Demographic modelling of health utilities using generalised linear models: an actuarial approach to cost-effectiveness

CHAPTER II: Analysis of variance (ANOVA) is one of the most important statistical models applied in agronomic experiments, especially in the seeds area. Based on strong assumptions, it lasted for many years with the support of techniques such as data transformation. As ANOVA being a special case of Generalized Linear Models (GLM), a classic experiment of seeds germination of tree species Copaifera langsdorffii Desf. can show the mirroring between both methods of analysis, and this is one of the goals of this research. It also aimed to compare the quality of the adjustment and the efficiency of the models for the germination, expressed in percentage with Normal distribution and number of germinated seeds with Binomial distribution. To meet these objectives, seeds of C. langsdorffii were arranged in a completely randomized design with four replications of 25 seeds in a 4 x 3 factorial scheme, in which the first factor refers to the methods to overcome dormancy (M1, M2, M3 and M4) and the second effect is related to samples (A1, A2 and A3). For the results expressed in percentage of germination, the assumptions of normality and independence of residuals and homoscedasticity were tested by Shapiro-Wilk, Durbin-Watson and Levene, respectively. Then, it was applied an ANOVA model, as well as GLM with Normal distribution and identity link function. About the data expressed as number of germinated seeds, GLM was performed with Binomial distribution and logistics link function. For both distributions, the quality of the adjustment was determined by Akaike information criterion (AIC) and Bayesian information criterion (BIC), Cook s distance and q-q plot analysis. As expected, ANOVA model was equal to GLM with Normal distribution for the percentage of copaiba seed germination, and they indicated a significant effect of sample and interaction, as a previous analysis confirmed that all assumptions of the model were held. The GLM with Binomial distribution had the same significance of the effects as the Normal GLM. However, AIC and BIC indicated that Binomial model was better adjusted to data, and the accommodation of values to the simulated envelope with 95% confidence was greater. Cook s distance did not discriminate the models, since they approached to the same amount of influential points. CHAPTER III: Seed germination experiments are constantly analyzed using ANOVA, but it is also faced the problem of not holding the assumptions; when these ones are violated, the reliability of all parametric tests is compromised. To solve this problem, some authors suggest angular transformation of the data, as in many other cases the use of this technique with no care. Another suggested alternative, with less impact to the data, is the application of statistics methodologies that do not need to answer these assumptions. Among the existing methodologies, Generalized Linear Models (GLM) stands out. Despite the common representation of the number of germinated seeds in percentage, the original nature of data is discrete and follows all the criteria of Binomial distribution. Thus, GLM emerge as an alternative to solve ANOVA restrictions and to bring different statistical techniques, allowing a better data processing. GLM are poorly known in agronomy, and there are not works to the seed analysis that investigate the applicability and the adjustment of this technique, comparing to ANOVA and data transformation. In this way, the objective of this study was to compare the GLM methodology with ANOVA by checking the impact caused by them within seed germination variable. It was also aimed to apply the data transformation and compares it to GLM, checking which the best one for the studied data is. Statistical analysis focused on the characteristic of normal seedlings obtained from the process of validation of methods for germination test of 50 forest species seeds. ANOVA is a part of GLM, and its incorporation was made assuming the Normal distribution of random component and the identity link function. The number of normal seedlings followed a Binomial distribution, corresponding to the event of success with a logistic link function for this GLM. Only 41% of species that hold the assumptions and 22% of those which did not had the same interpretation about the effects of the factors, which proves that the analysis change within GLM was radical even for species that attended the assumptions. Registrations of AIC can conclude that the Binomial model with logit function was more harmonious for the data set and have fewer parameters to explain the variation, which made it a more parsimonious model. Normal plots graphics allude to a better linearity of the residuals from Binomial distribution data. The angular transformation was able to correct the problems in a completely meeting the assumptions in only ten species, in relation to the 23 that were studied. It proves that the application of GLM with an immediately Binomial distribution was essential for 13 of them.

