Model Parameters Research Articles

Inference with cross-lagged effects-Problems in time.

The interpretation of cross-effects from vector autoregressive models to infer structure and causality among constructs is widespread and sometimes problematic. I describe problems in the interpretation of cross-effects when processes that are thought to fluctuate continuously in time are, as is typically done, modeled as changing only in discrete steps (as in e.g., structural equation modeling)-zeroes in a discrete-time temporal matrix do not necessarily correspond to zero effects in the underlying continuous processes, and vice versa. This has implications for the common case when the presence or absence of cross-effects is used for inference about underlying causal processes. I demonstrate these problems via simulation, and also show that when an underlying set of processes are continuous in time, even relatively few direct causal links can result in much denser temporal effect matrices in discrete-time. I demonstrate one solution to these issues, namely parameterizing the system as a stochastic differential equation and focusing inference on the continuous-time temporal effects. I follow this with some discussion of issues regarding the switch to continuous-time, specifically regularization, appropriate measurement time lag, and model order. An empirical example using intensive longitudinal data highlights some of the complexities of applying such approaches to real data, particularly with respect to model specification, examining misspecification, and parameter interpretation. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

The Impact of Sparse Datasets When Harmonizing Data from Studies with Different Measures of the Same Construct.

Prevention science has increasingly turned to integrative data analysis (IDA) to combine individual participant-level data from multiple studies of the same topic, allowing us to evaluate overall effect size, test and model heterogeneity, and examine mediation. Studies included in IDA often use different measures for the same construct, leading to sparse datasets. We introduce a graph theory method for summarizing patterns of sparseness and use simulations to explore the impact of different patterns on measurement bias within three different measurement models: a single common factor, a hierarchical model, and a bifactor model. We simulated 1000 datasets with varying levels of sparseness and used Bayesian methods to estimate model parameters and evaluate bias. Results clarified that bias due to sparseness will depend on the strength of the general factor, the measurement model employed, and the level of indirect linkage among measures. We provide an example using a synthesis dataset that combined data on youth depression from 4146 youth who participated in 16 randomized field trials of prevention programs. Given that different synthesis datasets will embody different patterns of sparseness, we conclude by recommending that investigators use simulation methods to explore the potential for bias given the sparseness patterns they encounter.

Comparing Functional Trend and Learning among Groups in Intensive Binary Longitudinal Eye-Tracking Data using By-Variable Smooth Functions of GAMM.

This paper presents a model specification for group comparisons regarding a functional trend over time within a trial and learning across a series of trials in intensive binary longitudinal eye-tracking data. The functional trend and learning effects are modeled using by-variable smooth functions. This model specification is formulated as a generalized additive mixed model, which allowed for the use of the freely available mgcv package (Wood in Package 'mgcv.' https://cran.r-project.org/web/packages/mgcv/mgcv.pdf , 2023) in R. The model specification was applied to intensive binary longitudinal eye-tracking data, where the questions of interest concern differences between individuals with and without brain injury in their real-time language comprehension and how this affects their learning over time. The results of the simulation study show that the model parameters are recovered well and the by-variable smooth functions are adequately predicted in the same condition as those found in the application.

Late-time constraints on barotropic fluid cosmology

We investigate the cosmological implications of the Friedmann-Robertson-Walker (FRW) model having a flat-spatial section with barotropic fluid. We examine the resulting cosmological scenario obtained by solving the continuity equation. The model may yield the accelerating universe expansion from the transition of decelerated phase, subjected to the best fit values. We confront the cosmological model with the recent observational data, namely the Observational Hubble Data (OHD) and Supernovae type Ia (SN Ia) data. The model exhibits good agreement with these observational data sets. For the best fit values of the model parameters, the universe approaches to the Λ cold dark matter (ΛCDM) model in the distant future. Energy conditions except strong energy conditions are satisfied in the model. Analysis of the equation of state (EoS) parameter and statefinder diagnostic highlight that the phantom scenario does not arise for the best fit values. The universe is free from the finite-time future singularities in the model.

Experimental parameter identification of scalable white and grey box jounce bumper models for ride comfort simulation

The design of a passenger car’s ride and handling goals requires an enormous amount of hardware and prototypes. To avoid time-consuming testing activities, one crucial trend is the virtualisation of suspension development. Another goal of the virtualisation is the determination of vehicle properties at an early stage of the development process. Highly accurate suspension models are required to transfer the full vehicle’s characteristics into simulation tools. Since the jounce bumper is an important component of the suspension system, modelling its functional behaviour is essential for virtualised chassis development. Therefore, two dynamic modelling approaches are derived and compared in this contribution. One approach is based on local linear model networks and thus can be seen as a grey box model. The other approach consists of white box rheological elements, which allow the physical interpretability of the model parameters. The comparison of the approaches is based on experimental parameter identification, which includes synthetic and real excitations recorded on representative roads. The advantages of the proposed approaches will be discussed in terms of their suitability for the virtual design of the driving behaviour.

