Exponential regression with correlated observations

The action of antithrombotic drugs can be evaluated by measuring the deposition of111In-labelled platelets on peripheral bypass grafts several days after injection. This evaluation can be performed qualitatively (visual interpretation on the daily images) or quantitatively. Four different methods which calculate the ratio of platelet uptake with a reference region are compared: two methods use a gamma camera and two a detector. A blood sample or the region under the sternal angle are used as reference. The daily ratio of the counts, recorded by a gamma camera in a region of interest covering the graft, and the blood radioactivity interpolated from a platelet survival curve appears to be the most reliable method. The information of all the ratios can be combined in a single thrombogenicity index which reflects the daily rise of a linear or exponential regression versus time.

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ANALISIS MODEL KEBUTUHAN PERGERAKAN PENUMPANG DAN BARANG BANDARA RAHADI OESMAN KETAPANG

Jurnal Teknik Sipil ◽

10.26418/jtsft.v10i1.215 ◽

2012 ◽

Vol 10 (1) ◽

Author(s):

. Elsa Trimukti

Keyword(s):

Growth Rate ◽

Trend Analysis ◽

Polynomial Regression ◽

Air Transport ◽

Trip Generation ◽

Analysis Model ◽

Exponential Regression ◽

Share Model ◽

Strategic Role ◽

Analysis Models

Airport of Rahadi Oesman in Kabupaten Ketapang Kalimantan Barat represent the main and important gate for air transport in Kabupaten Ketapang, where this airport own the strategic role in service activities of this transportation even for domestic transportation or regional. Activity in Airport of Rahadi Oesman in a few this the last year has growth so fast growth, so that felt the infrastructure and also available facility in this time have is not adequate again to support the growth rate of air traffic in this airport. In the plan development of facility of air side and also land side of the airport require to be conducted an analysis model of trip generation or attraction of passenger and goods. These models need for the prediction of mount the growth of passenger and goods/cargo and estimate the amount of passenger and aircraft movement in the future pursuant to aircraft characteristic that to be used. The models used for prediction of passenger and goods in this study are Trend Analysis Models consisted of linear regression trend method, exponential regression trend method, and polynomial regression trend method. Besides model of trend analysis, in this study also analyzed Market Share Model. Result from third model then compared to one another to obtain the most appropriate model. Pursuant to analyses result obtained that the best or most appropriate model is Model of Trend Analysis.Model for the attraction passenger is Y = 21,18X2+ 6181X + 5788 by R2= 0,922.Model for the generation passenger is Y = 128,3X2+ 7515X + 4965 by R2= 0,907.Model for the passenger of transit is Y = 795X2+ 561X + 3361 by R2= 1Model for the cargo movement is Y = 2468X2+ 41054X 28341 by R2= 0,918.

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CO<sub>2</sub> flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

Biogeosciences ◽

10.5194/bg-4-1005-2007 ◽

2007 ◽

Vol 4 (6) ◽

pp. 1005-1025 ◽

Cited By ~ 190

Author(s):

L. Kutzbach ◽

J. Schneider ◽

T. Sachs ◽

M. Giebels ◽

H. Nykänen ◽

...

Keyword(s):

Linear Regression ◽

Nonlinear Regression ◽

Co2 Flux ◽

Exponential Model ◽

Co2 Uptake ◽

Co2 Fluxes ◽

Closed Chamber ◽

Exponential Regression ◽

Closure Time ◽

Over Time

Abstract. Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach has been justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatlands sites in Finland and a tundra site in Siberia. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. However, a rather large percentage of the exponential regression functions showed curvatures not consistent with the theoretical model which is considered to be caused by violations of the underlying model assumptions. Especially the effects of turbulence and pressure disturbances by the chamber deployment are suspected to have caused unexplainable curvatures. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes. The degree of underestimation increased with increasing CO2 flux strength and was dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

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Relationships between test positivity rate, total laboratory confirmed cases of malaria, and malaria incidence in high burden settings of Uganda: an ecological analysis

Malaria Journal ◽

10.1186/s12936-021-03584-7 ◽

2021 ◽

Vol 20 (1) ◽

Author(s):

Jaffer Okiring ◽

Adrienne Epstein ◽

Jane F. Namuganga ◽

Victor Kamya ◽

Asadu Sserwanga ◽

...