Mapping disease-specific measures onto generic preference-based indexes allows estimating utility values in specific conditions to determine gain of quality-adjusted-life-years when the status of condition varies. The aim of this study was to map a disease specific scale, the Overactive Bladder Questionnaire 5-dimensional health classification system (OAB-5D) derived from the Overactive Bladder questionnaire-Short Form (OABq-SF), onto a preference-based scale, the EuroQol-5D (EQ-5D), in a sample of patients with overactive bladder (OAB) in a Spanish population. A survey addressed to value the health states was conducted among 246 patients at 18 clinics of urology from Spain. A total of 43 out of 243 possible health states have been valued, using VAS (Visual Analog Scale) and TTO (time trade-off) techniques. In addition, ordinary least squares (OLS), generalized linear models (GLM) and Tobit models were estimated. Resulting models were compared and the best one was selected in terms of goodness of fit measures, attribute sign, coefficient magnitude, and statistical significance of regression coefficients. Finally, the internal validity of the best model was calculated by bootstrap resampling. The best model to map the OAB-5D onto EQ-5D could be estimated and the stability of parameter estimations was proved. The mentioned model estimated through OLS regression attained R (2) value of 0.892, with the aggregated data; with GLM (efficient maximum likelihood regression), Pearson χ (2) of 15.3 has been obtained; AIC (Akaike information criterion)=-550.9 and BIC (Bayesian information criterion)=-475.4. OLS model included the following OABq-SF items (and range of weights): A1 (0.102, 0.216); A3 (0.070, 0.171); B3 (0.071, 0.078); B1 (0.076, 0.136); B2 (-0.132, -0.028). It is possible to map the OAB-5D scores onto EQ-5D in the Spanish population, allowing estimating EQ-5D utility scores from OAB specific health conditions.

BackgroundImmunoglobulin A nephropathy (IgAN) is a rare progressive disease that can lead to kidney failure. The current study aimed to estimate health state utility values for IgAN from a UK societal perspective.MethodsWe used the time trade-off (TTO) method to derive utility values for various health states in IgAN, defined based on chronic kidney disease (CKD) stage, proteinuria, dialysis, and nephrotic syndrome (CKD stages 1–4, proteinuria < 1 g/day vs ≥ 1 g/day; CKD stage 5, dialysis vs non-dialysis). We developed health state vignettes to describe typical symptoms and quality-of-life impairments of IgAN. Eligible participants from the UK general public completed a computer-assisted telephone interview. Estimated TTO utility values were reviewed against visual analogue scale (VAS)-derived values.ResultsIn total, 200 participants were included in the study (mean age, 48.9 years; female, 59.0%). Mean (standard deviation [SD]) utility values were 0.84 (0.17) and 0.71 (0.23) for CKD stage 1/2 with proteinuria < 1 g/day and with proteinuria ≥ 1 g/day, respectively; 0.68 (0.23) and 0.61 (0.25) for CKD stage 3; and 0.55 (0.26) and 0.49 (0.27) for CKD stage 4. Mean (SD) utility of CKD stage 5 with and without dialysis was 0.38 (0.30) and 0.42 (0.28), respectively. The mean (SD) utility value of nephrotic syndrome was 0.43 (0.33).ConclusionsOur results indicated that various IgAN health states are associated with impaired health status, with substantial utility decrements related to disease progression, elevated proteinuria, and nephrotic syndrome.Supplementary InformationThe online version contains supplementary material available at 10.1007/s41669-024-00527-1.

Mapping between non-preference- and preference-based health-related quality-of-life instruments has become a common technique for estimating health state utility values for use in economic evaluations. Despite the increased use of mapped health state utility estimates in health technology assessment and economic evaluation, the methods for deriving them have not been fully justified. Recent guidelines aim to standardise reporting of the methods used to map between instruments but do not address fundamental concerns in the underlying conceptual model. Current mapping methods ignore the important conceptual issues that arise when extrapolating results from potentially unrelated measures. At the crux of the mapping problem is a question of validity; because one instrument can be used to predict the scores on another, does this mean that the same preference for health is being measured in actual and estimated health state utility values? We refer to this as conceptual validity. This paper aims to (1) explain the idea of conceptual validity in mapping and its implications; (2) consider the consequences of poor conceptual validity when mapping for decision making in the context of healthcare resource allocation; and (3) offer some preliminary suggestions for improving conceptual validity in mapping.