An EGF technique to infer the source parameters of a circular crack growing at a variable rupture velocity

Circular crack models with a constant rupture velocity struggle to effectively model both the amplitude and duration of first P-wave pulses generated by small magnitude seismic events. Assuming a constant rupture velocity is unphysical, necessitating a deceleration phase in the rupture velocity to uphold the causality of the healing process. Moreover, a comprehensive failure model might encompass an initial nucleation phase, typically characterized by an increase of the initial rupture velocity. Studies have demonstrated that quasi-dynamic circular crack models featuring variable rupture velocities can accurately model the shape of the observed first P-wave pulse. Based on these principles, an Empirical Green’s function (EGF) approach was previously formulated to estimate the source parameters of small magnitude earthquakes, called MAIN. In addition to determine the source radius and stress drop, this method also enables the inference of the temporal evolution of rupture velocity. However, this method encounters difficulties when the noise-to-signal ratio in the recordings of smaller earthquakes used as EGF exceeds 5%, a common situation when employing regional-scale recordings of small-magnitude earthquakes as EGF. Through synthetic tests, we demonstrated that, in such instances, the problem of this technique is that the alignment between the onset of P waves of EGF and MAIN is not rightly recovered after the initial inversion step. Consequently, a novel inversion method has been developed to address this issue, enabling the identification of the optimal alignment of P-wave arrivals in EGF and MAIN across all stations. A Bayesian statistical approach is proposed to meticulously investigate the solutions of model parameters and their correlations. Using the new technique on a small magnitude earthquake (ML = 3.3) occurred in Central Italy enabled us to identify the most likely rupture models and examine the issue of correlation among model parameters. Application of Occam’s Razor Principle suggests that, for the investigated event, a circular crack model should be favored over a heterogeneous rupture model.

Incorporating boron distribution variations in microdosimetric kinetic model-based relative biological effectiveness calculations for boron neutron capture therapy.

This study introduces the MKM_B model, an approach derived from the MKM model, designed to evaluate the biological effectiveness of Boron Neutron Capture Therapy (BNCT) in the face of challenges from varying microscopic boron distributions. The model introduces a boron compensation factor, allowing for the assessment of compound Biological Effectiveness (CBE) values for different boron distributions. Utilizing the TOPAS simulation platform, the lineal energy spectrum of particles in BNCT was simulated, and the sensitivity of the MKM_B model to parameter variations and the influence of cell size on the model were thoroughly investigated. The CBE values for 10B-boronphenylalanine (BPA) and 10B-sodium (BSH) were determined to be 3.70 and 1.75, respectively. These calculations were based on using the nucleus radius of 2.5 μm and the cell radius of 5 μm while considering a 50% surviving fraction. It was observed that as cell size decreased, the CBE values for both BPA and BSH increased. Additionally, the model parameter rd was identified as having the most significant impact on CBE, with other parameters showing moderate effects. The development of the MKM_B model enables the accurate prediction of CBE under different boron distributions in BNCT. This model offers a promising approach to optimize treatment planning by providing increased accuracy in biological effectiveness.

Low Resource Malay Dialect Automatic Speech Recognition Modeling Using Transfer Learning from a Standard Malay Model

Approaches to automatic speech recognition have transited from Hidden Markov Model (HMM)-based ASR to deep neural networks. The advantages of deep neural network approaches are that they can be developed quickly and perform better given large language resources. Nevertheless, dialect speech recognition is still challenging due to the limited resources. Transfer learning approaches have been proposed to improve speech recognition for low resources. In the first approach, the model is pre-trained on a large and diverse labeled dataset to learn the acoustic and language patterns from the speech signal. Then, the model parameters are updated with a new dataset, and the pre-trained model is fine-tuned on a low-resource language dataset. The fine-tuning process is usually completed by freezing the pre-trained layers and training the remaining layers of the model on the low-resource language corpus. Another approach is to use a pre-trained model to capture the compact and meaningful features as input to the encoder. Pre-training in this approach usually involves using unsupervised learning methods to train models on a corpus of large amounts of unmarked data. It enables the model to learn the general patterns and relationships between the input speech signals. This paper proposes a training recipe using transfer learning and Standard Malay models to improve automatic speech recognition for Kelantan and Sarawak Malay dialects.

