Estimation Approach Research Articles

An investigation to improve a nonlinear mixed-effects approach for EC50 estimation based on multi-donor dose-response data.

Dose-response relationships are important in assessing the efficacy and potency of compounds, which can usually be characterized by a 4-parameter logistic (4-PL) model estimating EC50, slope factor, lower asymptote, and upper asymptote. EC50, the concentration of a compound that induces a response halfway between the baseline and maximum, is a key quantity to evaluate compound potency. For multi-donor dose-response data, it is often of interest to estimate the overall EC50 (i.e. the average EC50 of the population of donors) and its 95% confidence interval (CI). A few multi-donor EC50 estimation methods have been proposed in the literature. Jiang and Kopp-Schneider (2014) systematically compared the meta-analysis approach and the nonlinear mixed-effects approach and concluded that the meta-analysis approach is simple and robust to summarize EC50 estimates from multiple experiments, especially suited in the case of a small number of experiments, while the nonlinear mixed-effects approach has the issue of convergence failures probably due to overparameterization. In this article, we propose a modification of the nonlinear mixed-effects approach by using the stochastic approximation expectation-maximization (SAEM) algorithm to estimate model parameters and using multiple starting points to search for globally optimal values, which can substantially alleviate the issue of convergence failures even for small number of donors (e.g. n = 3), and achieve a smaller absolute median bias and better coverage probability of 95% confidence interval than the meta-analysis approach when the number of donors is not too small (e.g. n ≥ 7).

A Food Intake Estimation System Using an Artificial Intelligence-Based Model for Estimating Leftover Hospital Liquid Food in Clinical Environments: Development and Validation Study.

Medical staff often conduct assessments, such as food intake and nutrient sufficiency ratios, to accurately evaluate patients' food consumption. However, visual estimations to measure food intake are difficult to perform with numerous patients. Hence, the clinical environment requires a simple and accurate method to measure dietary intake. This study aims to develop a food intake estimation system through an artificial intelligence (AI) model to estimate leftover food. The accuracy of the AI's estimation was compared with that of visual estimation for liquid foods served to hospitalized patients. The estimations were evaluated by a dietitian who looked at the food photo (image visual estimation) and visual measurement evaluation was carried out by a nurse who looked directly at the food (direct visual estimation) based on actual measurements. In total, 300 dishes of liquid food (100 dishes of thin rice gruel, 100 of vegetable soup, 31 of fermented milk, and 18, 12, 13, and 26 of peach, grape, orange, and mixed juices, respectively) were used. The root-mean-square error (RMSE) and coefficient of determination (R2) were used as metrics to determine the accuracy of the evaluation process. Corresponding t tests and Spearman rank correlation coefficients were used to verify the accuracy of the measurements by each estimation method with the weighing method. The RMSE obtained by the AI estimation approach was 8.12 for energy. This tended to be smaller and larger than that obtained by the image visual estimation approach (8.49) and direct visual estimation approach (4.34), respectively. In addition, the R2 value for the AI estimation tended to be larger and smaller than the image and direct visual estimations, respectively. There was no difference between the AI estimation (mean 71.7, SD 23.9 kcal, P=.82) and actual values with the weighing method. However, the mean nutrient intake from the image visual estimation (mean 75.5, SD 23.2 kcal, P<.001) and direct visual estimation (mean 73.1, SD 26.4 kcal, P=.007) were significantly different from the actual values. Spearman rank correlation coefficients were high for energy (ρ=0.89-0.97), protein (ρ=0.94-0.97), fat (ρ=0.91-0.94), and carbohydrate (ρ=0.89-0.97). The measurement from the food intake estimation system by an AI-based model to estimate leftover liquid food intake in patients showed a high correlation with the actual values with the weighing method. Furthermore, it also showed a higher accuracy than the image visual estimation. The errors of the AI estimation method were within the acceptable range of the weighing method, which indicated that the AI-based food intake estimation system could be applied in clinical environments. However, its lower accuracy than that of direct visual estimation was still an issue.