In early 2020, the COVID-19 disease, caused by the SARS-CoV-2 virus infection, became a global pandemic impacting the entire world, including Indonesia. To monitor the spread of COVID-19 and determine appropriate strategies to mitigate its impact, the World Health Organization (WHO) routinely reported confirmed case data and death case data due to COVID-19. Mathematical modeling can help understanding the relationship between the number of deaths based on daily confirmed cases. One simple mathematical model is the linear regression model. The linear regression model requires the assumption of homoscedasticity, and when this assumption fails, linear regression cannot be used. In this research, a generalized linear model (GLM) is used to address the shortcomings of the linear regression model. This research will predict the number of daily deaths based on daily confirmed case data using GLM based on historical data from Indonesia, Malaysia, Thailand, and Philippines. The functions used to describe the relationship between predictor and response variables include normal or Gaussian, Poisson, gamma, and negative binomial distributions. To evaluate whether the model fits the data, we used Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC). Additionally, the goodness of fit of the model in predicting the number of deaths is measured by finding the mean squared error (MSE). The best model is determined by considering the smallest AIC, BIC, and MSE values. The simulation results show that the GLM using the normal distribution is the best model in Indonesia, Malaysia, and Philippines, while the GLM using the negative binomial distribution is the best model in Thailand. Using the GLM, it was found that deaths occurred 14 days after a patient was confirmed with COVID-19 in Indonesia, 11 days in Malaysia, 12 days in Thailand, and 13 days in Philippines.

The 9th edition of tumour-node-metastasis (TNM) staging for lung cancer was announced by Prof Hisao Asamura at the 2023 World Conference on Lung Cancer in Singapore. The purpose of this study was to externally validate and compare the latest staging of lung cancer. We collected 19193 patients with stage IA-IIIA non-small cell lung cancer (NSCLC) who underwent lobectomy from the Surveillance, Epidemiology and End Results database. Survival analysis by TNM stages was compared using the Kaplan-Meier method and further analysed using univariable and multivariable Cox regression analyses. Receiver operating characteristic curves were used to assess model accuracy, Akaike information criterion, Bayesian information criterion and consistency index were used to compare the prognostic, predictive ability between the current 8th and 9th edition TNM classification. The 9th edition of the TNM staging system can better distinguish between IB and IIA patients on the survival curve (P < 0.0001). In both univariable and multivariable regression analysis, the 9th edition of the TNM staging system can differentiate any 2 adjacent staging patients more evenly than the 8th edition. The 9th and the 8th edition TNM staging have similar predictive power and accuracy for the overall survival of patients with NSCLC [TNM 9th vs 8th, area under the curve: 62.4 vs 62.3; Akaike information criterion: 166182.1 vs 166131.6; Bayesian information criterion: 166324.3 vs 166273.8 and consistency index: 0.650 (0.003) vs 0.651(0.003)]. Our external validation demonstrates that the 9th edition of TNM staging for NSCLC is reasonable and valid. The 9th edition of TNM staging for NSCLC has near-identical prognostic accuracy to the 8th edition.

