Monte Carlo Confidence Intervals Research Articles

A Robust Indicator Mean-Based Method for Estimating Generalizability Theory Absolute Error and Related Dependability Indices within Structural Equation Modeling Frameworks

In this study, we introduce a novel and robust approach for computing Generalizability Theory (GT) absolute error and related dependability indices using indicator intercepts that represent observed means within structural equation models (SEMs). We demonstrate the applicability of our method using one-, two-, and three-facet designs with self-report measures having varying numbers of scale points. Results for the indicator mean-based method align well with those obtained from the GENOVA and R gtheory packages for doing conventional GT analyses and improve upon previously suggested methods for deriving absolute error and corresponding dependability indices from SEMs when analyzing three-facet designs. We further extend our approach to derive Monte Carlo confidence intervals for all key indices and to incorporate estimation procedures that correct for scale coarseness effects commonly observed when analyzing binary or ordinal data.

Monte Carlo confidence intervals for the indirect effect with missing data.

Missing data is a common occurrence in mediation analysis. As a result, the methods used to construct confidence intervals around the indirect effect should consider missing data. Previous research has demonstrated that, for the indirect effect in data with complete cases, the Monte Carlo method performs as well as nonparametric bootstrap confidence intervals (see MacKinnon et al., Multivariate Behavioral Research, 39(1), 99-128, 2004; Preacher & Selig, Communication Methods and Measures, 6(2), 77-98, 2012; Tofighi & MacKinnon, Structural Equation Modeling: A Multidisciplinary Journal, 23(2), 194-205, 2015). In this manuscript, we propose a simple, fast, and accurate two-step approach for generating confidence intervals for the indirect effect, in the presence of missing data, based on the Monte Carlo method. In the first step, an appropriate method, for example, full-information maximum likelihood or multiple imputation, is used to estimate the parameters and their corresponding sampling variance-covariance matrix in a mediation model. In the second step, the sampling distribution of the indirect effect is simulated using estimates from the first step. A confidence interval is constructed from the resulting sampling distribution. A simulation study with various conditions is presented. Implications of the results for applied research are discussed.

Sample size and power calculations for causal mediation analysis: A Tutorial and Shiny App.

When designing a study for causal mediation analysis, it is crucial to conduct a power analysis to determine the sample size required to detect the causal mediation effects with sufficient power. However, the development of power analysis methods for causal mediation analysis has lagged far behind. To fill the knowledge gap, I proposed a simulation-based method and an easy-to-use web application ( https://xuqin.shinyapps.io/CausalMediationPowerAnalysis/ ) for power and sample size calculations for regression-based causal mediation analysis. By repeatedly drawing samples of a specific size from a population predefined with hypothesized models and parameter values, the method calculates the power to detect a causal mediation effect based on the proportion of the replications with a significant test result. The Monte Carlo confidence interval method is used for testing so that the sampling distributions of causal effect estimates are allowed to be asymmetric, and the power analysis runs faster than if the bootstrapping method is adopted. This also guarantees that the proposed power analysis tool is compatible with the widely used R package for causal mediation analysis, mediation, which is built upon the same estimation and inference method. In addition, users can determine the sample size required for achieving sufficient power based on power values calculated from a range of sample sizes. The method is applicable to a randomized or nonrandomized treatment, a mediator, and an outcome that can be either binary or continuous. I also provided sample size suggestions under various scenarios and a detailed guideline of app implementation to facilitate study designs.

Benefits of Doing Generalizability Theory Analyses within Structural Equation Modeling Frameworks: Illustrations Using the Rosenberg Self-Esteem Scale

Although generalizability theory (GT) designs typically are analyzed using analysis of variance (ANOVA) procedures, they also can be integrated into structural equation models (SEMs). In this tutorial, we review basic concepts for conducting univariate and multivariate GT analyses and demonstrate advantages of doing such analyses within SEM frameworks using multi-occasion data from the Rosenberg Self-Esteem Scale. We show how GT-SEMs can reproduce variance components for both relative and absolute error obtained from ANOVA models, estimate effects of changes made to measurement procedures and universes of generalization, incorporate estimation methods to correct for scale coarseness, represent essential tau-equivalent or congeneric relationships, include additional method factors for negatively and positively worded items, incorporate bifactor designs, allow for formal tests of model fit when warranted, and derive Monte Carlo confidence intervals for key parameters of interest. We provide code for conducting the demonstrated analyses using several statistical packages in extended online Supplemental Material.

