Estudo da previsão de propriedades do biodiesel utilizando espectros de infravermelho e calibração multivariada

O biodiesel tem sido amplamente utilizado como uma fonte de energia renovável, que contribui para a diminuição de demanda por diesel mineral. Portanto, existem várias propriedades que devem ser monitoradas, a fim de produzir e distribuir biodiesel com a qualidade exigida. Neste trabalho, as propriedades físicas do biodiesel, tais como massa específica, índice de refração e ponto de entupimento de filtro a frio foram medidas e associadas a espectrometria no infravermelho próximo (NIR) e espectrometria no infravermelho médio (Mid-IR) utilizando ferramentas quimiométricas. Os métodos de regressão por mínimos quadrados parciais (PLS), regressão de mínimos quadrados parciais por intervalos (iPLS), e regressão por máquinas de vetor de suporte (SVM) com seleção de variáveis por Algoritmo Genético (GA) foram utilizadas para modelar as propriedades mencionadas. As amostras de biodiesel foram sintetizadas a partir de diferentes fontes, tais como canola, girassol, milho e soja. Amostras adicionais de biodiesel foram adquiridas de um fornecedor da região sul do Brasil. Em primeiro lugar, o pré-processamento de correção de linha de base foi usado para normalizar os dados espectrais de NIR, seguidos de outros tipos de pré-processamentos que foram aplicados, tais como centralização dos dados na média, 1 derivada e variação de padrão normal. O melhor resultado para a previsão do ponto de entupimento de filtro a frio foi utilizando os espectros de Mid-IR e o método de regressão GA-SVM, com alto coeficiente de determinação da previsão, R2Pred=0,96 e baixo valor da Raiz Quadrada do Erro Médio Quadrático da previsão, RMSEP (C)= 0,6. Para o modelo de previsão da massa específica, o melhor resultado foi obtido utilizando os espectros de Mid-IR e regressão por PLS, com R2Pred=0,98 e RMSEP (g/cm3)= 0,0002. Quanto ao modelo de previsão para o índice de refração, o melhor resultado foi obtido utilizando os espectros de Mid-IR e regressão por PLS, com excelente R2Pred=0,98 e RMSEP= 0,0001. Para esses conjuntos de dados, o PLS e o SVM demonstraram sua robustez, apresentando-se como ferramentas úteis para a previsão das propriedades do biodiesel estudadas

Gaussian Approximation Potential: an interatomic potential derived from first principles Quantum Mechanics

Simulation of materials at the atomistic level is an important tool in studying microscopic structure and processes. The atomic interactions necessary for the simulation are correctly described by Quantum Mechanics. However, the computational resources required to solve the quantum mechanical equations limits the use of Quantum Mechanics at most to a few hundreds of atoms and only to a small fraction of the available configurational space. This thesis presents the results of my research on the development of a new interatomic potential generation scheme, which we refer to as Gaussian Approximation Potentials. In our framework, the quantum mechanical potential energy surface is interpolated between a set of predetermined values at different points in atomic configurational space by a non-linear, non-parametric regression method, the Gaussian Process. To perform the fitting, we represent the atomic environments by the bispectrum, which is invariant to permutations of the atoms in the neighbourhood and to global rotations. The result is a general scheme, that allows one to generate interatomic potentials based on arbitrary quantum mechanical data. We built a series of Gaussian Approximation Potentials using data obtained from Density Functional Theory and tested the capabilities of the method. We showed that our models reproduce the quantum mechanical potential energy surface remarkably well for the group IV semiconductors, iron and gallium nitride. Our potentials, while maintaining quantum mechanical accuracy, are several orders of magnitude faster than Quantum Mechanical methods.

Correcting the systematic error of the density functional theory calculation: the alternate combination approach of genetic algorithm and neural network

The alternate combinational approach of genetic algorithm and neural network (AGANN) has been presented to correct the systematic error of the density functional theory (DFT) calculation. It treats the DFT as a black box and models the error through external statistical information. As a demonstration, the AGANN method has been applied in the correction of the lattice energies from the DFT calculation for 72 metal halides and hydrides. Through the AGANN correction, the mean absolute value of the relative errors of the calculated lattice energies to the experimental values decreases from 4.93% to 1.20% in the testing set. For comparison, the neural network approach reduces the mean value to 2.56%. And for the common combinational approach of genetic algorithm and neural network, the value drops to 2.15%. The multiple linear regression method almost has no correction effect here.