In molecular phylogenetics, partition models and mixture models provide different approaches to accommodating heterogeneity in genomic sequencing data. Both types of models generally give a superior fit to data than models that assume the process of sequence evolution is homogeneous across sites and lineages. The Akaike Information Criterion (AIC), an estimator of Kullback–Leibler divergence, and the Bayesian Information Criterion (BIC) are popular tools to select models in phylogenetics. Recent work suggests that AIC should not be used for comparing mixture and partition models. In this work, we clarify that this difficulty is not fully explained by AIC misestimating the Kullback–Leibler divergence. We also investigate the performance of the AIC and BIC at comparing amongst mixture models and amongst partition models. We find that under nonstandard conditions (i.e. when some edges have small expected number of changes), AIC underestimates the expected Kullback–Leibler divergence. Under such conditions, AIC preferred the complex mixture models and BIC preferred the simpler mixture models. The mixture models selected by AIC had a better performance in estimating the edge length, while the simpler models selected by BIC performed better in estimating the base frequencies and substitution rate parameters. In contrast, AIC and BIC both prefer simpler partition models over more complex partition models under nonstandard conditions, despite the fact that the more complex partition model was the generating model. We also investigated how mispartitioning (i.e., grouping sites that have not evolved under the same process) affects both the performance of partition models compared with mixture models and the model selection process. We found that as the level of mispartitioning increases, the bias of AIC in estimating the expected Kullback–Leibler divergence remains the same, and the branch lengths and evolutionary parameters estimated by partition models become less accurate. We recommend that researchers are cautious when using AIC and BIC to select among partition and mixture models; other alternatives, such as cross-validation and bootstrapping, should be explored, but may suffer similar limitations [AIC; BIC; mispartitioning; partitioning; partition model; mixture model].

Bu çalışma, genel doğrusal ve çok seviyeli doğrusal büyüme modellerini kullanarak büyüme eğrisi modellerini karşılaştırmak ve etlik piliçlerde büyümedeki farklılıkların tespit edilmesi amacıyla yapılmıştır. Bu amaçla 74 erkek etlik pilicin canlı ağırlık kayıtlarını içeren veri seti kullanılmıştır. Ölçümler yumurtadan çıkıştan altıncı haftaya kadar haftada bir olmak üzere bireysel olarak kaydedilmiştir. Verilerin analizi için, genel doğrusal modellerden iki ve çok seviyeli doğrusal modellerden üç olmak üzere beş farklı büyüme modeli kullanılmıştır. Değişimi en iyi açıklayan modeli bulmak için; log olabilirlik (log-likelihood, ll), Akaiki bilgi ölçütü (Akaike Information Criteria, AIC), Bayes bilgi ölçütü (Bayesian Information Criteria, BIC), düzeltilmiş Akaiki bilgi ölçütü (AIC Corrected, AICC) ve olabilirlik oran testi (Likelihood Ratio Test, LRT)’nden faydalanılmıştır. Çalışmanın sonuçları, çok seviyeli büyüme modellerinin genel doğrusal modellerden daha hassas tahminler yaptığını ve büyümeyi en iyi açıklayan modelin en küçük uyum ölçütlerine sahip “kesim noktası ve eğimin şansa bağlı olduğu kuadratik büyüme modeli” olduğunu ortaya koymuştur. Bu modele göre, erkek etlik piliçlerde büyüme üzerine zamanın lineer ve kuadratik etkisiyle birlikte yumurtadan çıkıştan itibaren büyümenin takip edildiği süre boyunca bireysel farklılıkların anlamlı olduğu sonucuna varılmıştır.

