A Bayesian Measure of Model Accuracy.

Ensuring that the proposed probabilistic model accurately represents the problem is a critical step in statistical modeling, as choosing a poorly fitting model can have significant repercussions on the decision-making process. The primary objective of statistical modeling often revolves around predicting new observations, highlighting the importance of assessing the model's accuracy. However, current methods for evaluating predictive ability typically involve model comparison, which may not guarantee a good model selection. This work presents an accuracy measure designed for evaluating a model's predictive capability. This measure, which is straightforward and easy to understand, includes a decision criterion for model rejection. The development of this proposal adopts a Bayesian perspective of inference, elucidating the underlying concepts and outlining the necessary procedures for application. To illustrate its utility, the proposed methodology was applied to real-world data, facilitating an assessment of its practicality in real-world scenarios.

Assessment of spatial variation in lung cancer incidence and air pollutants: spatial regression modeling approach.

A notable finding is that Kerala's capital Thiruvananthapuram has shown an increasing trend in lung cancer (LC) incidence. Long-term exposure to air pollution is a significant environmental risk factor for LC. This study investigated the spatial association between LC and exposure to air pollutants in Thiruvananthapuram, using Spatial Lag Model (SLM), Spatial Error Model (SEM), and Geographically Weighted Regression (GWR). The results showed that overall LC incidence rate was 111 per 105 males (age >60 years), whereas spatial distribution map revealed that 48% of the area had an incidence rate greater than 150. The results revealed a significant association between PM2.5 and LC. SLM was identified as the best model that predicted 62% variation in LC. GWR model improved model performance and made better local predictions in the southeastern parts of the study area. This study explores the effectiveness of spatial regression techniques for dealing spatial effects and pinpointing high-risk areas.

The healthcare costs of increased body mass index-evidence from The Trøndelag Health Study.

BACKGROUND: Earlier studies have estimated the impact of increased body mass index (BMI) on healthcare costs. Various methods have been used to avoid potential biases and inconsistencies. Each of these methods measure different local effects and have different strengths and weaknesses. METHODS: In the current study we estimate the impact of increased BMI on healthcare costs using nine common methods from the literature: multivariable regression analyses (ordinary least squares, generalized linear models, and two-part models), and instrumental variable models (using previously measured BMI, offspring BMI, and three different weighted genetic risk scores as instruments for BMI). We stratified by sex, investigated the implications of confounder adjustment, and modelled both linear and non-linear associations. RESULTS: There was a positive effect of increased BMI in both males and females in each approach. The cost of elevated BMI was higher in models that, to a greater extent, account for endogenous relations. CONCLUSION: The study provides solid evidence that there is an association between BMI and healthcare costs, and demonstrates the importance of triangulation.

Aqueous size exclusion chromatography applied to polymer analysis: experimental conditions and molecular weight calibration curves.

Aqueous mode size exclusion chromatography (SEC) was employed for the analysis and construction of molecular weight (MW) calibration curves of three water-soluble polymers, namely, polyethylene glycol, polyethylene oxide, and polyacrylic acid sodium salt. Several calibration curves were obtained, varying chromatographic conditions such as columns arrangement, ionic strength, temperature and pH, in addition trends in polymeric chromatographic behavior were examined. The variation in SEC distribution coefficients at different temperatures was found to be below 10 %, indicating that the studied polymers follow an ideal SEC mechanism under the tested conditions. Thus, differences in chromatographic behavior were ascribed to changes in polymer configuration induced by media and/or temperature. These variations in morphology were consistent with the observed SEC behavior. Regarding MW calibration, polynomial regression models ranging from first to fifth order were applied, and the most adequate ones were selected based on their fit and prediction capabilities. Third order polynomials were the preferred models for polyethylene glycol and polyacrylic acid sodium salt, independently of chromatographic conditions. Meanwhile for polyethylene oxide, either third or fifth-order polynomial models were optimal depending on the chromatographic conditions. All the selected regression models presented coefficients of multiple determination (R2) above 0.990, while achieving relative errors of prediction (REP%) in MW ranging from 0.3 to 4 % for cross-validation.

Associations between exposure to pesticides mixture and semen quality among the non-occupationally exposed males: Four statistical models.