SOFTWARE COST EFFORT AND TIME ESTIMATION USING DRAGONFLY WHALE LION OPTIMIZED DEEP NEURAL NETWORK

Effective software development depends on the exact estimation of effort, time, cost, and customer satisfaction. Software project management requires an accurate evaluation of software development's effort, time, and cost, often underestimated or overestimated. So far, methodology has yet to accurately and reliably estimate the cost of software development. To overcome this issue, this paper proposed a constructive rapid application development model based on software cost effort and time estimation approach (CORADMO-based CETA) for accurate software cost estimation. The data requirements, cost drivers, constraints, and priorities are given as input to the fuzzy inference system (FIS). The processed output, such as effort, time, and cost for the nominal plan, shortest schedule plan, and least cost plan, is computed in the FIS. To reduce the effort, time, and cost, the output is optimized by dragonfly whale lion optimization (DWLO), which provides the best-estimated effort, time, and cost as an output for software development. The proposed CORADMO-based CETA model is tested in the NASA 93 dataset using MATLAB. The performance of the CORADMO-based CETA method is measured in terms of Pred (25 %), magnitude of relative error, and mean magnitude of relative error, attaining the values of 80.72 %, 87.94 %, and 98.13 %, respectively. Finally, the CORADMO-based CETA model justifies the suitability of dragonfly whale lion optimization with the proposed fuzzy logic.

Efficient High Heating Value estimation using Latin Hypercube Sampling and Artificial Neural Network-based approach.

To maximize energy recovery in waste-to-energy (WTE) systems, the High Heating Value (HHV) of municipal solid waste (MSW) must be accurately estimated. To forecast the HHV of MSW, this study proposes a unique method that combines an Artificial Neural Network (ANN) model with Latin Hypercube Sampling (LHS), with a focus on Solan City, Himachal Pradesh, India. In the present study, the elemental characteristics of waste have been used to deal with uncertainty and to find the suitable parameters responsible for the HHV of the MSW. Initially, Latin Hypercube Sampling (LHS) has been used to deal with uncertainty in the elemental composition of MSW, which includes carbon (C), hydrogen (H), nitrogen (N), sulfur (S), and oxygen (O) content. This elemental composition has been used as input parameters to the ANN model for predicting the HHV of MSW. The network 5-28-5-1 offered a minimum MAPE value of 2.18%, MSE, RMSE and R2 values are 0.012, 0.107 and 0.767, respectively. Thereafter, a synaptic weight approach was used to find the most significant parameters responsible for HHV in MSW. It was observed that carbon is the most suitable parameter for HHV of MSW. By dealing with the uncertainty in MSW characteristics, the integration of LHS strengthens the robustness of the model. The results offer an accurate and economical approach for HHV estimation, which will be useful for improving the MSW management and WTE conversion procedures.

Application of Multiple Linear Regression Models in Deriving Water Quality Criteria for Lead: Comparison of Metal Bioavailability Estimation Approaches

Application of Multiple Linear Regression Models in Deriving Water Quality Criteria for Lead: Comparison of Metal Bioavailability Estimation Approaches

Empirical Sandwich Variance Estimator for Iterated Conditional Expectation g-Computation.

Iterated conditional expectation (ICE) g-computation is an estimation approach for addressing time-varying confounding for both longitudinal and time-to-event data. Unlike other g-computation implementations, ICE avoids the need to specify models for each time-varying covariate. For variance estimation, previous work has suggested the bootstrap. However, bootstrapping can be computationally intense. Here, we present ICE g-computation as a set of stacked estimating equations. Therefore, the variance for the ICE g-computation estimator can be consistently estimated using the empirical sandwich variance estimator. Performance of the variance estimator was evaluated empirically with a simulation study. The proposed approach is also demonstrated with an illustrative example on the effect of cigarette smoking on the prevalence of hypertension. In the simulation study, the empirical sandwich variance estimator appropriately estimated the variance. When comparing runtimes between the sandwich variance estimator and the bootstrap for the applied example, the sandwich estimator was substantially faster, even when bootstraps were run in parallel. The empirical sandwich variance estimator is a viable option for variance estimation with ICE g-computation.

Multichannel Analysis of Surface Waves based on Common Virtual Source Gathers of Seismic Ambient Noise Cross-Correlations: A Case Study at an Earth Dam in Brazil

The S-wave velocity (Vs) is a valuable parameter for assessing the mechanical properties of subsurface materials for geotechnical purposes. Seismic surface wave methods have become prominent for estimating near-surface Vs models. Researchers have proposed methods based on passive seismic signals as efficient alternatives to enhance depth of investigation, lateral resolution and reduce field effort. This study presents the Multichannel Analysis of Surface Waves (MASW) utilizing Common Virtual Source Gathers (CVSGs) derived from seismic ambient noise cross-correlations, based on Ambient Noise Seismic Interferometry concepts. The method is applied to passive data acquired with an array of receivers at the Paranoá earth dam in Brasília, Brazil, to construct a pseudo-2D Vs image of the massif for interpretation. Our findings showcase the adopted processing flow and combination of methods as an effective approach for near-surface Vs estimation, demonstrating its usability also for large earth dam embankments.