侵蚀细沟水力学特性及细沟侵蚀与形态特征的试验研究

本文进行了一系列水槽试验 ,研究不同长度的侵蚀细沟在坡度及入流量影响下的浅水水流水力学特性、侵蚀量及细沟的形态特征 .所采用的土壤材料为砂壤土 ,试验使用四种入流流量 ,四种坡度 ,四种细沟长度 .记录水流速度、沟宽及径流中的泥沙含量 ,并用多元回归方法分析了它们与坡度、入流量或它们的交互项之间的关系 .提出了一种数学模型来描述试验中沟宽的周期性形态变化 .提出了通过试验得出的不同细沟长度的产沙量来确定水流输沙能力的方法 ,并得出出测定输沙能力的采样长度为 2～ 4m ,通过对细沟形态变化分析进一步说明了所确定的水流输沙能力采样长度的正确性

In situ circular dichroic electrochemical study of bilirubin and bovine serum albumin complex

The electrooxidation of bilirubin (BR) and bovine serum albumin (BSA) complexes was studied by in situ circular dichroism (CD) spectroelectrochemistry. The result showed that the mechanism of the whole electrooxidation process of this complex corresponded to electrochemical processes (EE mechanism) in aqueous solution. Some parameters of the process were obtained by double logarithm method, differential method and nonlinear regression method. In visible region, CD spectra of the two enantiomeric components of the complex and their fraction distribution against applied potentials were obtained by singular value decomposition least-square (SVDLS) method. Meanwhile, the distribution of the five components of secondary structure was also obtained by the same method in far-UV region. The peak potential gotten from EE mechanism corresponds to a turning point for the component transition, beyond which the whole reaction reaches a new equilibrium. Under applied positive potentials, the enantiomeric equilibrium between M and P form is broken and M form transfers to its enantiomer of P, while the fraction of alpha-helix increases and that improves the transition to P form.

The relation between formal potential and structure of indophenols and molecular mechnism of electrooxidation

The molecular structural parameters of indophenol and its derivatives were calculated by semi-empirical molecular orbital quantum chemical method,The relation between molecular structural parameters and formal potentials was analyzed by principal factor analysis and multiple Linear regression method. It was found that the formal potential of indophenols has a good relation with two-center electron exchange energy, E-ex (2), resonance energy of O-C bond, E-ex (C-1-O), and molecular ionization potential, I-p, among 19 moleclular structural parameters. The regression equation is E-0' = 1. 47 x 10 (-3) E-ex (two) - 5. 74 x 10 (-2) E-ex (C-1 - O) - 1. 41 x 10 (-2) I-p with RC = 0. 9999 and SD = 0. 00424. It was confirmed by the relation between structure parameters and formal potentials, and the thermodynamic stability of its intermediate products that the H (+) ionization is prior to the electron transfer step in the oxidation mechanism.