The Laplace distribution and its extensions have been widely utilized in statistical modelling due to their ability to capture real-world data characteristics such as skewness and heavy tails. This study evaluated the performance of the classical Laplace (L) distribution against three of its variants: the Transmuted Laplace (TL), Alternative Laplace (AL), and Asymmetric Laplace (ASL) distributions. While these extensions introduce additional parameters to enhance flexibility, their empirical performance remains a subject of interest. Using three datasets Rent prices, Voltage Drop, and Nigeria’s Unemployment Rate, this study assessed model fit based on the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Mean Squared Error (MSE). Findings revealed that the standard Laplace (L) distribution consistently outperforms its counterparts. In the Rent dataset, it achieves the lowest AIC (613.636), BIC (609.2266), and a reasonable MSE (2343.761), whereas the TL and AL distributions yield significantly higher AIC and BIC values, and the ASL distribution demonstrates an extremely high MSE (9.34 × 10¹²), indicating poor fit. A similar trend is observed in the Voltage Drop dataset, where the L distribution records the lowest AIC (201.1564), BIC (197.7293), and MSE (132.7978), while TL and ASL show excessive model instability. In the Unemployment Rate dataset, the L distribution again provides the best fit, with an AIC of 349.7985, a BIC of 345.896, and a moderate MSE of 186.4666. On average, across all datasets, the L distribution remains the most robust model, with the lowest AIC (388.197), BIC (384.284), and MSE (887.6751). The AL distribution follows closely with an MSE of 888.9518 but exhibits significantly higher AIC (2426.027) and BIC (2424.071). The ASL distribution, while demonstrating moderate AIC (1443.016) and BIC (1448.885), suffers from poor predictive accuracy with an extremely high MSE (3.19E+12). The TL distribution performs the worst, with the highest AIC (34,686.77), BIC (20,112.08), and an MSE of 76,038.22, highlighting its instability. In conclusion, this study established that the standard Laplace (L) distribution provides the most reliable and accurate fit across diverse datasets. While alternative forms introduce additional flexibility, their increased complexity does not necessarily yield superior model performance. Future research should explore modifications to improve the parameter stability of Laplace extensions and investigate alternative estimation techniques to enhance predictive accuracy in real-world applications.

In Response: We thank Dr. Arunajadai for his comments about the statistical simulations in our editorial (text NLP, algorithm WMB) demonstrating the perils of stepwise logistic regression.1 This allows us to clarify an ambiguity in the nomenclature of the stepwise automatic variable selection algorithm. Correctly specified, the algorithm should be described as either stepwise forward selection, stepwise backward elimination, or stepwise with forward selection and/or backward elimination; however, the word stepwise itself is also commonly used to refer to any of the three variants or to just the third variant. Arunajadai2 has correctly stated that our particular simulations used the stepwise backward elimination variant. Our simulations used randomly created covariates to demonstrate how commonly there was the creation of spurious associations by stepwise modeling (backward elimination variant). Dr. Arunajadai has also provided R software code to perform the other two variants; he reports that there were no spurious associations with no covariate significant at P < 0.05 using either the forward selection or the forward selection/ backward elimination variants. In his code, Arunajadai estimates a mean intercept model object, i.e., “fit <- glm(y ∼ 1, data = w, family = binomial),” for submission to the stepwise function. The submission of a mean intercept model to the stepwise process cannot identify any association, true or spurious. When a full (all covariates) model, i.e., “fit <- glm(y ∼., data = w, family = binomial)” is used, all three variants have qualitatively the same results of numerous spurious associations (appendix available at www.anesthesia-analgesia.org). The inclusion of noise variables during stepwise modeling regardless of the variant has been demonstrated elsewhere.3–5 Dr. Arunajadai also raised the very interesting question of which information criterion should be used at each step for adding or removing a covariate; he advocates the Bayesian Information Criterion (BIC) in contrast to the Akaike Information Criterion (AIC) used in our simulation. Both the AIC and the BIC are indexes in which twice the negative maximized log likelihood of the model fit is penalized by subtracting either twice the number of model parameters (AIC) or the number of model parameters multiplied by the log of the sample size (BIC). Of the candidate models possible, the model with the higher AIC or higher BIC is favored. As Arunajadai noted, the BIC is more heavily penalized and will produce more parsimonious models (fewer significant covariates). However, there is a competition in choosing between AIC and BIC; the AIC will yield optimal regression estimation while the BIC represents consistent model identification rules. It is not possible to create models with the properties favored by both the AIC and the BIC.6 Using the BIC index in our simulation still produces spurious associations. Automatic variable selection via a stepwise process is a hazardous undertaking. As J. B. Copas3 humorously noted, “If you torture the data for long enough, in the end they will confess …. What more brutal torture can there be than subset selection? The data will always confess, and the confession will usually be wrong.” Nathan L. Pace, MD, MStat Department of Anesthesiology University of Utah Salt Lake City, Utah William M. Briggs, PhD Department of Emergency Medicine New York Methodist Hospital Brooklyn, New York [email protected]