Modeling pediatric antibiotic use in an area of declining malaria prevalence

In malaria-endemic areas of Sub-Saharan Africa, overlap of clinical symptoms between malarial and non-malarial febrile illnesses can lead to empiric use of antibiotics among children. Our study aimed to illustrate the potential impact of decreasing malaria prevalence from malaria control efforts on antibiotic use. We constructed a probabilistic decision tree model representing antibiotic prescription in febrile children < 5 years. This model was used to predict change in absolute antibiotic use compared to baseline under levels of decreasing malaria prevalence. Model parameters were based on data from a hospital study in Ghana and validated via literature review. The baseline prevalence of malaria diagnoses was 52% among all hospitalized children. For our main results, we reported outcomes for a scenario representing a 50% decrease in malaria prevalence. Compared to baseline, absolute antibiotic prescription decreased from a baseline of 639 doses (95% CI 574–694) to 575 (95% CI 502–638). This reflected a 10% (95% CI 7%–13%) decrease in absolute antibiotic use. Our findings demonstrate that effective malaria control can reduce pediatric antibiotic use. However, until substantial progress is made in developing accurate diagnostics for non-malarial febrile illnesses, further reductions in antibiotic use will remain a challenge.

Abnormal Behavior Recognition Based on 3D Dense Connections.

Abnormal behavior recognition is an important technology used to detect and identify activities or events that deviate from normal behavior patterns. It has wide applications in various fields such as network security, financial fraud detection, and video surveillance. In recent years, Deep Convolution Networks (ConvNets) have been widely applied in abnormal behavior recognition algorithms and have achieved significant results. However, existing abnormal behavior detection algorithms mainly focus on improving the accuracy of the algorithms and have not explored the real-time nature of abnormal behavior recognition. This is crucial to quickly identify abnormal behavior in public places and improve urban public safety. Therefore, this paper proposes an abnormal behavior recognition algorithm based on three-dimensional (3D) dense connections. The proposed algorithm uses a multi-instance learning strategy to classify various types of abnormal behaviors, and employs dense connection modules and soft-threshold attention mechanisms to reduce the model's parameter count and enhance network computational efficiency. Finally, redundant information in the sequence is reduced by attention allocation to mitigate its negative impact on recognition results. Experimental verification shows that our method achieves a recognition accuracy of 95.61% on the UCF-crime dataset. Comparative experiments demonstrate that our model has strong performance in terms of recognition accuracy and speed.

A traffic and road signal recognition method through deep learning

Before deep learning became popular, some researchers used traditional computer vision algorithms, including support vector machines, decision trees, and random forests to deal with traffic and road signal recognition problems. These methods often require manual design of features and may not perform well when dealing with complex scenarios and changing conditions. Therefore, traffic and road signal recognition have witnessed a transformative shift with the advent of deep learning technologies. Convolutional neural networks (CNNs) developed from deep learning has shown prominent capabilities in accurately detecting and interpreting traffic signs and signals from images and videos. In this project, the whole method is mainly based on two parts, which refers to the process of signal-capturing and the detecting process. The CNN model used in the latter part consists of various function layers, including max-pooling layer, linear layer, 2D convolution layer and batch- normalization layer to modify accuracy. This model is trained and tested with Chinese Traffic Sign Dataset, with 58 categories of over 6000 pictures. With the assistance of OpenCV, the model may detect real-time traffic signals and convey messages to vehicles. After adjusting parameters in the CNN model, high probability tags are obtained during the process, with both accuracy and average loss labeled after each epoch. The results demonstrate that the proposed model achieved the testing accuracy of over 95 percent, after undergoing 200 epochs.

ANCF-based dynamic modeling of variable curvature soft pneumatic actuators with experimental verifications

Abstract Accurate and computationally efficient models of soft pneumatic actuators are crucial for utilizing their compliance in various fields. However, existing research primarily relies on the piecewise constant curvature (PCC) assumption or the quasi-static assumption, only valid in limited situations. In this paper, we present a dynamic model based on absolute nodal coordinate formulation (ANCF) that simultaneously accounts for variable curvature deformation and dynamic properties. To this end, deformed configurations of soft pneumatic actuators are firstly discretized into ANCF-based beam elements. Based on this parameterization method, the dynamic model is derived by the principle of virtual work. After identifying model parameters, Newmark algorithm is utilized to solve the dynamic model in real-time, averagely consuming 6.76 s of a 10 s simulation. The derived dynamic model is experimental verified using a soft pneumatic actuator. The experimental results demonstrate that the maximum simulation errors of the tip remain below 2.5 % of the actuator’s length when the actuator is subjected to various pressure and tip loads. In addition, the overshoot behavior and period of vibration in the oscillations are also predicted by the dynamic model. Moreover, the dynamic model exhibits an average 46.53 % reduction in simulation error compared with the static ANCF-based model. Overall, this work paves the way to a deeper insight to dynamic motion analysis of soft pneumatic actuators.&amp;#xD;