滑坡泥石流信息遥感获取与空间预测

On the issue of geological hazard evaluation（GHE）, taking remote sensing and GIS systems as experimental environment, assisting with some programming development, this thesis combines multi-knowledges of geo-hazard mechanism, statistic learning, remote sensing (RS), high-spectral recognition, spatial analysis, digital photogrammetry as well as mineralogy, and selects geo-hazard samples from Hong Kong and Three Parallel River region as experimental data, to study two kinds of core questions of GHE, geo-hazard information acquiring and evaluation model. In the aspect of landslide information acquiring by RS, three detailed topics are presented, image enhance for visual interpretation, automatic recognition of landslide as well as quantitative mineral mapping. As to the evaluation model, the latest and powerful data mining method, support vector machine (SVM), is introduced to GHE field, and a serious of comparing experiments are carried out to verify its feasibility and efficiency. Furthermore, this paper proposes a method to forecast the distribution of landslides if rainfall in future is known baseing on historical rainfall and corresponding landslide susceptibility map. The details are as following: (a) Remote sensing image enhancing methods for geo-hazard visual interpretation. The effect of visual interpretation is determined by RS data and image enhancing method, for which the most effective and regular technique is image merge between high-spatial image and multi-spectral image, but there are few researches concerning the merging methods of geo-hazard recognition. By the comparing experimental of six mainstream merging methods and combination of different remote sensing data source, this thesis presents merits of each method ,and qualitatively analyzes the effect of spatial resolution, spectral resolution and time phase on merging image. (b) Automatic recognition of shallow landslide by RS image. The inventory of landslide is the base of landslide forecast and landslide study. If persistent collecting of landslide events, updating the geo-hazard inventory in time, and promoting prediction model incessantly, the accuracy of forecast would be boosted step by step. RS technique is a feasible method to obtain landslide information, which is determined by the feature of geo-hazard distribution. An automatic hierarchical approach is proposed to identify shallow landslides in vegetable region by the combination of multi-spectral RS imagery and DEM derivatives, and the experiment is also drilled to inspect its efficiency. (c) Hazard-causing factors obtaining. Accurate environmental factors are the key to analyze and predict the risk of regional geological hazard. As to predict huge debris flow, the main challenge is still to determine the startup material and its volume in debris flow source region. Exerting the merits of various RS technique, this thesis presents the methods to obtain two important hazard-causing factors, DEM and alteration mineral, and through spatial analysis, finds the relationship between hydrothermal clay alteration minerals and geo-hazards in the arid-hot valleys of Three Parallel Rivers region. (d) Applying support vector machine (SVM) to landslide susceptibility mapping. Introduce the latest and powerful statistical learning theory, SVM, to RGHE. SVM that proved an efficient statistic learning method can deal with two-class and one-class samples, with feature avoiding produce ‘pseudo’ samples. 55 years historical samples in a natural terrain of Hong Kong are used to assess this method, whose susceptibility maps obtained by one-class SVM and two-class SVM are compared to that obtained by logistic regression method. It can conclude that two-class SVM possesses better prediction efficiency than logistic regression and one-class SVM. However, one-class SVM, only requires failed cases, has an advantage over the other two methods as only "failed" case information is usually available in landslide susceptibility mapping. (e) Predicting the distribution of rainfall-induced landslides by time-series analysis. Rainfall is the most dominating factor to bring in landslides. More than 90% losing and casualty by landslides is introduced by rainfall, so predicting landslide sites under certain rainfall is an important geological evaluating issue. With full considering the contribution of stable factors (landslide susceptibility map) and dynamic factors (rainfall), the time-series linear regression analysis between rainfall and landslide risk mapis presented, and experiments based on true samples prove that this method is perfect in natural region of Hong Kong. The following 4 practicable or original findings are obtained: 1) The RS ways to enhance geo-hazards image, automatic recognize shallow landslides, obtain DEM and mineral are studied, and the detailed operating steps are given through examples. The conclusion is practical strongly. 2) The explorative researching about relationship between geo-hazards and alteration mineral in arid-hot valley of Jinshajiang river is presented. Based on standard USGS mineral spectrum, the distribution of hydrothermal alteration mineral is mapped by SAM method. Through statistic analysis between debris flows and hazard-causing factors, the strong correlation between debris flows and clay minerals is found and validated. 3) Applying SVM theory (especially one-class SVM theory) to the landslide susceptibility mapping and system evaluation for its performance is also carried out, which proves that advantages of SVM in this field. 4) Establishing time-serial prediction method for rainfall induced landslide distribution. In a natural study area, the distribution of landslides induced by a storm is predicted successfully under a real maximum 24h rainfall based on the regression between 4 historical storms and corresponding landslides.

Promedio bayesiano de modelos para la predicción del consumo máximo de oxígeno en deportistas con datos de no-ejercicio