Accuracy of second and third molar maturity indices, Olze, Haavikko, and Demirjian methods for 14- and 16-year-old age thresholds assessment in Croatian children and adolescents.

This study explores the reliability of four established legal age threshold estimation approaches in a Croatian sample. We applied Haavikko stages, Demirjian stages, Olze's third molar eruption stages, and second and third molar maturity indices measurement in 593 orthopantomograms of Croatian children and adolescents aged 11.00-20.99years old. The left mandibular second and third molar were assessed. Logistic regression analysis was conducted to test the significance of predictive variables. Logistic Receiver operating characteristic (ROC) curves were performed to evaluate the classification ability of variables for estimating 14- and 16-year-old thresholds. The areas under the ROC curve (AUC), accuracy (Acc), sensitivity (Se), specificity (Sp), Positive Likelihood Ratio (LR +), Negative Likelihood Ratio (LR-), and Bayes post-test probability (Bayes PTP) were calculated to evaluate classification performance. Results suggest that the combination of I2M&I3M is the best classifier for the 14-year-old threshold (AUC = 0.879); for males alone, I2M is an even better classifier (AUC = 0.881). The highest Acc 80.1% (95%CI, 75.9%-83.9%), Bayes PTP 86.5% (95%CI, 82.8%-89.7%) and Sp 88.9% (95%CI, 83.0%-93.3%) were by I3M < 0.81 & I2M < 0.03 in total samples; the highest Acc 86.1% (80.6%- 90.6%), Bayes PTP 87.2% (95%CI, 81.7%- 91.4%) and Sp 87.8% (95%CI, 78.2%- 94.3%) were by I2M < 0.01 in males, Acc of Haavikko Ac and Demirjian H stage in second molar is very close with slightly lower Bayes PTP and Sp. I3M is a good classifier for 16-year-old threshold (AUC = 0.889). The cut-off value I3M < 0.34 can be used to classify the 16-year-old threshold with Acc of 80.6% (95%CI, 77.2%-83.7%), Sp of 83.4% (95%CI, 79.0%-87.3%), and 81.7% (95%CI, 78.4%-84.8%) Bayes PTP. In conclusion, to classify the 14-year-old threshold, a pair of cut-off values I3M < 0.81 & I2M < 0.03 can be used in Croatian females; I2M < 0.01, Demirjian H stage, Haavikko Ac stage in second molar, and the pair I3M < 0.81 & I2M < 0.03 can all be used in Croatian males. I3M < 0.34 can classify the 16-year-old threshold in Croatian populations.

Discrete Joint Random Variables in Fréchet-Weibull Distribution: A Comprehensive Mathematical Framework with Simulations, Goodness-of-Fit Analysis, and Informed Decision-Making

This paper introduces a novel four-parameter discrete bivariate distribution, termed the bivariate discretized Fréchet–Weibull distribution (BDFWD), with marginals derived from the discretized Fréchet–Weibull distribution. Several statistical and reliability properties are thoroughly examined, including the joint cumulative distribution function, joint probability mass function, joint survival function, bivariate hazard rate function, and bivariate reversed hazard rate function, all presented in straightforward forms. Additionally, properties such as moments and their related concepts, the stress–strength model, total positivity of order 2, positive quadrant dependence, and the median are examined. The BDFWD is capable of modeling asymmetric dispersion data across various forms of hazard rate shapes and kurtosis. Following the introduction of the mathematical and statistical frameworks of the BDFWD, the maximum likelihood estimation approach is employed to estimate the model parameters. A simulation study is also conducted to investigate the behavior of the generated estimators. To demonstrate the capability and flexibility of the BDFWD, three distinct datasets are analyzed from various fields, including football score records, recurrence times to infection for kidney dialysis patients, and student marks from two internal examination statistical papers. The study confirms that the BDFWD outperforms competitive distributions in terms of efficiency across various discrete data applications.