When to Use Different Inferential Methods for Power Analysis and Data Analysis for Between-Subjects Mediation

Several options exist for conducting inference on indirect effects in mediation analysis. Although methods that use bootstrapping are the preferred inferential approach for testing mediation, they are time-consuming when the test must be performed many times for a power analysis. Alternatives that are more computationally efficient are not as robust, meaning accuracy of the inferences from these methods is more affected by nonnormal and heteroskedastic data. Previous research has shown that different sample sizes are needed to achieve the same amount of statistical power for different inferential approaches with data that meet all the statistical assumptions of linear regression. By contrast, we explore how similar power estimates are at the same sample size, including when assumptions are violated. We compare the power estimates from six inferential methods for between-subjects mediation using a Monte Carlo simulation study. We varied the path coefficients, inferential methods for the indirect effect, and degree to which assumptions are met. We found that when the assumptions of linear regression are met, three inferential methods consistently perform similarly: the joint significance test, the Monte Carlo confidence interval, and the percentile bootstrap confidence interval. When the assumptions were violated, the nonbootstrapping methods tended to have vastly different power estimates compared with the bootstrapping methods. On the basis of these results, we recommend using the more computationally efficient joint significance test for power analysis only when no assumption violations are hypothesized a priori. We also recommend the joint significance test to pick an optimal starting sample size value for power analysis using the percentile bootstrap confidence interval when assumption violations are suspected.

Causal mediation effects in single case experimental designs.

Single case experimental designs (SCEDs) are used to test treatment effects in a wide range of fields and consist of repeated measurements for a single case throughout one or more baseline phases and throughout one or more treatment phases. Recently, mediation analysis has been applied to SCEDs. Mediation analysis decomposes the total treatment-outcome effect into a direct and indirect effect, and therefore aims to unravel the causal processes underlying treatment-outcome effects. The most recent methodological advancement for mediation analysis is the development of causal mediation analysis methodology which clarifies the necessary causal assumptions for mediation analysis. The goal of this article is to derive the causal mediation effects and corresponding standard errors based on piecewise linear regression models for the mediator and outcome and to evaluate the performance of these regression estimators and standard errors. Whereas previous studies estimated the direct and indirect effects as either the change in level or change in trend, we showed that the causal direct and indirect effects incorporate both the change in level and change in trend. Based on our simulation study we showed that for the causal indirect effects, Monte Carlo confidence intervals provided accurate (i.e., p = .05) Type I error rates and higher statistical power than normal theory confidence intervals. For the causal direct effects and total effect, normal theory confidence intervals provided accurate Type I error rates and higher statistical power than the Monte Carlo confidence intervals. Limitations and future directions are discussed. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Evaluating sensitivity to classification uncertainty in latent subgroup effect analyses

BackgroundIncreasing attention is being given to assessing treatment effect heterogeneity among individuals belonging to qualitatively different latent subgroups. Inference routinely proceeds by first partitioning the individuals into subgroups, then estimating the subgroup-specific average treatment effects. However, because the subgroups are only latently associated with the observed variables, the actual individual subgroup memberships are rarely known with certainty in practice and thus have to be imputed. Ignoring the uncertainty in the imputed memberships precludes misclassification errors, potentially leading to biased results and incorrect conclusions.MethodsWe propose a strategy for assessing the sensitivity of inference to classification uncertainty when using such classify-analyze approaches for subgroup effect analyses. We exploit each individual’s typically nonzero predictive or posterior subgroup membership probabilities to gauge the stability of the resultant subgroup-specific average causal effects estimates over different, carefully selected subsets of the individuals. Because the membership probabilities are subject to sampling variability, we propose Monte Carlo confidence intervals that explicitly acknowledge the imprecision in the estimated subgroup memberships via perturbations using a parametric bootstrap. The proposal is widely applicable and avoids stringent causal or structural assumptions that existing bias-adjustment or bias-correction methods rely on.ResultsUsing two different publicly available real-world datasets, we illustrate how the proposed strategy supplements existing latent subgroup effect analyses to shed light on the potential impact of classification uncertainty on inference. First, individuals are partitioned into latent subgroups based on their medical and health history. Then within each fixed latent subgroup, the average treatment effect is assessed using an augmented inverse propensity score weighted estimator. Finally, utilizing the proposed sensitivity analysis reveals different subgroup-specific effects that are mostly insensitive to potential misclassification.ConclusionsOur proposed sensitivity analysis is straightforward to implement, provides both graphical and numerical summaries, and readily permits assessing the sensitivity of any machine learning-based causal effect estimator to classification uncertainty. We recommend making such sensitivity analyses more routine in latent subgroup effect analyses.