Históricamente, los modelos de no-ejercicio para predecir el consumo máximo de oxígeno (VO2max) han sido construidos mediante regresión lineal frecuentista, usando técnicas estándar de selección de modelos. Sin embargo, existe incertidumbre acerca de la estructura estadística en el proceso de selección del modelo. En este estudio se propuso construir un modelo de no-ejercicio para predecir el VO2max en deportistas orientados al rendimiento, considerando la incertidumbre de modelo a través del Promedio Bayesiano de Modelos (BMA). Un objetivo adicional fue comparar la performance predictiva del BMA con las de los modelos derivados de varias técnicas frecuentistas usuales de selección de variables. Con tal fin, se implementó un submuestreo aleatorio estratificado repetido. Los datos incluyeron observaciones de la variable respuesta (en L·min-1), así como registros de Género, Deporte, Edad, Peso, Talla e Índice de masa corporal (BMI) (Edad = 22.1 ± 4.9 años, media ± SD; n = 272). Se propuso una clasificación de deportes con el objetivo de incluirla dentro del proceso de construcción del modelo: Combate, Juego, Resistencia 1 y Resistencia 2. El enfoque BMA se implementó en base a dos métodos: Occam's window y Composición de Modelo mediante el método de Monte Carlo con Cadenas de Markov (MC²). Se observaron discrepancias en la selección de variables entre los procedimientos frecuentistas. Ambos métodos de BMA produjeron resultados muy similares. Los modelos que incluyeron Género y las variables dummies para Resistencia 1 y Resistencia 2 acumularon virtualmente toda la probabilidad de modelo a posteriori. El Peso fue el predictor continuo con la más alta probabilidad de inclusión a posteriori (menor a 0.8). Las combinaciones de variables que involucraron predictores con un alto nivel de multicolinealidad fueron desacreditadas. Los modelos con sustancial contribución para el BMA presentaron un ajuste apreciable (R² ajustado menor a 0.8). Entre los modelos seleccionados por estrategias frecuentistas, el obtenido mediante el método de regresión por pasos (Stepwise regression method) con alfa igual a 0.05 fue el más respaldado por los datos, en términos de probabilidad de modelo a posteriori. En concordancia con la literatura, el BMA tuvo mejor performance predictiva de los datos fuera de la muestra que los modelos seleccionados por técnicas frecuentistas, medida por la cobertura del intervalo de predicción de 90 por ciento. La clasificación de deportes reveló resultados consistentes.

Real-time sea surface air temperature retrieval over Southern Ocean using AMSR-E data

The AMSR-E satellite data and in-situ data were applied to retrieve sea surface air temperature (Ta) over the Southern Ocean. The in-situ data were obtained from the 24~(th) -26~(th) Chinese Antarctic Expeditions during 2008-2010. First, Ta was used to analyze the relativity with the bright temperature (Tb) from the twelve channels of AMSR-E, and no high relativity was found between Ta and Tb from any of the channels. The highest relativity was 0.38 (with 23.8 GHz). The dataset for the modeling was obtained by using in-situ data to match up with Tb, and two methods were applied to build the retrieval model. In multi-parameters regression method, the Tbs from 12 channels were used to the model and the region was divided into two parts according to the latitude of 50°S. The retrieval results were compared with the in-situ data. The Root Mean Square Error (RMS) and relativity of high latitude zone were 0.96℃and 0.93, respectively. And those of low latitude zone were 1.29 ℃ and 0.96, respectively. Artificial neural network (ANN) method was applied to retrieve Ta.The RMS and relativity were 1.26 ℃ and 0.98, respectively.