Most epidemiological studies on the associations between pesticides exposure and semen quality have been based on a single pesticide, with inconsistent major results. In contrast, there was limited human evidence on the potential effect of pesticides mixture on semen quality. Our study aimed to investigate the relationship of pesticide profiles with semen quality parameters among 299 non-occupationally exposed males aged 25-50 without any clinical abnormalities. Serum concentrations of 21 pesticides were quantified by gas chromatography-tandem mass spectrometry (GC-MS/MS). Semen quality parameters were abstracted from medical records. Generalized linear regression models (GLMs) and three mixture approaches, including weighted quantile sum regression (WQS), elastic net regression (ENR) and Bayesian kernel machine regression (BKMR), were applied to explore the single and mixed effects of pesticide exposure on semen quality. In GLMs, as the serum levels of Bendiocarb, ß-BHC, Clomazone, Dicrotophos, Dimethenamid, Paclobutrazole, Pentachloroaniline and Pyrimethanil increased, the straight-line velocity (VSL), linearity (LIN) and straightness (STR) decreased. This negative association also occurred between the concentration of ß-BHC, Pentachloroaniline, Pyrimethanil and progressive motility, total motility. In the WQS models, pesticides mixture was negatively associated with total motility and several sperm motility parameters (ß: -3.07∼-1.02 per decile, FDR-P<0.05). After screening the important pesticides derived from the mixture by ENR model, the BKMR models showed that the decreased qualities for VSL, LIN, and STR were also observed when pesticide mixtures were at ≥ 70th percentiles. Clomazone, Dimethenamid, and Pyrimethanil (Posterior inclusion probability, PIP: 0.2850-0.8900) were identified as relatively important contributors. The study provides evidence that exposure to single or mixed pesticide was associated with impaired semen quality.

A Regularized Bayesian Dirichlet-multinomial Regression Model for Integrating Single-cell-level Omics and Patient-level Clinical Study Data.

The abundance of various cell types can vary significantly among patients with varying phenotypes and even those with the same phenotype. Recent scientific advancements provide mounting evidence that other clinical variables, such as age, gender, and lifestyle habits, can also influence the abundance of certain cell types. However, current methods for integrating single-cell-level omics data with clinical variables are inadequate. In this study, we propose a regularized Bayesian Dirichlet-multinomial regression framework to investigate the relationship between single-cell RNA sequencing data and patient-level clinical data. Additionally, the model employs a novel hierarchical tree structure to identify such relationships at different cell-type levels. Our model successfully uncovers significant associations between specific cell types and clinical variables across three distinct diseases: pulmonary fibrosis, COVID-19, and non-small cell lung cancer. This integrative analysis provides biological insights and could potentially inform clinical interventions for various diseases.

Predictive modeling and regression analysis of diverse sulfonamide compounds employed in cancer therapy.

Topological indices (TIs) have rich applications in various biological contexts, particularly in therapeutic strategies for cancer. Predicting the performance of compounds in the treatment of cancer is one such application, wherein TIs offer insights into the molecular structures and related properties of compounds. By examining, various compounds exhibit different degree-based TIs, analysts can pinpoint the treatments that are most efficient for specific types of cancer. This paper specifically delves into the topological indices (TIs) implementations in forecasting the biological and physical attributes of innovative compounds utilized in addressing cancer through therapeutic interventions. The analysis being conducted to derivatives of sulfonamides, namely, 4-[(2,4-dichlorophenylsulfonamido)methyl]cyclohexanecarboxylic acid (1), ethyl 4-[(naphthalene-2-sulfonamido)methyl]cyclohexanecarboxylate (2), ethyl 4-[(2,5-dichlorophenylsulfonamido)methyl]cyclohexanecarboxylate (3), 4-[(naphthalene-2-sulfonamido)methyl]cyclohexane-1-carboxylic acid (4) and (2S)-3-methyl-2-(naphthalene-1-sulfonamido)-butanoic acid (5), is performed by utilizing edge partitioning for the computation of degree-based graph descriptors. Subsequently, a linear regression-based model is established to forecast characteristics, like, melting point and formula weight in a quantitative structure-property relationship. The outcomes emphasize the effectiveness or capability of topological indices as a valuable asset for inventing and creating of compounds within the realm of cancer therapy.

A robust regression model for bounded count health data.