Summary1. Capture–recapture mixture models are important tools in evolution and ecology to estimate demographic parameters and abundance while accounting for individual heterogeneity. A key step is to select the correct number of mixture components i) to provide unbiased estimates that can be used as reliable proxies of fitness or ingredients in management strategies and ii) classify individuals into biologically meaningful classes. However, there is no consensus method in the statistical literature for selecting the number of components.2. In ecology, most studies rely on the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) that has recently gained attention in ecology. The Integrated Completed Likelihood criterion (ICL; IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22, 719) was specifically developed to favour well‐separated components, but its use has never been investigated in ecology.3. We compared the performance of AIC, BIC and ICL for selecting the number of components with regard to a) bias and accuracy of survival and detection estimates and b) success in selecting the true number of components using extensive simulations and data on wolf (Canis lupus) that were used for management through survival and abundance estimation.4. Bias in survival and detection estimates was &lt;0.02 for both AIC and BIC, and more than 0.09 for ICL, while mean square error was &lt;0.05 for all criteria. As expected, bias increased as heterogeneity increased. Success rates of AIC and BIC in selecting the ‘true’ number of components were better than ICL (68% for AIC, 58% for BIC, and 16% for ICL). As the degree of heterogeneity increased, AIC (and BIC in a lesser extent) overestimated the number of components, while ICL often underestimated this number. For the wolf study, the 2‐class model was selected by BIC and ICL, while AIC could not decide between the 2‐ and 3‐class models.5. We recommend using AIC or BIC when the aim is to estimate parameters. Regarding classification, we suggest taking the classification quality into account by using ICL in conjunction with BIC, pending further work to adapt its penalty term for capture–recapture data.

Objectives: This study investigated the efficiency of Multiple Imputation (MI) and Maximum Likelihood (ML) methods for estimating missing values. The study was set to use the findings to make recommendations for future studies about the impact of missing data imputation on the accuracy of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Methods: The completedset (with no missing values) used in this study was collected in 2010/11 through the Income and Expenditure Survey (IES) and had 25328 observations. Missing data were generated by randomly deleting 10%, 20%, 30%, 40% and 50% of the values from the complete dataset. The missing values in each of the five datasets were imputed using MI and ML methods. Subsequently, absolute error values of AIC and BIC from multiple regression analysis were computed for each dataset. The study then compared the absolute errors for each missing value imputation method. Findings: The findings of the study revealed that AIC and BIC are more accurate when missing values are estimated by the Full Information Maximum Likelihood (FIML) of the ML algorithm, provided 10% of the data are missing. For all datasets, AIC and BIC were least accurate when missing values were imputed by Expectation Maximisation (EM) of the ML algorithm. The findings also showed that AIC and BIC are more accurate when the rate of MISSINGNESS gets large provided missing values were estimated using either the Fully Conditional Specification (FCS) or Markov Chain Monte Carlo (MCMC), MI algorithms. Application: When the rate of MISSINGNESS is small (at most 10%), FIML should be used to handle missing data if AIC and BIC are going to be used. Also both FCS and MCMC should be considered over EM algorithms when the rate of MISSINGNESS is high (at least 40% missing). Keywords: Maximum Likelihood Imputation, Multiple Imputation, AIC, BIC