A Monte Carlo Confidence Interval Method for Testing Measurement Invariance

We propose a new method, the Monte Carlo confidence interval (MCCI) method, for studying measurement invariance. This method allows researchers to examine the invariance of all items simultaneously by comparing the observed between-group differences in parameters with those obtained under the null hypothesis of invariance. We compare the performance of our method to two other methods: the multigroup confirmatory factor analysis (MG-CFA) and the forward method using confidence intervals (forward CI). The results show that our method performed better than the MG-CFA method and comparably with the forward CI method. The code to implement our method and an empirical example are provided in the Supplementary materials.

Satellite observations document trends consistent with a boreal forest biome shift.

The boreal forest biome is a major component of Earth's biosphere and climate system that is projected to shift northward due to continued climate change over the coming century. Indicators of a biome shift will likely first be evident along the climatic margins of the boreal forest and include changes in vegetation productivity, mortality, and recruitment, as well as overall vegetation greenness. However, the extent to which a biome shift is already underway remains unclear because of the local nature of most field studies, sparsity of systematic ground‐based ecological monitoring, and reliance on coarse resolution satellite observations. Here, we evaluated early indicators of a boreal forest biome shift using four decades of moderate resolution (30 m) satellite observations and biogeoclimatic spatial datasets. Specifically, we quantified interannual trends in annual maximum vegetation greenness using an ensemble of vegetation indices derived from Landsat observations at 100,000 sample sites in areas without signs of recent disturbance. We found vegetation greenness increased (greened) at 38 [29, 42] % and 22 [15, 26] % of sample sites from 1985 to 2019 and 2000 to 2019, whereas vegetation greenness decreased (browned) at 13 [9, 15] % and 15 [13, 19] % of sample sites during these respective periods [95% Monte Carlo confidence intervals]. Greening was thus 3.0 [2.6, 3.5] and 1.5 [0.8, 2.0] times more common than browning and primarily occurred in cold sparsely treed areas with high soil nitrogen and moderate summer warming. Conversely, browning primarily occurred in the climatically warmest margins of both the boreal forest biome and major forest types (e.g., evergreen conifer forests), especially in densely treed areas where summers became warmer and drier. These macroecological trends reflect underlying shifts in vegetation productivity, mortality, and recruitment that are consistent with early stages of a boreal biome shift.

Traumatic stress, body shame, and internalized weight stigma as mediators of change in disordered eating: a single-arm pilot study of the Body Trust® framework

ABSTRACT To enhance access to evidence-based treatment it is increasingly important to evaluate scalable virtual programs that support the needs of those struggling with disordered eating. This study described a scientifically grounded, trauma-informed framework known as Body Trust,® and aimed to pilot test the preliminary effectiveness and mechanisms of change in a Body Trust® program to improve disordered eating. Using quality outcomes data, we examined 70 mostly white (87%) female-identifying (97%) individuals enrolled in a 6-module online program based in the Body Trust® framework (Mage = 45.5 ±10.9; MBMI = 33.7 ±8.0). Putative mediators included traumatic stress, internalized weight stigma, and body shame. Outcomes were objective and subjective binge episodes, overvaluation of weight and shape, and eating concerns. Generalized estimating equations were applied to determine pre-to-post changes. We applied Montoya’s MEMORE macro, the joint-significance test, and calculated 95% Monte Carlo confidence intervals to assess mediation. Significant pre-to-post improvements with medium to large effect sizes were detected for all outcomes and mediators (ps<.008). All hypothesized mechanisms supported mediation. Using the Body Trust® framework shows early promise for alleviating disordered eating symptoms through targeting traumatic stress, body shame, and internalized weight stigma. Given the program’s use of mindfulness techniques, future research should test target mechanisms like interoception.