Comparative Analysis of Tsunami Casualty Estimation Approaches: Agent-Based Modeling versus Simplified Approach in Japanese Coastal Cities

AbstractEstimating potential casualties from a significant earthquake and tsunami event is crucial to enhance disaster preparedness and response. Although various approaches exist to assess potential casualties, few studies have made direct comparisons between them. The present study aimed to clarify the differences in the estimation of casualties between an agent-based model (ABM), which can capture detailed evacuation behavior but demands significant computational resources, and a simplified approach at less computational cost by assuming that evacuees would move along a straight line from their initial location to the closest evacuation destination. These different approaches were applied to three coastal cities in Japan—Mihama, Kushimoto, and Shingu in Wakayama Prefecture—revealing significant differences in the estimated results between the ABM and the simplified approach. Notably, when the effects of building collapse due to an earthquake were considered, the mortality rates estimated by the ABM were higher than those estimated by the simplified approach in the three cities. There were also significant differences in the spatial distribution of the estimated mortality rates between the ABM and the simplified approach. The findings suggest that while the simplified approach can yield results more quickly, casualty estimates derived from such models should be interpreted with caution.

An efficient deep learning approach for ultimate bond strength estimations of corroded bar and concrete

Abstract The corrosion behavior of the reinforced concrete structure depends heavily on the interfacial bond behavior between steel and concrete. Over the years, the deterioration of integrated reinforced steel has weakened this bond and potentially led to structural problems. Conventional methods of bond strength evaluation, such as pullout and bond beam tests, is frequently intrusive and tedious. Therefore, there is a growing need for non-intrusive, effective, and reliable forecasting algorithms capable of assessing bond deterioration caused by corrosion. Traditional algorithms for predicting bond strength make it difficult to capture the complex nature of steel-concrete bonds. The present study proposes two different deep learning algorithms, i.e., convolutional neural networks (CNN) and long short-term memory (LSTM), for predicting maximum bond strength in the presence of corrosion. The predictive model is based on a comprehensive dataset comprising 218 datasets from previous studies encompassing diverse input and output variables for predicting the models. The models were trained and tested using the given data to improve early predictions of corrosion-induced bond degradations. The predictive model’s effectiveness was assessed by applying various performance metrics. From this study, the CNN model exhibits higher accuracy and efficiency with mean absolute error, root mean square error, and mean absolute percentage error of 0.25, 0.28, and 95.72, respectively, for predicting ultimate bond strength estimations. The findings of this study provide an accurate and robust prediction model to improve the reliability and safety of the concrete structure by enhancing the residual load-bearing capacity of the concrete structure that has undergone corrosion.

Deep Learning for Opportunistic Rain Estimation via Satellite Microwave Links

Accurate precipitation measurement is critical for managing flood and drought risks. Traditional meteorological tools, such as rain gauges and remote sensors, have limitations in resolution, coverage, and cost-effectiveness. Recently, the opportunistic use of microwave communication signals has been explored to improve precipitation estimation. While there is growing interest in using satellite-to-earth microwave link (SMLs) for machine learning-based precipitation estimation, direct rainfall estimation from raw signal-to-noise ratio (SNR) data via deep learning remains underexplored. This study investigates a range of machine learning (ML) approaches, including deep learning (DL) models and traditional methods like gradient boosting machine (GBM), for estimating rainfall rates from SNR data collected by interactive satellite receivers. We develop real-time models for rainfall detection and estimation using downlink SNR signals from satellites to user terminals. By leveraging a year-long dataset from multiple locations—including SNR measurements paired with disdrometer and rain-gauge data—we explore and evaluate various ML models. Our final models include ensemble approaches for both rainfall detection and cumulative rainfall estimation. The proposed models provide a reliable solution for estimating precipitation using Earth–satellite microwave links, potentially improving precipitation monitoring. Compared to the state-of-the-art power-law-based models applied to similar datasets reported in the literature, our ML models achieve a 46% reduction in the RMSE