Bounded count response data arise naturally in health applications. In general, the well-known beta-binomial regression model form the basis for analyzing this data, specially when we have overdispersed data. Little attention, however, has been given to the literature on the possibility of having extreme observations and overdispersed data. We propose in this work an extension of the beta-binomial regression model, named the beta-2-binomial regression model, which provides a rather flexible approach for fitting a regression model with a wide spectrum of bounded count response data sets under the presence of overdispersion, outliers, or excess of extreme observations. This distribution possesses more skewness and kurtosis than the beta-binomial model but preserves the same mean and variance form of the beta-binomial model. Additional properties of the beta-2-binomial distribution are derived including its behavior on the limits of its parametric space. A penalized maximum likelihood approach is considered to estimate parameters of this model and a residual analysis is included to assess departures from model assumptions as well as to detect outlier observations. Simulation studies, considering the robustness to outliers, are presented confirming that the beta-2-binomial regression model is a better robust alternative, in comparison with the binomial and beta-binomial regression models. We also found that the beta-2-binomial regression model outperformed the binomial and beta-binomial regression models in our applications of predicting liver cancer development in mice and the number of inappropriate days a patient spent in a hospital.

Three-dimensional prediction of the nose for facial reconstruction: A preliminary study on North Indian adults.

Forensic facial reconstruction is the last recourse to establish the identity of an unknown skull. The facial soft-tissue thickness (FSTT) is required to reconstruct various facial features on a skull. Unlike other facial features, the nose is made of cartilaginous tissue except for a small nasal bone. A large cavity (pyriform aperture) exists on the skull in place of the nose, which makes it a challenging job for reconstruction. The nose is a vital feature for the recognition of a face. Any change in the shape or size of the nose can alter the original aesthetic of the face. The present study proposes angles and regression functions on the bony structure to predict the various parts of the soft nose. A sample of computed tomography (CT) images of 100 males and 100 females aged between 18 and 45 years were included in the study. Apart from measuring fourteen linear parameters with three angles, simple linear regression models were derived for five pairs of parameters. Pearson's correlation coefficients for most of the parameters ranging between 0.221 and 0.872 were found to be significant at p ≤ 0.05 level. FSTT at three anatomical landmarks of the nose was also measured. A morphological observation study was undertaken to find the most frequent direction of the bony anterior nasal spine (ans) and its relation with the position of the pronasale (prn) on the soft nose. The devised parameters proposed in the study may also prove useful for reconstructing the nose in other populations.

Assessment of the influence of chewing pattern on glucose homeostasis through linear regression model.

OBJECTIVE: Maintaining plasma glucose homeostasis is vital for mammalian survival, but the masticatory function, which influences glucose regulation, has, to our knowledge, been overlooked. RESEARCH METHODS AND PROCEDURES: In this study, we investigated the relationship between the glycemic response curve and chewing performance in a group of 8 individuals who consumed 80 g of apple. A device called "Chewing" utilizing electromyographic (EMG) technology quantitatively assesses chewing pattern, while glycemic response is analyzed using continuous glucose monitoring. We assessed chewing pattern characterizing chewing time (tchew), number of bites (nchew), work (w), power (wr), and chewing cycles (tcyc). Moreover, we measured the principal features of the glycemic response curve, including the area under the curve (α) and the mean time to reach the glycemic peak (tmean). We used linear regression models to examine the correlations between these variables. RESULTS: tchew, nchew, and wr were correlated with α (R2 =  0.44,   P  <  0.05 for tchew and nchew, P  <  0.001 for wr), and tmean was correlated with tchew (R2  =  0.25,  P  <  0.05). These findings suggest that increasing chewing time and power, while reducing the number of chews, resulted in a wider glycemic curve and an earlier attainment of the glycemic peak. CONCLUSIONS: These results emphasize the influence of proper chewing techniques on blood sugar levels. Implementing correct chewing habits could serve as an additional approach to managing the glycemic curve, particularly for individuals with diabetes.

Improvement of Heterologous Soluble Expression of L-amino Acid Oxidase Using Logistic Regression.

Successful implementation of enzymes in practical application hinges on the development of efficient mass production techniques. However, in a heterologous expression system, the protein is often unable to fold correctly and, thus, forms inclusion bodies, resulting in the loss of its original activity. In this study, we present a new and more accurate model for predicting amino acids associated with an increased L-amino acid oxidase (LAO) solubility. Expressing LAO from Rhizoctonia solani in Escherichia coli and combining random mutagenesis and statistical logistic regression, we modified 108 amino acid residues by substituting hydrophobic amino acids with serine and hydrophilic amino acids with alanine. Our results indicated that specific mutations in Euclidean distance, glycine, methionine, and secondary structure increased LAO expression. Furthermore, repeated mutations were performed for LAO based on logistic regression models. The mutated LAO displayed a significantly increased solubility, with the 6-point and 58-point mutants showing a 2.64- and 4.22-fold increase, respectively, compared with WT-LAO. Ultimately, using recombinant LAO in the biotransformation of α-keto acids indicates its great potential as a biocatalyst in industrial production.