Alcohol and marijuana protective behavioral strategies mediate the relationship between substance use identity and use-related outcomes: A multi-sample examination

Substance use identity has been consistently associated with problematic substance use. Limited attention has considered mechanisms of this association. This research examined whether greater identification as a drinker or marijuana user would be associated with the use of fewer alcohol/marijuana protective behavioral strategies (PBS; e.g., avoiding drinking games/avoiding using marijuana in public places). Further, PBS have been associated with lower levels of negative alcohol/marijuana-related outcomes (i.e., frequency, quantity, consequences). In the current multi-sample study, PBS were examined as a mediator of the relationship between drinking/marijuana identity and alcohol/marijuana-related outcomes across three studies. Study 1 was an intervention study with heavy drinking college students (N = 605), Study 2 was a multisite study of marijuana outcomes among college students (N = 2,077), and Study 3 was a study of substance use in a community sample (n = 369alcohol; n = 146marijuana). Cross-sectional and/or longitudinal data were collected across studies. Substance use identity, PBS, and use-related outcomes were measured across the three studies. Indirect effects were evaluated by Monte Carlo confidence intervals. Manner of Drinking PBS were found to be the only statistically significant mediator of the relationship between drinking identity and alcohol-related outcomes (i.e., quantity and consequences) cross-sectionally. These significant cross-sectional mediation effects for alcohol were replicated in one of three longitudinal models. Marijuana PBS were also found to mediate the relationship between marijuana identity and all marijuana-related outcomes examined in the current study. Study findings may help to inform the development of identity-based and PBS-based interventions that aim to reduce negative alcohol/marijuana-related outcomes.

Adiposity, Depression Symptoms and Inflammation in Hispanic/Latino Youth: Results From HCHS/SOL Youth.

Inflammation is implicated as one of many factors related to the development of chronic disease; thus, identifying its modifiable risk factors offers potential intervention targets to reduce risk. To investigate whether depression and anxiety symptoms may indirectly affect high-sensitivity C-reactive protein (hs-CRP) and plasminogen activator inhibitor-1 (PAI-1) through sleep duration and adiposity (i.e., percentage body fat and waist circumference). Multiple regression analyses were performed on Hispanic Community Health Study/Study of Latinos Youth (ages 8-16 years) cross-sectional baseline data, which were weighted to adjust for sampling design. Data were collected at a clinical assessment, including fasting blood samples, self-report surveys, and objectively measured anthropometrics. Adjusting for sociodemographic covariates, depression symptoms were associated with log hs-CRP (β = .011, p = .047) but not PAI-1 (p = .285). Percentage body fat and waist circumference were positively related to depression symptoms (p = .026 and p = .028, respectively) and log hs-CRP (p < .001 for both). When including adiposity in the hs-CRP model, the associations of depression symptoms with hs-CRP were attenuated and became nonsignificant. Monte Carlo confidence intervals (CIs) showed that the indirect effects from depression symptoms to CRP through percentage body fat (95% CI: .0006, .0119) and waist circumference (95% CI: .0004, .0109) were statistically significant. Results indicate that the association between psychological distress and inflammation may occur indirectly through adiposity in Hispanic/Latino children. If findings are replicated in causal designs, reducing depression symptoms and adiposity among Hispanic/Latino children may be avenues for primary prevention of inflammation in later years.

Modelling P2P Airbnb online host advertising effectiveness: the role of emotional appeal information completeness creativity and social responsibility

Purpose This study aims to examine the factors that influence peer-to-peer online host advertising effectiveness (POHAE). The study posits that POHAE is a multidimensional construct supported by emotional appeal, information completeness, advertising creativity and social responsibility practices influencing purchase intention and positive word of mouth. Perceived value is hypothesised as the moderating variable for the relationship between POHAE and purchase intention. Design/methodology/approach Quantitative data were collected from New Zealand through a quasi-experimental survey. A total of 95 people participated in the experiment. The study uses one-way repeated measures design ANOVA to test Hypothesis 1 and MEMORE model to test the effects of mediation and moderation for repeated measures. Findings Results are significant to the study model. ANOVA results show that the assumption of sphericity is not violated: Mauchly’s W, Greenhouse–Geisser, Huynh–Feldt estimates are equal to one, suggesting that the data are perfectly spherical. The mediation and moderation effects for repeated measure designs are also significant. The tests are based on 95 per cent Monte Carlo confidence interval and 20,000 bootstrapping samples. Research limitations/implications This study enhances the hierarchy of effects theory (HOE) (Lavidge and Steiner, 1961), which posits that consumers respond to a specific marketing communication through three components: the cognitive component, which is measured by an individual’s intellectual, mental or rational states; the affective component that refers to an individual’s emotional and feeling states; and finally the conative or motivational state, that is, the striving state relating to the tendency to treat objects as positive or negative. This study observes significant paths from POHAE to purchase intention and word of mouth. Limitations include a small sample size (95) and not regressing the POHAE variables individually on purchase intention and word of mouth. Practical implications Given the absence of a brand, as in the Airbnb host advertisement, attention should be given to writing the adverts effectively. Advertising creativity does not only hold for graphics and personal pictures but also for the hosts who need to be creative in crafting their advertisement text. Elements such as social responsibility practice and creativity should also not be overlooked. Social implications This study provides insights on how to effectively communicate with potential customers in a peer-to-peer marketplace. Originality/value This study provides an insight into peer-to-peer marketplaces on the importance of marketing communication strategies by providing more attention to writing advertisement texts. It is important to understand the variables that influence consumers’ motivation in responding to Airbnb online advertisements.