PurposeIron deficiency anemia is common in people with inflammatory bowel disease (IBD), causing deterioration in quality of life, which can be reversed by treatment that increases iron stores and hemoglobin levels. The present post hoc analyses estimate health state utility values for patients with IBD after treatment with ferric derisomaltose or ferric carboxymaltose and evaluate the health domains driving the changes.MethodsSF-36v2 responses were recorded at baseline and day 14, 35, 49, and 70 from 97 patients enrolled in the randomized, double-blind, PHOSPHARE-IBD trial (ClinicalTrials.gov ID: NCT03466983), in which patients with IBD across five European countries were randomly allocated to either ferric derisomaltose or ferric carboxymaltose. Changes in SF-36v2 scale scores and SF-6Dv2 health utility values were analyzed by mixed models.ResultsIn both treatment arms, SF-6Dv2 utility values and all SF-36v2 scale scores, except Bodily Pain, improved significantly (p = < 0.0001). The improvement in SF-6Dv2 utility values showed no significant treatment group difference. The improvement in utility values was completely explained by improvement in Vitality scores. Vitality scores showed significantly larger improvement with ferric derisomaltose versus ferric carboxymaltose (p = 0.026). Patients with the smallest decrease in phosphate had significantly larger improvements in Vitality scores at each time point (p = < 0.05 for all comparisons) and overall (p = 0.0006).ConclusionsUtility values improved significantly with intravenous iron treatment. Improvement in utility values was primarily driven by Vitality scores, which showed significantly greater improvement in the ferric derisomaltose arm. Smaller decreases in phosphate were associated with significantly higher Vitality scores, suggesting that quality of life improvement is attenuated by hypophosphatemia. The utility values can inform future cost-utility analysis.

Models are essential tools for effective forest management. Tree height-diameter models are used for the management of stand structure in forest plantations. The heterogeneity in species composition and structure of tropical forests constitutes a major challenge in developing height models, especially in Okomu Forest Reserve (OFR), Nigeria. There is inadequate information on height models’ application in Nigeria for most natural forests. Hence, tree height models were developed for rainforest of OFR, Nigeria. Using a systematic sampling technique, 2949 tree species with Diameter at Breast Height ≥ 10 cm found within 60 plots of 50 m × 50 m alternately laid at 200 m intervals on 15 transects (one kilometer each) were identified to species level and enumerated. Eighty-seven tree species were identified. Following standard procedure, cluster analysis was used to classify the trees into 5 species groups (SG 1-5). Data were analysed using non-linear regression at α0.05. Ordinary Least square (OLS) modelling technique was used in fitting the height model for each SG. The best fitted height models were evaluated based on the lowest Standard Error of Estimation (SEE), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The results revealed that Gompertz model performed best for SG 1 with lowest values of SEE (5.12), AIC (2197.52), and BIC (2211.05), SG 2 with SEE (5.53), (AIC) 3514.14, and BIC (3528.94) and SG 5 with SEE (5.30), AIC (2526.19) and BIC (2540.07); while power model performed best for SG 2 with the lowest SEE (3.75), AIC (524.38) and BIC (530.95) and SG 4 with lowest SEE (5.09), AIC (980.38) and BIC (987.79) respectively. This study concluded that total height of mixed tree species in each SG in OFR, Nigeria can be determined with these models. Thus, these models are recommended for modelling height-diameter relationships of mixed tree species in tropical rainforest.

This article reviews the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) in model selection and the appraisal of psychological theory. The focus is on latent variable models, given their growing use in theory testing and construction. Theoretical statistical results in regression are discussed, and more important issues are illustrated with novel simulations involving latent variable models including factor analysis, latent profile analysis, and factor mixture models. Asymptotically, the BIC is consistent, in that it will select the true model if, among other assumptions, the true model is among the candidate models considered. The AIC is not consistent under these circumstances. When the true model is not in the candidate model set the AIC is efficient, in that it will asymptotically choose whichever model minimizes the mean squared error of prediction/estimation. The BIC is not efficient under these circumstances. Unlike the BIC, the AIC also has a minimax property, in that it can minimize the maximum possible risk in finite sample sizes. In sum, the AIC and BIC have quite different properties that require different assumptions, and applied researchers and methodologists alike will benefit from improved understanding of the asymptotic and finite-sample behavior of these criteria. The ultimate decision to use the AIC or BIC depends on many factors, including the loss function employed, the study's methodological design, the substantive research question, and the notion of a true model and its applicability to the study at hand.