A New Iterative Algorithm for Magnetic Motion Tracking

Motion analysis is of great interest to a variety of applications, such as virtual and augmented reality and medical diagnostics. Hand movement tracking systems, in particular, are used as a human–machine interface. In most cases, these systems are based on optical or acceleration/angular speed sensors. These technologies are already well researched and used in commercial systems. In special applications, it can be advantageous to use magnetic sensors to supplement an existing system or even replace the existing sensors. The core of a motion tracking system is a localization unit. The relatively complex localization algorithms present a problem in magnetic systems, leading to a relatively large computational complexity. In this paper, a new approach for pose estimation of a kinematic chain is presented. The new algorithm is based on spatially rotating magnetic dipole sources. A spatial feature is extracted from the sensor signal, the dipole direction in which the maximum magnitude value is detected at the sensor. This is introduced as the “maximum vector”. A relationship between this feature, the location vector (pointing from the magnetic source to the sensor position) and the sensor orientation is derived and subsequently exploited. By modelling the hand as a kinematic chain, the posture of the chain can be described in two ways: the knowledge about the magnetic correlations and the structure of the kinematic chain. Both are bundled in an iterative algorithm with very low complexity. The algorithm was implemented in a real-time framework and evaluated in a simulation and first laboratory tests. In tests without movement, it could be shown that there was no significant deviation between the simulated and estimated poses. In tests with periodic movements, an error in the range of 1° was found. Of particular interest here is the required computing power. This was evaluated in terms of the required computing operations and the required computing time. Initial analyses have shown that a computing time of 3 μs per joint is required on a personal computer. Lastly, the first laboratory tests basically prove the functionality of the proposed methodology.

Penalized Likelihood Estimation for Current Status Data with Informative Censoring

Current status data occurs when failure time of subjects in a survival study is only known to be either less or greater than the censoring time. Thus, the failure time is either left – or right – censored. Analyzing data of this structure under the Cox Proportional Hazards model with dependent censoring assumption can be challenging. To address this, a Penalized Maximum Likelihood Estimation (PMLE) approach was proposed. The unknown baseline cumulative hazard functions for both the failure time and the censoring time were estimated using splines. The advantage of penalized approach over unpenalized method is that that the desired smoothness level of the functions are controlled by their respective penalty terms. The possible dependence between the failure and censoring times was accounted for using the gamma-frailty model. An easy to implement hybrid computational algorithm is proposed to estimate the PMLEs and the Bayesian technique was employed for the estimation of the variances of the parameters. Extensive simulation studies were conducted to assess the statistical properties of the PMLEs. It was observed that the realized estimators were not only consistent, asymptotically normal and efficient, but also, were robust to the number of knots chosen, the proportion of dependent censoring used and the frailty distribution employed. The proposed PMLE method was further applied to real data obtained from tumorigenicity experiment.

Measuring How AI Innovations and Financial Accessibility Influence Environmental Sustainability in the G-7: The Role of Globalization with Panel ARDL and Quantile Regression Analysis

This study investigates the impact of AI innovation on environmental sustainability in the G-7 region from 2010 to 2022. Additionally, it tests the Load Capacity Curve (LCC) hypothesis in relation to financial accessibility, globalization, and urbanization. Cross-sectional dependence and slope homogeneity tests reveal the presence of cross-sectional dependence and heterogeneity issues. Panel unit root and panel cointegration tests confirm that the variables are free from unit root problems and are cointegrated in the long run. To identify significant factors influencing environmental sustainability, this study employs Panel ARDL and Quantile Regression methods. Both methods confirm the LCC hypothesis in the G-7 region, demonstrating a U-shaped relationship between income and the load capacity factor. The results indicate that AI innovation and financial accessibility are significantly positively correlated with the load capacity factor, while globalization and urbanization are negatively correlated, leading to lower environmental sustainability. To validate the robustness of the Panel ARDL and Quantile Regression results, Driscoll-Kraay standard errors, Augmented Mean Group, and Common Correlated Effects Mean Group estimation approaches are applied, all of which support the initial findings. Furthermore, the D-H causality test reveals unidirectional causality from economic growth, financial accessibility, globalization, and urbanization to the load capacity factor, and bidirectional causality between AI innovation and the load capacity factor.

A New Generalized Family of Weibull-Exponentiated Half Logistic-G Distribution with Applications

We propose a new extension of the Weibull-exponentiated half logistic-G (WEHL-G) distribution, called the Marshall-Olkin-Weibull-exponentiated half logistic-G (MO-WEHL-G) family of distributions. The properties of this family of distributions including quantile function, distribution of the order statistics, hazard rate function, Rényi entropy and moments of residual life are presented. To estimate the parameters of the MO-WEHL-G family of distributions, six different estimation approaches are used, namely, maximum likelihood, Anderson-Darling, Ordinary Least Squares, Weighted Least Squares, Cramér-von Mises and Maximum Product of Spacing. The consistency properties of the six estimation methods were assessed using Monte Carlo simulations for a special case of the MO-WEHL-G family of distributions. The flexibility and importance of the proposed model was assessed using numerous goodness-of-fit statistics on three different data sets.