Multilevel Reliability Measures of Latent Scores Within an Item Response Theory Framework

This paper evaluated multilevel reliability measures in two-level nested designs (e.g., students nested within teachers) within an item response theory framework. A simulation study was implemented to investigate the behavior of the multilevel reliability measures and the uncertainty associated with the measures in various multilevel designs regarding the number of clusters, cluster sizes, and intraclass correlations (ICCs), and in different test lengths, for two parameterizations of multilevel item response models with separate item discriminations or the same item discrimination over levels. Marginal maximum likelihood estimation (MMLE)-multiple imputation and Bayesian analysis were employed to evaluate the accuracy of the multilevel reliability measures and the empirical coverage rates of Monte Carlo (MC) confidence or credible intervals. Considering the accuracy of the multilevel reliability measures and the empirical coverage rate of the intervals, the results lead us to generally recommend MMLE-multiple imputation. In the model with separate item discriminations over levels, marginally acceptable accuracy of the multilevel reliability measures and empirical coverage rate of the MC confidence intervals were found in a limited condition, 200 clusters, 30 cluster size, .2 ICC, and 40 items, in MMLE-multiple imputation. In the model with the same item discrimination over levels, the accuracy of the multilevel reliability measures and the empirical coverage rate of the MC confidence intervals were acceptable in all multilevel designs we considered with 40 items under MMLE-multiple imputation. We discuss these findings and provide guidelines for reporting multilevel reliability measures.

Self-Efficacy and Resilience: Mediating Mechanisms in the Relationship Between the Transformational Leadership Dimensions and Well-Being

The objective of this article is to test the roles of self-efficacy and resilience as consecutive mediators in the relationship between the four dimensions of transformational leadership and well-being (operationalized as psychosomatic complaints and psychological distress). The sample consists of 225 social services employees in Spain. Data were gathered at two time points with a time-lag of 6 months. We used path analysis to test the hypothesized model and Monte Carlo confidence intervals to check the significance of the indirect effects. Our results showed that only two of the four transformational leadership dimensions have a direct impact on self-efficacy: inspirational motivation and individualized consideration, although contrary to our hypothesis, the latter had a negative effect on self-efficacy. As for the indirect effects, self-efficacy did not mediate between the leadership dimensions and well-being, whereas resilience mediated between self-efficacy and well-being. Self-efficacy and resilience consecutively mediated between the leadership dimensions and well-being. Our findings contribute to understanding the underlying mechanisms connecting different dimensions of transformational leadership and well-being, and they highlight the importance of developing employees’ personal resources.

Actitudes en la adolescencia inicial y rendimiento académico: el rol mediacional del autoconcepto académico

This study was designed to examine academic self-concept as a potential mediator to better understand the relations between academic attitudes and academic achievement in early adolescence. A total of 1400 high school students from Alicante, Spain (47% female, M=12.5 years), participated in the study. Multilevel mediation analyses with Monte Carlo confidence intervals were used to measure within-subject effects at the student level (L1) and between-subject effects at the class level (L2). Academic attitudes (attitudes towards teachers and attitudes towards school) and academic self-concept were measured with validated scales, whereas academic achievement was assessed using the end-of-term grades obtained by the students in nine subjects. The results show, first, significant effects of the academic attitude constructs on the mediational and dependent variables at both the within and between levels. Second, academic self-concept was an important mediator for all academic attitude constructs at both levels of analysis. These results highlight the importance of academic self-concept during early adolescence and suggest that academic attitudes are crucial for the future development of educational models.