Application of the Surface Regression Technique for Enhancing the Input Factors and Responses for Processing Coconut Oil under Vertical Compression.

This study optimized the input processing factors, namely compression force, pressing speed, heating temperature, and heating time, for extracting oil from desiccated coconut medium using a vertical compression process by applying a maximum load of 100 kN. The samples' pressing height of 100 mm was measured using a vessel chamber of diameter 60 mm with a plunger. The Box-Behnken design was used to generate the factors' combinations of 27 experimental runs with each input factor set at three levels. The response surface regression technique was used to determine the optimum input factors of the calculated responses: oil yield (%), oil expression efficiency (%), and energy (J). The optimum factors' levels were the compression force 65 kN, pressing speed 5 mm min-1, heating temperature 80 °C, and heating time 52.5 min. The predicted values of the responses were 48.48%, 78.35%, and 749.58 J. These values were validated based on additional experiments producing 48.18 ± 0.45%, 77.86 ± 0.72%, and 731.36 ± 8.04 J. The percentage error values between the experimental and the predicted values ranged from 0.82 ± 0.65 to 2.43 ± 1.07%, confirming the suitability of the established regression models for estimating the responses.

High-Resolution Estimates of N2O Emissions from Inland Waters and Wetlands in China.

Inland waters (rivers, lakes, and reservoirs) and wetlands (marshes and coastal wetlands) represent large and continuous sources of nitrous oxide (N2O) emissions, in view of adequate biomass and anaerobic conditions. Considerable uncertainties remain in quantifying spatially explicit N2O emissions from aquatic systems, attributable to the limitations of models and a lack of comprehensive data sets. Herein, we conducted a synthesis of 1659 observations of N2O emission rates to determine the major environmental drivers across five aquatic systems. A framework for spatially explicit estimates of N2O emissions in China was established, employing a data-driven approach that upscaled from site-specific N2O fluxes to robust multiple-regression models. Results revealed the effectiveness of models incorporating soil organic carbon and water content for marshes and coastal wetlands, as well as water nitrate concentration and dissolved organic carbon for lakes, rivers, and reservoirs for predicting emissions. Total national N2O emissions from inland waters and wetlands were 1.02 × 105 t N2O yr-1, with contributions from marshes (36.33%), rivers (27.77%), lakes (25.27%), reservoirs (6.47%), and coastal wetlands (4.16%). Spatially, larger emissions occurred in the Songliao River Basin and Continental River Basin, primarily due to their substantial terrestrial biomass. This study offers a vital national inventory of N2O emissions from inland waters and wetlands in China, providing paradigms for the inventorying work in other countries and insights to formulate effective mitigation strategies for climate change.

Identification of endophenotypes supporting outcome prediction in hemodialysis patients based on mechanistic markers of statin treatment.

Background: Statins are widely used to reduce the risk of cardiovascular disease (CVD). Patients with end-stage renal disease (ESRD) on hemodialysis have significantly increased risk of developing CVD. Statin treatment in these patients however did not show a statistically significant benefit in large trials on a patient cohort level. Methods: We generated gene expression profiles for statins to investigate the impact on cellular programs in human renal proximal tubular cells and mesangial cells in-vitro. We subsequently selected biomarkers from key statin-affected molecular pathways and assessed these biomarkers in plasma samples from the AURORA cohort, a double-blind, randomized, multi-center study of patients on hemodialysis or hemofiltration that have been treated with rosuvastatin. Patient clusters (phenotypes) were created based on the identified biomarkers using Latent Class Model clustering and the associations with outcome for the generated phenotypes were assessed using Cox proportional hazards regression models. The multivariable models were adjusted for clinical and biological covariates based on previously published data in AURORA. Results: The impact of statin treatment on mesangial cells was larger as compared with tubular cells with a large overlap of differentially expressed genes identified for atorvastatin and rosuvastatin indicating a predominant drug class effect. Affected molecular pathways included TGFB-, TNF-, and MAPK-signaling and focal adhesion among others. Four patient clusters were identified based on the baseline plasma concentrations of the eight biomarkers. Phenotype 1 was characterized by low to medium levels of the hepatocyte growth factor (HGF) and high levels of interleukin 6 (IL6) or matrix metalloproteinase 2 (MMP2) and it was significantly associated with outcome showing increased risk of developing major adverse cardiovascular events (MACE) or cardiovascular death. Phenotype 2 had high HGF but low Fas cell surface death receptor (FAS) levels and it was associated with significantly better outcome at 1 year. Conclusions: In this translational study, we identified patient subgroups based on mechanistic markers of statin therapy that are associated with disease outcome in patients on hemodialysis.