The Effect of Measurement Error on Hypothesis Testing in Small Sample Structural Equation Modeling: A Comparison of Various Estimation Approaches

Researchers seeking valid statistical inference in the presence of measurement error often apply approaches that ignore measurement error. This may result in biased estimates, inflated type I error rates, diminished power, and therefore, increases the risk of drawing erroneous conclusions. However, current advice on accounting for random measurement error is limited to large samples and traditional linear models. This article aims to address this gap for small samples and recent estimation approaches in structural equation modeling. Our results show substantial type I error rate inflation for approaches that ignore measurement error when the model contains correlated latent predictors.

Sustainability of Groundwater Exploitation Under Climate Change Scenarios in a Mountainous Area of South Korea

The excessive extraction of groundwater is a globally significant issue, as it can lead to the permanent loss of groundwater system sustainability. Sustainable groundwater requires development that appropriately balances the needs of both humans and the environment. In this study, the exploitable groundwater (EGW) of the So-Yang-gang Dam (SYD) Basin was estimated based on simulated groundwater recharge rates using SWAT, and the sustainability of future groundwater development was evaluated under different climate change scenarios. The EGW in each sub-watershed of the SYD was estimated to range from 60 to 240 mm/year, with higher values in the upstream watersheds. A sustainability index (SI) was evaluated, ranging from 0.56 to 1.0 across various GCMs. The analysis revealed that uniform EGW across a watershed is overestimated value in sub-watersheds with low recharge rates, potentially accelerating groundwater depletion in those areas. Thus, a flexible EGW estimation approach is essential to balance groundwater conservation with human water demands.

Estimation of Rice Crop Acreage in Kuttanad Region, Kerala Using Landsat 8 OLI IMAGES and GIS Techniques

Aims: The study aimed to delineate rice accurately (Oryza sativa L.) cultivation areas in the Kuttanad region, Kerala, during the Puncha season of 2023-24 using medium- to high-resolution optical satellite data, particularly Landsat 8 Operational Land Imager (OLI), to aid in preharvest prediction of agricultural production and policy making. Study Design: This study used a remote sensing-based approach for rice area estimation, focusing on supervised classification methods. Place and Duration of Study: The study was conducted in Kuttanad, Kerala, a low-lying agroecosystem, during the Puncha season of 2023-24. Methodology: The study utilised two cloud-free Landsat 8 OLI images to delineate rice-growing areas. The images were pre-processed, mosaicked, and analysed using ArcGIS software. A supervised classification approach was employed using the Maximum Likelihood Classification algorithm. The study area was classified into five categories: rice fields, other crops, low vegetation, built-up areas, and water bodies. Ground-truth data was used to validate the classification accuracy. Results: The total rice area delineated during the Puncha season was 43,550.28 hectares. The classification achieved an accuracy of 93.33%, with a kappa coefficient of 0.87, indicating high reliability. Conclusion: The accurate delineation of rice-growing areas using satellite imagery provides valuable information for assessing production levels and planning for food security. This methodology can aid in agricultural planning and contingency strategies, particularly in regions like Kuttanad, which face challenges such as flooding and soil toxicity.

Preliminary study on the feasibility of approximating children's engagement level from their emotions estimation by a picture-based, three-model AI in a family-robot cohabitation scenario

Haru4Kids (H4K) is a system that emulates the physical, social, family-oriented robot Haru, designed with the goal of cohabitating with children in their homes for extended periods of time. In a previous experiment [Garcia GA, Perez G, Levinson L, et al. Living with Haru4Kids: study on children's activity and engagement in a family-robot cohabitation scenario. In: 2023 IEEE ROMAN; 2023 Aug. p. 1428–1435], seven families kept H4K for a span of two weeks in their homes. Throughout this period of cohabitation, we collected child-robot interaction data, including images that were later hand-annotated to estimate user engagement. In this present work, we used a novel AI-based, four-stage framework available from Roboflow for the automatic estimation of children's level of engagement from their inferred emotions. We did a deep study of the performance and behaviour of that framework over our dataset of users' pictures and characterized its response in order to understand its advantages and limitations, including the technique used to translate emotions into engagement levels. We also tested a different approach for that mapping, using a machine learning technique based on Support Vector Machine (SVM). The framework yielded promising results just ‘off-the-shelf’: 0.47–0.68 accuracy and 0.46–0.70 F1 using the original mapping, and 0.39–0.75 and 0.37–0.78 respectively using SVM. Therefore, we propose this emotion-based approach for engagement estimation from pictures.