Keyword(s):

Regression Models ◽

Malaria Incidence ◽

Temporal Changes ◽

Linear Regression Models ◽

High Burden ◽

Exponential Regression ◽

Malaria Morbidity ◽

Laboratory Test Results ◽

Combining Data ◽

Catchment Areas

Abstract Background Malaria surveillance is critical for monitoring changes in malaria morbidity over time. National Malaria Control Programmes often rely on surrogate measures of malaria incidence, including the test positivity rate (TPR) and total laboratory confirmed cases of malaria (TCM), to monitor trends in malaria morbidity. However, there are limited data on the accuracy of TPR and TCM for predicting temporal changes in malaria incidence, especially in high burden settings. Methods This study leveraged data from 5 malaria reference centres (MRCs) located in high burden settings over a 15-month period from November 2018 through January 2020 as part of an enhanced health facility-based surveillance system established in Uganda. Individual level data were collected from all outpatients including demographics, laboratory test results, and village of residence. Estimates of malaria incidence were derived from catchment areas around the MRCs. Temporal relationships between monthly aggregate measures of TPR and TCM relative to estimates of malaria incidence were examined using linear and exponential regression models. Results A total of 149,739 outpatient visits to the 5 MRCs were recorded. Overall, malaria was suspected in 73.4% of visits, 99.1% of patients with suspected malaria received a diagnostic test, and 69.7% of those tested for malaria were positive. Temporal correlations between monthly measures of TPR and malaria incidence using linear and exponential regression models were relatively poor, with small changes in TPR frequently associated with large changes in malaria incidence. Linear regression models of temporal changes in TCM provided the most parsimonious and accurate predictor of changes in malaria incidence, with adjusted R2 values ranging from 0.81 to 0.98 across the 5 MRCs. However, the slope of the regression lines indicating the change in malaria incidence per unit change in TCM varied from 0.57 to 2.13 across the 5 MRCs, and when combining data across all 5 sites, the R2 value reduced to 0.38. Conclusions In high malaria burden areas of Uganda, site-specific temporal changes in TCM had a strong linear relationship with malaria incidence and were a more useful metric than TPR. However, caution should be taken when comparing changes in TCM across sites.

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On the BIC for determining the number of control points in B-spline surface approximation in case of correlated observations

Journal of Geodetic Science ◽

10.1515/jogs-2020-0110 ◽

2020 ◽

Vol 10 (1) ◽

pp. 110-123

Author(s):

Gaël Kermarrec ◽

Hamza Alkhatib

Keyword(s):

Shape Control ◽

Simple Procedure ◽

Spline Approximation ◽

Autoregressive Process ◽

Optimal Number ◽

Information Criteria ◽

General Effect ◽

Control Points ◽

B Spline ◽

Correlated Observations

Abstract B-spline curves are a linear combination of control points (CP) and B-spline basis functions. They satisfy the strong convex hull property and have a fine and local shape control as changing one CP affects the curve locally, whereas the total number of CP has a more general effect on the control polygon of the spline. Information criteria (IC), such as Akaike IC (AIC) and Bayesian IC (BIC), provide a way to determine an optimal number of CP so that the B-spline approximation fits optimally in a least-squares (LS) sense with scattered and noisy observations. These criteria are based on the log-likelihood of the models and assume often that the error term is independent and identically distributed. This assumption is strong and accounts neither for heteroscedasticity nor for correlations. Thus, such effects have to be considered to avoid under-or overfitting of the observations in the LS adjustment, i.e. bad approximation or noise approximation, respectively. In this contribution, we introduce generalized versions of the BIC derived using the concept of quasi- likelihood estimator (QLE). Our own extensions of the generalized BIC criteria account (i) explicitly for model misspecifications and complexity (ii) and additionally for the correlations of the residuals. To that aim, the correlation model of the residuals is assumed to correspond to a first order autoregressive process AR(1). We apply our general derivations to the specific case of B-spline approximations of curves and surfaces, and couple the information given by the different IC together. Consecutively, a didactical yet simple procedure to interpret the results given by the IC is provided in order to identify an optimal number of parameters to estimate in case of correlated observations. A concrete case study using observations from a bridge scanned with a Terrestrial Laser Scanner (TLS) highlights the proposed procedure.

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