Model Selection for Exponential Power Mixture Regression Models.

Finite mixture of linear regression (FMLR) models are among the most exemplary statistical tools to deal with various heterogeneous data. In this paper, we introduce a new procedure to simultaneously determine the number of components and perform variable selection for the different regressions for FMLR models via an exponential power error distribution, which includes normal distributions and Laplace distributions as special cases. Under some regularity conditions, the consistency of order selection and the consistency of variable selection are established, and the asymptotic normality for the estimators of non-zero parameters is investigated. In addition, an efficient modified expectation-maximization (EM) algorithm and a majorization-maximization (MM) algorithm are proposed to implement the proposed optimization problem. Furthermore, we use the numerical simulations to demonstrate the finite sample performance of the proposed methodology. Finally, we apply the proposed approach to analyze a baseball salary data set. Results indicate that our proposed method obtains a smaller BIC value than the existing method.

Interaction between mental disorders and social disconnectedness on mortality: a population-based cohort study.

BACKGROUND: Despite the recognised importance of mental disorders and social disconnectedness for mortality, few studies have examined their co-occurrence. AIMS: To examine the interaction between mental disorders and three distinct aspects of social disconnectedness on mortality, while taking into account sex, age and characteristics of the mental disorder. METHOD: This cohort study included participants from the Danish National Health Survey in 2013 and 2017 who were followed until 2021. Survey data on social disconnectedness (loneliness, social isolation and low social support) were linked with register data on hospital-diagnosed mental disorders and mortality. Poisson regression was applied to estimate independent and joint associations with mortality, interaction contrasts and attributable proportions. RESULTS: A total of 162 497 individuals were followed for 886 614 person-years, and 9047 individuals (5.6%) died during follow-up. Among men, interaction between mental disorders and loneliness, social isolation and low social support, respectively, accounted for 47% (95% CI: 21-74%), 24% (95% CI: -15 to 63%) and 61% (95% CI: 35-86%) of the excess mortality after adjustment for demographics, country of birth, somatic morbidity, educational level, income and wealth. In contrast, among women, no excess mortality could be attributed to interaction. No clear trends were identified according to age or characteristics of the mental disorder. CONCLUSIONS: Mortality among men, but not women, with a co-occurring mental disorder and social disconnectedness was substantially elevated compared with what was expected. Awareness of elevated mortality rates among socially disconnected men with mental disorders could be of importance to qualify and guide prevention efforts in psychiatric services.

Insight into soft chemometric computational learning for modelling oily-wastewater separation efficiency and permeate flux of polypyrrole-decorated ceramic-polymeric membranes.

Reliable modeling of oily wastewater emphasizes the paramount importance of sustainable and health-conscious wastewater management practices, which directly aligns with the Sustainable Development Goals (SDG) while also meeting the guidelines of the World Health Organization (WHO). This research explores the efficiency of utilizing polypyrrole-coated ceramic-polymeric membranes to model oily wastewater separation efficiency (SE) and permeate flux (PF) based on established experimental procedures. In this area, computational simulation still needs to be explored. The study developed predictive regression models, including robust linear regression (RLR), stepwise linear regression (SWR) and linear regression (LR) for the ceramic-polymeric porous membrane, aiming to interpret its complex performance across diverse conditions and, thus, develop its utility in oily wastewater treatment applications. Subsequently, a novel, simple average ensemble paradigm was explored to reduce errors and improve prediction skills. Prior to the development of the model, stability and reliability analysis of the data was conducted based on Philip Perron tests with the Bartlett kernel estimation method. The accuracy of the SE exhibited a high consistency, averaging 99.92% with minimal variability (standard deviation of 0.026%), potentially simplifying its prediction compared to PF. The modes were validated and evaluated using metrics like MAE, RMSE, Speed, and MSE, in addition to 2D graphical and cumulative distribution function graphs. The LR model emerged as the best with the lowest RMSE =0.21951, indicating superior prediction accuracy, followed closely by RLR with an RMSE = 0.22359. SWLR, while having the highest RMSE = 0.34573, marked its dominance in prediction speed with 110 observations per second. Notably, the RLR model justified a reduction in error by approximately 35.29% compared to SWLR. Moreover, the training efficiency of the LR model exceeded, demanding a mere 2.9252 s, marking a reduction of about 32.54% compared to SWLR. The improved simple ensemble learning proved merit over the three models regarding error accuracy. This study emphasizes the essential role of soft-computing learning in optimizing the design and performance of ceramic-polymeric membranes.