Methods to increase response to postal and electronic questionnaires

Background: Postal and electronic questionnaires are widely used for data collection in epidemiological studies but non-response reduces the effective sample size and can introduce bias. Finding ways to increase response to postal and electronic questionnaires would improve the quality of health research. Objectives: To identify effective strategies to increase response to postal and electronic questionnaires. Search strategy: We searched 14 electronic databases to February 2008 and manually searched the reference lists of relevant trials and reviews, and all issues of two journals. We contacted the authors of all trials or reviews to ask about unpublished trials. Where necessary, we also contacted authors to confirm methods of allocation used and to clarify results presented. We assessed the eligibility of each trial using pre-defined criteria. Selection criteria: Randomised controlled trials of methods to increase response to postal or electronic questionnaires. Data collection and analysis: We extracted data on the trial participants, the intervention, the number randomised to intervention and comparison groups and allocation concealment. For each strategy, we estimated pooled odds ratios (OR) and 95% confidence intervals (CI) in a random-effects model. We assessed evidence for selection bias using Egger's weighted regression method and Begg's rank correlation test and funnel plot. We assessed heterogeneity among trial odds ratios using a Chi 2 test and the degree of inconsistency between trial results was quantified using the I 2 statistic. Main results: Postal We found 481 eligible trials.The trials evaluated 110 different ways of increasing response to postal questionnaires.We found substantial heterogeneity among trial results in half of the strategies. The odds of response were at least doubled using monetary incentives (odds ratio 1.87; 95% CI 1.73 to 2.04; heterogeneity P < 0.00001, I 2 = 84%), recorded delivery (1.76; 95% CI 1.43 to 2.18; P = 0.0001, I 2 = 71%), a teaser on the envelope - e.g. a comment suggesting to participants that they may benefit if they open it (3.08; 95% CI 1.27 to 7.44) and a more interesting questionnaire topic (2.00; 95% CI 1.32 to 3.04; P = 0.06, I 2 = 80%). The odds of response were substantially higher with pre-notification (1.45; 95% CI 1.29 to 1.63; P < 0.00001, I 2 = 89%), follow-up contact (1.35; 95% CI 1.18 to 1.55; P < 0.00001, I 2 = 76%), unconditional incentives (1.61; 1.36 to 1.89; P < 0.00001, I 2 = 88%), shorter questionnaires (1.64; 95%CI 1.43 to 1.87; P < 0.00001, I 2 = 91%), providing a second copy of the questionnaire at follow up (1.46; 95% CI 1.13 to 1.90; P < 0.00001, I 2 = 82%), mentioning an obligation to respond (1.61; 95% CI 1.16 to 2.22; P = 0.98, I 2 = 0%) and university sponsorship (1.32; 95% CI 1.13 to 1.54; P < 0.00001, I 2 = 83%). The odds of response were also increased with non-monetary incentives (1.15; 95% CI 1.08 to 1.22; P < 0.00001, I 2 = 79%), personalised questionnaires (1.14; 95% CI 1.07 to 1.22; P < 0.00001, I 2 = 63%), use of hand-written addresses (1.25; 95% CI 1.08 to 1.45; P = 0.32, I 2 = 14%), use of stamped return envelopes as opposed to franked return envelopes (1.24; 95% CI 1.14 to 1.35; P < 0.00001, I 2 = 69%), an assurance of confidentiality (1.33; 95% CI 1.24 to 1.42) and first class outward mailing (1.11; 95% CI 1.02 to 1.21; P = 0.78, I 2 = 0%). The odds of response were reduced when the questionnaire included questions of a sensitive nature (0.94; 95% CI 0.88 to 1.00; P = 0.51, I 2 = 0%). Electronic: We found 32 eligible trials. The trials evaluated 27 different ways of increasing response to electronic questionnaires. We found substantial heterogeneity among trial results in half of the strategies. The odds of response were increased by more than a half using non-monetary incentives (1.72; 95% CI 1.09 to 2.72; heterogeneity P < 0.00001, I 2 = 95%), shorter e-questionnaires (1.73; 1.40 to 2.13; P = 0.08, I 2 = 68%), including a statement that others had responded (1.52; 95% CI 1.36 to 1.70), and a more interesting topic (1.85; 95% CI 1.52 to 2.26). The odds of response increased by a third using a lottery with immediate notification of results (1.37; 95% CI 1.13 to 1.65), an offer of survey results (1.36; 95% CI 1.15 to 1.61), and using a white background (1.31; 95% CI 1.10 to 1.56). The odds of response were also increased with personalised e-questionnaires (1.24; 95% CI 1.17 to 1.32; P = 0.07, I 2 = 41%), using a simple header (1.23; 95% CI 1.03 to 1.48), using textual representation of response categories (1.19; 95% CI 1.05 to 1.36), and giving a deadline (1.18; 95% CI 1.03 to 1.34). The odds of response tripled when a picture was included in an e-mail (3.05; 95% CI 1.84 to 5.06; P = 0.27, I 2 = 19%). The odds of response were reduced when "Survey" was mentioned in the e-mail subject line (0.81; 95% CI 0.67 to 0.97; P = 0.33, I 2 = 0%), and when the e-mail included a male signature (0.55; 95% CI 0.38 to 0.80; P = 0.96, I 2 = 0%). Authors' conclusions: Health researchers using postal and electronic questionnaires can increase response using the strategies shown to be effective in this systematic review. Copyright © 2009 The Cochrane Collaboration. Published by John Wiley & Sons, Ltd.


