares and maximum likelihood estimation with Poisson error structure. We analyze two phenomenological models the generalized growth model and generalized logistic growth model to assess how results of parameter estimation are affected by the level of overdispersion underlying in the data. We use simulation to obtain confidence intervals and mean squared error of parameter estimates. We also analyze the impact of the amount of data, or ascending phase length, on the results of the generalized growth model for increasing levels of overdispersion. The results show a clear pattern of increasing uncertainty, or confidence interval width, as the overdispersion in the data increases. While maximum likelihood estimation consistently yields narrower confidence intervals and smaller mean squared error, differences between the two methods were minimal and not practically significant. At moderate levels of overdispersion, both estimation methods yielded similar performance. Importantly, it is shown that issues of parameter uncertainty and bias in the presence of overdispersion can be mitigated with the inclusion of more data. parameter uncertainty overdispersion phenomenological models generalized growth model epidemiological models parameter estimation Biotechnology Mathematics Ruiyan Luo verfasserin aut Gerardo Chowell verfasserin aut In Mathematical Biosciences and Engineering AIMS Press, 2020 16(2019), 5, Seite 4299-4313 (DE-627)522894844 (DE-600)2265126-3 15510018 nnns volume:16 year:2019 number:5 pages:4299-4313 https://doi.org/10.3934/mbe.2019214 kostenfrei https://doaj.org/article/8f5f8970b4cf4546b8ef5e6c7c9d4d6d kostenfrei https://www.aimspress.com/article/doi/10.3934/mbe.2019214?viewType=HTML kostenfrei https://doaj.org/toc/1551-0018 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 16 2019 5 4299-4313
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callnumber-first	T - Technology
author	Kimberlyn Roosa
spellingShingle	Kimberlyn Roosa misc TP248.13-248.65 misc QA1-939 misc parameter uncertainty misc overdispersion misc phenomenological models misc generalized growth model misc epidemiological models misc parameter estimation misc Biotechnology misc Mathematics Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study
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topic_title	TP248.13-248.65 QA1-939 Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study parameter uncertainty overdispersion phenomenological models generalized growth model epidemiological models parameter estimation
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title	Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study
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title_sort	comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study
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title_auth	Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study
abstract	The Poisson distribution is commonly assumed as the error structure for count data; however, empirical data may exhibit greater variability than expected based on a given statistical model. Greater variability could point to model misspecification, such as missing crucial information about the epidemiology of the disease or changes in population behavior. When the mechanism producing the apparent overdispersion is unknown, it is typically assumed that the variance in the data exceeds the mean (by some scaling factor). Thus, a probability distribution that allows for overdispersion (negative binomial, for example) may better represent the data. Here, we utilize simulation studies to assess how misspecifying the error structure affects parameter estimation results, specifically bias and uncertainty, as a function of the level of random noise in the data. We compare results for two parameter estimation methods: nonlinear least squares and maximum likelihood estimation with Poisson error structure. We analyze two phenomenological models the generalized growth model and generalized logistic growth model to assess how results of parameter estimation are affected by the level of overdispersion underlying in the data. We use simulation to obtain confidence intervals and mean squared error of parameter estimates. We also analyze the impact of the amount of data, or ascending phase length, on the results of the generalized growth model for increasing levels of overdispersion. The results show a clear pattern of increasing uncertainty, or confidence interval width, as the overdispersion in the data increases. While maximum likelihood estimation consistently yields narrower confidence intervals and smaller mean squared error, differences between the two methods were minimal and not practically significant. At moderate levels of overdispersion, both estimation methods yielded similar performance. Importantly, it is shown that issues of parameter uncertainty and bias in the presence of overdispersion can be mitigated with the inclusion of more data.
abstractGer	The Poisson distribution is commonly assumed as the error structure for count data; however, empirical data may exhibit greater variability than expected based on a given statistical model. Greater variability could point to model misspecification, such as missing crucial information about the epidemiology of the disease or changes in population behavior. When the mechanism producing the apparent overdispersion is unknown, it is typically assumed that the variance in the data exceeds the mean (by some scaling factor). Thus, a probability distribution that allows for overdispersion (negative binomial, for example) may better represent the data. Here, we utilize simulation studies to assess how misspecifying the error structure affects parameter estimation results, specifically bias and uncertainty, as a function of the level of random noise in the data. We compare results for two parameter estimation methods: nonlinear least squares and maximum likelihood estimation with Poisson error structure. We analyze two phenomenological models the generalized growth model and generalized logistic growth model to assess how results of parameter estimation are affected by the level of overdispersion underlying in the data. We use simulation to obtain confidence intervals and mean squared error of parameter estimates. We also analyze the impact of the amount of data, or ascending phase length, on the results of the generalized growth model for increasing levels of overdispersion. The results show a clear pattern of increasing uncertainty, or confidence interval width, as the overdispersion in the data increases. While maximum likelihood estimation consistently yields narrower confidence intervals and smaller mean squared error, differences between the two methods were minimal and not practically significant. At moderate levels of overdispersion, both estimation methods yielded similar performance. Importantly, it is shown that issues of parameter uncertainty and bias in the presence of overdispersion can be mitigated with the inclusion of more data.
abstract_unstemmed	The Poisson distribution is commonly assumed as the error structure for count data; however, empirical data may exhibit greater variability than expected based on a given statistical model. Greater variability could point to model misspecification, such as missing crucial information about the epidemiology of the disease or changes in population behavior. When the mechanism producing the apparent overdispersion is unknown, it is typically assumed that the variance in the data exceeds the mean (by some scaling factor). Thus, a probability distribution that allows for overdispersion (negative binomial, for example) may better represent the data. Here, we utilize simulation studies to assess how misspecifying the error structure affects parameter estimation results, specifically bias and uncertainty, as a function of the level of random noise in the data. We compare results for two parameter estimation methods: nonlinear least squares and maximum likelihood estimation with Poisson error structure. We analyze two phenomenological models the generalized growth model and generalized logistic growth model to assess how results of parameter estimation are affected by the level of overdispersion underlying in the data. We use simulation to obtain confidence intervals and mean squared error of parameter estimates. We also analyze the impact of the amount of data, or ascending phase length, on the results of the generalized growth model for increasing levels of overdispersion. The results show a clear pattern of increasing uncertainty, or confidence interval width, as the overdispersion in the data increases. While maximum likelihood estimation consistently yields narrower confidence intervals and smaller mean squared error, differences between the two methods were minimal and not practically significant. At moderate levels of overdispersion, both estimation methods yielded similar performance. Importantly, it is shown that issues of parameter uncertainty and bias in the presence of overdispersion can be mitigated with the inclusion of more data.
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title_short	Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study
url	https://doi.org/10.3934/mbe.2019214 https://doaj.org/article/8f5f8970b4cf4546b8ef5e6c7c9d4d6d https://www.aimspress.com/article/doi/10.3934/mbe.2019214?viewType=HTML https://doaj.org/toc/1551-0018
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We analyze two phenomenological models the generalized growth model and generalized logistic growth model to assess how results of parameter estimation are affected by the level of overdispersion underlying in the data. We use simulation to obtain confidence intervals and mean squared error of parameter estimates. We also analyze the impact of the amount of data, or ascending phase length, on the results of the generalized growth model for increasing levels of overdispersion. The results show a clear pattern of increasing uncertainty, or confidence interval width, as the overdispersion in the data increases. While maximum likelihood estimation consistently yields narrower confidence intervals and smaller mean squared error, differences between the two methods were minimal and not practically significant. At moderate levels of overdispersion, both estimation methods yielded similar performance. 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Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study

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