Design of Modified Polymer Membranes Using Machine Learning.

Surface modification is an attractive strategy to adjust the properties of polymer membranes. Unfortunately, predictive structure-processing-property relationships between the modification strategies and membrane performance are often unknown. One possibility to tackle this challenge is the application of data-driven methods such as machine learning. In this study, we applied machine learning methods to data sets containing the performance parameters of modified membranes. The resulting machine learning models were used to predict performance parameters, such as the pure water permeability and the zeta potential of membranes modified with new substances. The predictions had low prediction errors, which allowed us to generalize them to similar membrane modifications and processing conditions. Additionally, machine learning methods were able to identify the impact of substance properties and process parameters on the resulting membrane properties. Our results demonstrate that small data sets, as they are common in materials science, can be used as training data for predictive machine learning models. Therefore, machine learning shows great potential as a tool to expedite the development of high-performance membranes while reducing the time and costs associated with the development process at the same time.

Relation between Photogrammetry and Spinal Mouse for Lumbopelvic Assessment in Adolescents with Thoracic Kyphosis.

The evaluation of the lumbopelvic region is a crucial point during postural assessment in childhood and adolescence. Photogrammetry (PG) and Spinal Mouse (SM) are two of the most debated tools to properly analyze postural alignment and avoid misleading data. This study aims to find out the best linear regression model that could relate the analytic measurements of the SM with one or more PG parameters in adolescents with kyphotic postures. Thirty-nine adolescents (female = 35.9%) with structural and non-structural kyphosis were analyzed (13.2 ± 1.8 years; 1.59 ± 0.12 m; 47.6 ± 11.8 kg) using the SM and PG on the sagittal plane in a standing and forward-bending position, allowing for the measurement of body vertical inclination, lumbar and pelvic alignment, trunk flexion, sacral inclination during bending, and hip position during bending. Lordosis lumbar angles (SM) were significantly (r = -0.379, r = -0.328) correlated with the SIPS-SIAS angle (PG) during upright standing, while in the bending position, the highest correlation appeared among the sacral-hip (SM) and the sacral tangent (ST_PG; r = -0.72) angles. The stepwise backward procedure was assessed to estimate the SM variability in the bending and standing positions. Only in the bending position did the linear regression model reach high goodness-of-fit values with two regressors (ST_PG η2=0.504, BMI η2=0.252; adjusted- R2 =0.558, p < 0.001, CCC = 0.972, r = 0.763). Despite gold-standard methods reducing error evaluation, physicians and kinesiologists may consider photogrammetry as a good method for spinal curve prediction.

Integrating portable NIR spectrometry with deep learning for accurate Estimation of crude protein in corn feed.

This study investigates the challenges encountered in utilizing portable near-infrared (NIR) spectrometers in agriculture, specifically in developing predictive models with high accuracy and robust generalization abilities despite limited spectral resolution and small sample sizes. The research concentrates on the near-infrared spectra of corn feed, utilizing spectral processing techniques and CNNs to precisely estimate crude protein content. Five preprocessing methods were implemented alongside two-dimensional (2D) correlation spectroscopy, resulting in the development of both one-dimensional (1D) and 2D regression models. A comparative analysis of these models in predicting crude protein content demonstrated that 1D-CNNs exhibited superior predictive performance within the 1D category. For the 2D models, CropNet and CropResNet were utilized, with CropResNet demonstrating more accurate and superior predictive capabilities. Overall, the integration of 2D correlation spectroscopy with suitable preprocessing techniques in deep learning models, particularly the 2D CropResNet, proved to be more precise in predicting the crude protein content in corn feed. This finding emphasis the potential of this approach in the portable spectrometer market.