Early Adolescents’ Attitudes and Academic Achievement: The Mediating Role of Academic Self-concept

This study was designed to examine academic self-concept as a potential mediator to better understand the relations between academic attitudes and academic achievement in early adolescence. A total of 1398 high school students from Alicante, Spain (47% female, M=12.5 years), participated in the study. Multilevel mediation analyses with Monte Carlo confidence intervals were used to measure within-subject effects at the student level (L1) and between-subject effects at the class level (L2). Academic attitudes (attitudes towards teachers and attitudes towards school) and academic self-concept were measured with validated scales, whereas academic achievement was assessed using the end-of-term grades obtained by the students in nine subjects. The results show, first, significant effects of the academic attitude constructs on the mediational and dependent variables at both the within and between levels. Second, academic self-concept was an important mediator for all academic attitude constructs at both levels of analysis. These results highlight the importance of academic self-concept during early adolescence and suggest that academic attitudes are crucial for the future development of educational models.

Relationship between parent involvement and academic achievement through metacognitive strategies: A multiple multilevel mediation analysis.

Different studies reveal an association between parent involvement, metacognition, and academic achievement; however, the majority analyse the developmental process of acquisition in experimental or quasi-experimental designs with students enrolled in child education. Adolescence is an important stage in personal and academic development. Given the complexity of learning, and according to the metacognitive and affective model of self-regulated learning (Efklides, 2011, Educational Psychologist, 46, 6), different types of metacognitive processes are relevant for the optimal development of individuals in academic contexts. At the same time, individuals need stimuli from the environment, based on observation of their own and other's behaviour, as well as through communication and interaction with others. The present study examined the relations among parent involvement, metacognitive strategies, and academic achievement to investigate the mediational role of metacognition in the relation between parent involvement and academic achievement. The participants were 1,398 high school students from Spain (47% female, M=12. 5years). Multiple multilevel mediation analyses with Monte Carlo confidence intervals were used for measuring within-subjects effects at the student level and between-subjects effects at the class level. Parent involvement (perception of support, organization, and interest in the educational process; expectations; school relationship; time of support with homework) and metacognition were measured by questionnaires, whereas academic achievement was assessed using the end-of-term grades obtained by students for nine subjects. First, there was a significant direct effect of most parent involvement constructs on the mediational and dependent variables at both the within and between levels. Expectations had the highest predictive power on academic achievement. On the other hand, metacognitive strategies were an important mediator for all parent involvement constructs at both levels of analysis. These results highlight the importance of metacognition during early adolescence and suggest that parent involvement is crucial for the future development of educational models.

Pathwise Dynamic Programming

We present a novel method for deriving tight Monte Carlo confidence intervals for solutions of stochastic dynamic programming equations. Taking some approximate solution to the equation as an input, we construct pathwise recursions with a known bias. Suitably coupling the recursions for lower and upper bounds ensures that the method is applicable even when the dynamic program does not satisfy a comparison principle. We apply our method to three nonlinear option pricing problems, pricing under bilateral counterparty risk, under uncertain volatility, and under negotiated collateralization.

Dealing with uncertainty in the probability of overtopping of a flood mitigation dam

Abstract. In recent years, copula multivariate functions were used to model, probabilistically, the most important variables of flood events: discharge peak, flood volume and duration. However, in most of the cases, the sampling uncertainty, from which small-sized samples suffer, is neglected. In this paper, considering a real reservoir controlled by a dam as a case study, we apply a structure-based approach to estimate the probability of reaching specific reservoir levels, taking into account the key components of an event (flood peak, volume, hydrograph shape) and of the reservoir (rating curve, volume–water depth relation). Additionally, we improve information about the peaks from historical data and reports through a Bayesian framework, allowing the incorporation of supplementary knowledge from different sources and its associated error. As it is seen here, the extra information can result in a very different inferred parameter set and consequently this is reflected as a strong variability of the reservoir level, associated with a given return period. Most importantly, the sampling uncertainty is accounted for in both cases (single-site and multi-site with historical information scenarios), and Monte Carlo confidence intervals for the maximum water level are calculated. It is shown that water levels of specific return periods in a lot of cases overlap, thus making risk assessment, without providing confidence intervals, deceiving.