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Biosorption of toxic chromium from aqueous phase by lignin: mechanism, effect of other metal ions and salts

Surface reaction methodology was implicated in the optimization of hexavalent chromium removal onto lignin with respect to the process parameters. The influence of altering the conditions for removal of chromium(VI), for instance; solution pH, ionic strength, initial concentration, the dose of biosorbent, presence of other metals (Zn and Cu), presence of salts and biosorption-desorption studies, were investigated. It was found that the biosorption capacity of lignin depends on solution pH, with a maximum biosorption capacity for chromium at pH 2. Experimental equilibrium data were fitted to five different isotherm models by non-linear regression method, however, the biosorption equilibrium data were well interpreted by the Freundlich isotherm. The maximum biosorption capacities (q(max)) obtained using Dubinin-Radushkevich and Khan isotherms for Cr(VI) biosorption are 31.6 and 29.1 mg/g. respectively. Biosorption showed pseudo second order rate kinetics at different initial concentrations of Cr(VI). The intraparticle diffusion study indicated that film diffusion may be involved in the current study. The percentage removal of chromium on lignin decreased significantly in the presence of NaHCO3 and K2P2O7 salts. Desorption data revealed that nearly 70% of the Cr(VI) adsorbed on lignin could be desorbed using 0.1 M NaOH. It was evident that the biosorption mechanism involves the attraction of both hexavalent chromium (anionic) and trivalent chromium (cationic) onto the surface of lignin. (C) 2011 Elsevier B.V. All rights reserved.

Chemistry and Mechanism of Alizarin Red S and Methylene Blue Biosorption onto Olive Stone: Equilibrium and Kinetic

The biosorption process of anionic dye Alizarin Red S (ARS) and cationic dye methylene blue (MB) as a function of solution pH, initial concentration and contact time onto olive stone (OS) biomass has been investigated. The main objectives of the current study are to: (i) study the chemistry and the mechanism of ARS and MB biosorption onto olive stone and the type of OS–ARS, MB interactions occurring, (ii) study the biosorption equilibrium and kinetic experimental data required for the design and operation of column reactors. Equilibrium biosorption isotherms and kinetics were also examined. Experimental equilibrium data were fitted to four different isotherms by non-linear regression method, however, the biosorption experimental data for ARS and MB dyes were well interpreted by the Temkin and Langmuir isotherms, respectively. The maximum monolayer adsorption capacity for ARS and MB dyes were 109.0 and 102.6 mg/g, respectively. The kinetic data of the two dyes could be better described by the pseudo second-order model. The data showed that olive stone can be effectively used for removing dyes from wastewater.

Estimating the size of the population of persons who inject drugs in the island of Montréal, Canada, using a six-source capture-recapture model

BACKGROUND: To plan and implement services to persons who inject drugs (PWID), knowing their number is essential. For the island of Montréal, Canada, the only estimate, of 11,700 PWID, was obtained in 1996 through a capture-recapture method. Thirteen years later, this study was undertaken to produce a new estimate. METHODS: PWID were defined as individuals aged 14-65 years, having injected recently and living on the island of Montréal. The study period was 07/01/2009 to 06/30/2010. An estimate was produced using a six-source capture-recapture log-linear regression method. The data sources were two epidemiological studies and four drug dependence treatment centres. Model selection was conducted in two steps, the first focusing on interactions between sources and the second, on age group and gender as covariates and as modulators of interactions. RESULTS: A total of 1480 PWID were identified in the six capture sources. They corresponded to 1132 different individuals. Based on the best-fitting model, which included age group and sex as covariates and six two-source interactions (some modulated by age), the estimated population was 3910 PWID (95% confidence intervals (CI): 3180-4900) which represents a prevalence of 2.8 (95% CI: 2.3-3.5) PWID per 1000 persons aged 14-65 years. CONCLUSIONS: The 2009-2010 estimate represents a two-third reduction compared to the one for 1996. The multisource capture-recapture method is useful to produce estimates of the size of the PWID population. It is of particular interest when conducted at regular intervals thus allowing for close monitoring of the injection phenomenon.

Relations entre le niveau de vie, la fécondité et les besoins non satisfaits en matière de planification familiale en Guinée

Tous mes travaux ont été réalisés à l'aide du logiciel stata 11.

Correcting Measurement Error Bias in Interaction Models with Small Samples

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression