Monte Carlo simulations arrive at their results by introducing randomness, sometimes derived from a physical randomizing device. Nonetheless, we argue, they open no new epistemic channels beyond that already employed by traditional simulations: the inference by ordinary argumentation of conclusions from assumptions built into the simulations. We show that Monte Carlo simulations cannot produce knowledge other than by inference, and that they resemble other computer simulations in the manner in which they derive their conclusions. Simple examples (...) of Monte Carlo simulations are analysed to identify the underlying inferences. (shrink)

Both Carnap and Quine made significant contributions to the philosophy of mathematics despite their diversedviews. Carnap endorsed the dichotomy between analytic and synthetic knowledge and classified certainmathematical questions as internal questions appealing to logic and convention. On the contrary, Quine wasopposed to the analytic-synthetic distinction and promoted a holistic view of scientific inquiry. The purpose of thispaper is to argue that in light of the recent advancement of experimental mathematics such as Monte Carlosimulations, limiting mathematical inquiry to the domain (...) of logic is unjustified. Robustness studies implemented inMonte Carlo Studies demonstrate that mathematics is on par with other experimental-based sciences. (shrink)

In many disciplines, mediating processes are usually investigated with randomized experiments and linear regression to determine if the treatment affects the outcome through a mediator. However, randomizing the treatment will not yield accurate causal direct and indirect estimates unless certain assumptions are satisfied since the mediator status is not randomized. This study describes methods to estimate causal direct and indirect effects and reports the results of a large Monte Carlo simulation study on the performance of the ordinary (...) regression and modern causal mediation analysis methods, including a previously untested doubly robust sequential g-estimation method, when there are confounders of the mediator-to-outcome relation. Results show that failing to measure and incorporate potential post-treatment confounders in a mediation model leads to biased estimates, regardless of the analysis method used. Results emphasize the importance of measuring potential confounding variables and conducting sensitivity analysis. (shrink)

This work compares Autometrics with dual penalization techniques such as minimax concave penalty and smoothly clipped absolute deviation under asymmetric error distributions such as exponential, gamma, and Frechet with varying sample sizes as well as predictors. Comprehensive simulations, based on a wide variety of scenarios, reveal that the methods considered show improved performance for increased sample size. In the case of low multicollinearity, these methods show good performance in terms of potency, but in gauge, shrinkage methods collapse, and higher gauge (...) leads to overspecification of the models. High levels of multicollinearity adversely affect the performance of Autometrics. In contrast, shrinkage methods are robust in presence of high multicollinearity in terms of potency, but they tend to select a massive set of irrelevant variables. Moreover, we find that expanding the data mitigates the adverse impact of high multicollinearity on Autometrics rapidly and gradually corrects the gauge of shrinkage methods. For empirical application, we take the gold prices data spanning from 1981 to 2020. While comparing the forecasting performance of all selected methods, we divide the data into two parts: data over 1981–2010 are taken as training data, and those over 2011–2020 are used as testing data. All methods are trained for the training data and then are assessed for performance through the testing data. Based on a root-mean-square error and mean absolute error, Autometrics remain the best in capturing the gold prices trend and producing better forecasts than MCP and SCAD. (shrink)

Traditional multiple-group confirmatory factor analysis is usually criticized for having too restrictive model assumption, namely the scalar measurement invariance. The new multiple-group analysis methodology, alignment, has become an effective alternative. The alignment evaluates measurement invariance and more importantly, permits factor mean comparisons without requiring scalar invariance which is usually required in traditional multiple-group CFA. Some simulation studies and empirical studies have investigated the applicability of alignment under different conditions, but some areas remain unexplored. Based on the simulation studies (...) of Asparouhov and Muthén and of Flake and McCoach, this current simulation study is broken into two sections. The first study investigates the minimal group sizes required for alignment in three-factor models. The second study compares the performance of multiple-group CFA, multiple-group exploratory structural equation model, and alignment by including different proportions and magnitudes of cross-loadings in the models. Study 1 shows that when the model has no noninvariant parameters, the alignment requires relatively lower group sizes. Explicitly, the minimal group size required for alignment was 250 when the amount of groups was three, the minimal group size was 150 when the amount of groups was nine, and 200 when the amount of groups was 15. When there are noninvariant parameters in the model and the amount of groups is low, a group size of 350 is a safe rule of thumb. When there are noninvariant parameters in the model and the amount of groups is high, a group size of 250 is required for trustworthy results. The magnitude of noninvariance and the noninvariance rate do not affect the minimal group size required for alignment. Study 2 shows that multiple-group CFA provides accurate factor mean estimates when each factor had 20% factor loading with small-sized cross-loading. Multiple-group ESEM provides accurate factor mean estimates when the magnitude of cross-loading is small or when each factor had 20% factor loading with medium-sized cross-loading. Alignment provides accurate factor mean estimates when there are only small-sized cross-loadings in the model. The parameter estimates, coverage rates and ratios of average standard error to standard deviation for each methodology are not influenced by the amount of groups. Recommendations are concluded for using multiple-group CFA, multiple-group ESEM, traditional alignment and aligned ESEM based on the results. Multiple-group CFA is more suitable for use when scalar invariance is established. Multiple-group ESEM works best when there are small-sized or only a few medium-sized cross-loadings in the model. Traditional alignment allows for small-sized cross-loadings and a few noninvariant parameters in the model. AESEM integrates the advantages of alignment and ESEM, can provide accurate estimates when noninvariant parameters and cross-loadings both exist in the model. Compared to multiple-group CFA, multiple-group ESEM, the alignment methodology performs well in more situations. (shrink)

Growth mixture models are regularly applied in the behavioral and social sciences to identify unknown heterogeneous subpopulations that follow distinct developmental trajectories. Marcoulides and Trinchera recently proposed a mixture modeling approach that examines the presence of multiple latent classes by algorithmically grouping or clustering individuals who follow the same estimated growth trajectory based on an evaluation of individual case residuals. The purpose of this article was to conduct a simulation study that examines the performance of this new approach for (...) determining the number of classes in growth mixture models. The performance of the approach to correctly identify the number of classes is examined under a variety of longitudinal data design conditions. The findings demonstrated that the new approach was a very dependable indicator of classes across all the design conditions considered. (shrink)

Correlational measures are probably the most spread statistical tools in psychological research. They are used by researchers to investigate, for example, relations between self-report measures usually collected using paper-pencil or online questionnaires. Like many other statistical analysis, also correlational measures can be seriously affected by specific sources of bias which constitute serious threats to the final observed results. In this contribution, we will focus on the impact of the fake data threat on the interpretation of statistical results for two well-know (...) correlational measures (the Pearson product-moment correlation and the Spearman rank-order correlation). By using the Sample Generation by Replacement (SGR) approach, we analyze uncertainty in inferences based on possible fake data and evaluate the implications of fake data for correlational results. A population-level analysis and a Monte Carlo simulation are performed to study different modulations of faking on bivariate discrete variables with finite supports and varying sample sizes. We show that by using our paradigm it is always possible, under specific faking conditions, to increase (resp. decrease) the original correlation between two discrete variables in a predictable and systematic manner. (shrink)

The term Monte Carlo method indicates any computer-aided procedure for numerical estimation that combines mathematical calculations with randomly generated numerical input values. Today it is an important tool in high energy physics while physicists and philosophers also often consider it a sort of virtual experiment. The Monte Carlo method was developed in the 1940s, in the context of U.S. American nuclear weapons research, an event often regarded as the origin of both computer simulation and “artificial (...) reality” (Galison 1997). The present paper interrogates this strong claim by focusing on the emergence of Monte Carlo event generators in particle physics in the early 1960s. This historical case study shows how, as Monte Carlo computation became part of the toolbox of particle physicists around 1960, it was neither usually referred to as a “computer simulation” nor was it regarded as a surrogate for experimentation. In revising the history of this method, this paper asks, in what context did particle physicists of the 1960s decide to create FAKE, the first high-energy-physics Monte Carlo event simulator? What was their goal? And what epistemic role did FAKE play? In answering these questions, it is argued that Monte Carlo computations were not introduced into particle physics to simulate experiments, but rather they played the role of theoretical tools. The Monte Carlo method was able to do this thanks to its random component, a property which provided a means of modeling a specific phenomenon, so-called “(particle) resonances”. Indeed, in doing so, event generators even came to mutually assimilate and reshape the notions of particle and resonance, taking up an epistemic function which had previously been confined to physical-mathematical formulae: that of a medium which could express aspects of particle theory. (shrink)

With small to modest sample sizes and complex models, maximum likelihood estimation of confirmatory factor analysis models can show serious estimation problems such as non-convergence or parameter estimates outside the admissible parameter space. In this article, we distinguish different Bayesian estimators that can be used to stabilize the parameter estimates of a CFA: the mode of the joint posterior distribution that is obtained from penalized maximum likelihood estimation, and the mean, median, or mode of the marginal posterior distribution that are (...) calculated by using Markov Chain Monte Carlo methods. In two simulation studies, we evaluated the performance of the Bayesian estimators from a frequentist point of view. The results show that the EAP produced more accurate estimates of the latent correlation in many conditions and outperformed the other Bayesian estimators in terms of root mean squared error. We also argue that it is often advantageous to choose a parameterization in which the main parameters of interest are bounded, and we suggest the four-parameter beta distribution as a prior distribution for loadings and correlations. Using simulated data, we show that selecting weakly informative four-parameter beta priors can further stabilize parameter estimates, even in cases when the priors were mildly misspecified. Finally, we derive recommendations and propose directions for further research. (shrink)

This paper presents the design, simulation, and experimental verification of the fractional-order multiscroll Lü chaotic system. We base them on op-amp-based approximations of fractional-order integrators and saturated series of nonlinear functions. The integrators are first-order active realizations tuned to reduce the inaccuracy of the frequency response. By an exponential curve fitting, we got a convenient design equation for realizing fractional-order integrators of orders from 0.1 to 0.95. The results include simulations in SPICE of the mathematical description and the electronic (...) implementation and experimental measurements that confirm them. Monte Carlo and sensitivity tests revealed a robust realization. Contrary to its passive counterparts, the suggested realizations significantly reduce design and implementation efforts by favoring resistors and capacitors with commercial values and reducing hardware requirements. (shrink)

Objective of the study: To analyze the costs and profits of sugarcane production regarding the cultural practices of sugarcane suppliers. Methodology/approach: This study positions itself in this gap by comparatively analyzing 6 types of cultural practices: unraveling, windrowing, application of correctives, herbicides, insecticides and fertilizers, with the option of two systems Fixed rate (TF) and Variable rate (TV). Originality/Relevance: Brazil is a world reference in sugarcane production, with the State of São Paulo being the largest Brazilian producer. However, for sugarcane (...) suppliers to maintain this activity there is a need to reduce production costs and increase profitability/ha. However, there is a theoretical-practical gap in the financial assessment (costs and profits) of different cultural practices inherent to sugarcane production. Main results: The results demonstrated that the costs of cultural practices represent more than 30% of the total sugarcane production costs. The TF system proved to be more cost-efficient in the following operations: correctives, herbicides and insecticides. In the application of fertilizers, the TV system, in broadcast mode, had the best result. Finally, the profit/ton was R$1.70, demonstrating a very low profit margin/ha given the risk of the activity. Theoretical/methodological contributions: The sample for this research comprised 55 sugarcane suppliers from the State of São Paulo, whose data were obtained through a survey. The comparative analysis was based on the difference in costs of cultural practices and the estimation of the level of certainty (profit/costs), analyzed through the cumulative frequency carried out through the Monte Carlo Simulation (SMC). (shrink)

Background: Mental healthcare needs person-tailored interventions. Experience Sampling Method (ESM) can provide daily life monitoring of personal experiences. This study aims to operationalize and test a measure of momentary reward-related Quality of Life (rQoL). Intuitively, quality of life improves by spending more time on rewarding experiences. ESM clinical interventions can use this information to coach patients to find a realistic, optimal balance of positive experiences (maximize reward) in daily life. rQoL combines the frequency of engaging in a relevant context (a (...) ‘behavior setting’) with concurrent (positive) affect. High rQoL occurs when the most frequent behavior settings are combined with positive affect or infrequent behavior settings co-occur with low positive affect. Methods: Resampling procedures (Monte Carlo experiments) were applied to assess the reliability of rQoL using various behavior setting definitions under different sampling circumstances, for real or virtual subjects with low-, average- and high contextual variability. Furthermore, resampling was used to assess whether rQoL is a distinct concept from positive affect. Virtual ESM beep datasets were extracted from 1058 valid ESM observations for virtual and real subjects. Results: Behavior settings defined by Who-What contextual information were most informative. Simulations of at least 100 ESM observations are needed for reliable assessment. Virtual ESM beep datasets of a real subject can be defined by Who-What-Where behavior setting combinations. Large sample sizes are necessary for reliable rQoL assessments, except for subjects with low contextual variability. rQoL is distinct from positive affect. Conclusion: rQoL is a feasible concept. Monte Carlo experiments should be used to assess the reliable implementation of an ESM statistic. Future research in ESM should asses the behavior of summary statistics under different sampling situations. This exploration is especially relevant in clinical implementation, where often only small datasets are available. (shrink)

The costs of agricultural inputs added to those of labor represent almost a third of the total cost of Brazilian sugarcane production. This study analyzes the behavior of the price per ton of sugarcane in Brazil, relating it to the main production costs of this cultivation. Twelve price indicators from January 2015 to December 2020 were evaluated. First, the data were adjusted to a multiple linear regression model to identify the significant variables on variation in the price per ton of (...) sugarcane. Then, the Monte Carlo simulation was used to measure the level of certainty of occurrence of these variables, and forecasts were obtained from the adjustment of ARIMA models. The results showed the influence of the costs of diesel oil, two agricultural pesticides, and daily laborers on the price of sugarcane, besides an increasing trend of its, providing relevant short-term projections for decision-making about investments in the agribusiness sector. (shrink)

The diversity in agronomic practices being used by sugarcane producers in Brazil determines differences in economic performance and cost structure. The purpose of this study is to evaluate the cost of six systems of agronomic practices using fixed or variable rates for soil amendment, fertilizer, and defensive applications and assess the profitability of these systems at three scales of sugarcane production. We then describe the data sample related to the 2019–2020 harvest season and collected from fifty-five sugarcane producers in the (...) central-south region of Brazil. Thereafter, using a quantitative approach, a cost analysis was performed, and the cumulative frequency of the net revenue for the three scales of production (small, medium, and large), was calculated using a Monte Carlo simulation. The cost analysis indicated that fertilizer had the highest cost considering the agronomic practices adopted at the three scales of production analyzed. The cumulative frequency analysis results from the Monte Carlo simulation showed the highest net revenue per hectare for medium sugarcane producers. In addition, the presence of economies of scale was not confirmed because the lowest cost was found in small-scale sugarcane producers and the highest net revenue was obtained by medium-scale sugarcane producers. (shrink)

This article introduces confirmatory composite analysis (CCA) as a structural equation modeling technique that aims at testing composite models. In doing so, it overcomes a current weakness of structural equation modeling, i.e., the operationalization and assessment of design concepts, so-called artifacts. CCA entails the same steps as confirmatory factor analysis: model specification, model identification, model estimation, and model assessment. Composite models are specified such that they consist of a set of interrelated composites, all of which emerge as linear combinations of (...) observable variables. Researchers must ensure theoretical identification of their specified model. For the estimation of the model, several estimators are available; in particular Kettenring's extensions of canonical correlation analysis provide consistent estimates. Model assessment mainly relies on the Bollen-Stine bootstrap to assess the discrepancy between the empirical and the estimated model-implied indicator covariance matrix. A Monte Carlo simulation examines the efficacy of CCA, and demonstrates that CCA is able to detect various forms of model misspecification. (shrink)

The probability ranking conclusion is an extension of the absolute form evaluation conclusion. Firstly, the random simulation evaluation model is introduced; then, the general idea of converting the traditional evaluation method to the random simulation evaluation model is analyzed; on this basis, based on the rule of “further ensuring the stability of the ranking chain on the basis of increasing the possibility of the ranking chain,” two methods of solving the probability ranking conclusion are given. Based on the (...) rule of “further guaranteeing the stability of the ranking chain on the basis of improving the likelihood of the ranking chain,” two methods are given to solve the likelihood conclusion. This paper argues that this absolute form of conclusion hinders the approximation of the theory to the essence of the actual problem and is an important reason for the problem of “non-consistency of multi-evaluation conclusions.” To address this problem, a stochastic simulation-based comprehensive evaluation solution algorithm based on the idea of “Monte Carlo simulation” is proposed, and the corresponding ranking method is investigated, which is characterized by generating evaluation conclusions with probability information, and thus has more advantages than the absolute conclusion form in terms of problem interpretability. The method is characterized by the generation of evaluation conclusions with probabilistic information and thus has more advantages than the absolute conclusion form in terms of problem interpretation. Because of the independence of the stochastic simulation solution method, it is applied to the “bottom-up” evaluation model as an example, and a novel autonomous evaluation method is constructed. Finally, the application of the stochastic simulation evaluation model is illustrated by an example and compared with the absolute form evaluation. The evaluation model is an extension of the traditional evaluation model, which can further broaden the practical application of comprehensive evaluation theory. (shrink)

Land use changes threaten agricultural land. If agricultural land is going to be preserved, the social and economic causes of conversion must be understood. However, analyzing the causes of agricultural conversion is complex because trends need to be documented before analyzing the causes. One of the leading uses of agricultural land is for residential purposes. This paper projects residential development in a Hudson River Valley watershed within Dutchess County in New York State using an integrated modeling framework consisting of an (...) econometric model, a geographic information system (GIS), and Monte Carlo simulation. The econometric model is used to project residential development, providing parcel-specific probabilities of residential development. The GIS is employed to extract socio-economic and county-level tax parcel data to be used in conjunction with bio-geophysical attributes, such as slope, soil, and location, to calculate and project growth trends on a residential level for undeveloped land parcels. Monte Carlo simulation is used to distribute these projections into the GIS to display outcomes of scenario analyses to provide policy-makers a demonstration of how policies would likely affect the agricultural landscape of the watershed. (shrink)

This paper provides the first systematic epistemological account of simulated data in empirical science. We focus on the epistemic issues modelers face when they generate simulated data to solve problems with empirical datasets, research tools, or experiments. We argue that for simulated data to count as epistemically reliable, a simulation model does not have to mimic its target. Instead, some models take empirical data as a target, and simulated data may successfully mimic such a target even if the model (...) does not. We show how to distinguish between simulated and empirical data, and we also offer a definition of simulation that can accommodate Monte Carlo models. We shed light on the epistemology of simulated data by providing a taxonomy of four different mimicking relations that differ concerning the nature of the relation or relata. We illustrate mimicking relations with examples from different sciences. Our main claim is that the epistemic evaluation of simulated data should start with recognizing the diversity of mimicking relations rather than presuming that only one relation existed. (shrink)