Structure of heavy mesons in the light-front quark model

We investigate the structure of ground-state heavy mesons within the light-front quark model, utilizing wave functions derived from the single Gaussian ansatz (SGA) and the Gaussian expansion method (GEM). By performing a χ2 fit to static properties such as mass spectra and decay constants, we determine the model parameters for each approach. We then compare the impacts of both methods on the light-front wave functions and structural observables. Our analysis reveals significant differences in the distribution amplitudes ϕ2;M(x) near the end points, with GEM showing enhanced amplitudes and correct asymptotic behavior ϕ2;M(x→1)∝(1−x), consistent with perturbative QCD. This end point behavior is linked to the short-range (high-momentum) wave function governed by color Coulomb interaction and relativistic kinematics. GEM accurately reproduces a power-law damping ψ0(k→∞)∝1/k⊥2, aligning with perturbative QCD predictions. Furthermore, the electromagnetic form factors of pseudoscalar mesons in the low-Q2 region fall off faster with GEM than with SGA. Overall, while both methods adequately describe static properties, GEM provides a more accurate description of structural properties, being more sensitive to details and asymptotic behaviors. Published by the American Physical Society 2024

Operational stability study of lactate biosensors: modeling, parameter identification, and stability analysis

IntroductionThis paper investigates the operational stability of lactate biosensors, crucial devices in various biomedical and biotechnological applications. We detail the construction of an amperometric transducer tailored for lactate measurement and outline the experimental setup used for empirical validation.MethodsThe modeling framework incorporates Brown and Michaelis–Menten kinetics, integrating both distributed and discrete delays to capture the intricate dynamics of lactate sensing. To ascertain model parameters, we propose a nonlinear optimization method, leveraging initial approximations from the Brown model’s delay values for the subsequent model with discrete delays.ResultsStability analysis forms a cornerstone of our investigation, centering on linearization around equilibrium states and scrutinizing the real parts of quasi-polynomials. Notably, our findings reveal that the discrete delay model manifests marginal stability, occupying a delicate balance between asymptotic stability and instability. We introduce criteria for verifying marginal stability based on characteristic quasi-polynomial roots, offering practical insights into system behavior.DiscussionQalitative examination of the model elucidates the influence of delay on dynamic behavior. We observe a transition from stable focus to limit cycle and period-doubling phenomena with increasing delay values, as evidenced by phase plots and bifurcation diagrams employing Poincaré sections. Additionally, we identify limitations in model applicability, notably the loss of solution positivity with growing delays, underscoring the necessity for cautious interpretation when employing delayed exponential function formulations. This comprehensive study provides valuable insights into the design and operational characteristics of lactate biosensors, offering a robust framework for understanding and optimizing their performance in diverse settings.

Bulge+disc decomposition of HFF and CANDELS galaxies: UVJ diagrams and stellar mass–size relations of galaxy components at 0.2 ≤ z ≤ 1.5

Abstract Using deep imaging from the CANDELS and HFF surveys, we present bulge+disc decompositions with GalfitM for ∼17,000 galaxies over 0.2 ≤ z ≤ 1.5. We use various model parameters to select reliable samples of discs and bulges, and derive their stellar masses using an empirically calibrated relation between mass-to-light ratio and colour. Across our entire redshift range, we show that discs follow stellar mass–size relations that are consistent with those of star-forming galaxies, suggesting that discs primarily evolve via star formation. In contrast, the stellar mass-size relations of bulges are mass-independent. Our novel dataset further enables us to separate components into star-forming and quiescent based on their specific star formation rates. We find that both star-forming discs and star-forming bulges lie on stellar mass-size relations that are similar to those of star-forming galaxies, while quiescent discs are typically smaller than star-forming discs and lie on steeper relations, implying distinct evolutionary mechanisms. Similar to quiescent galaxies, quiescent bulges show a flattening in the stellar mass-size relation at ∼1010M⊙, below which they show little mass dependence. However, their best-fitting relations have lower normalisations, indicating that at a given mass, bulges are smaller than quiescent galaxies. Finally, we obtain rest-frame colours for individual components, showing that bulges typically have redder colours than discs, as expected. We visually derive UVJ criteria to separate star-forming and quiescent components and show that this separation agrees well with component colour. HFF bulge+disc decomposition catalogues used for these analyses are publicly released with this paper.

Constructing a cataplexy face prediction model for narcolepsy type 1 based on ResNet-18

Objective: To establish a prediction model for the identifying of cataplexy facial features based on clinical shooting videos by using a deep learning image recognition network ResNet-18. Methods: A cross-sectional study. Twenty-five narcolepsy type 1 patients who were first diagnosed and never received treatment and 25 healthy controls recruited by advertisement in the Second Affiliated Hospital of Nanchang University from 2020 to 2023.After image preprocessing, a total of 1 180 images were obtained, including 583 cataplexy faces and 597 normal faces.90% were selected as the training set and validation set, and then expanded the data by 5 times.80% of the expanded data set was extracted as the training set and 20% as the validation set, that is, the number of the training set was (583+597)×0.9×0.8×5=4 248, the number of the validation set was (583+597)×0.9×0.2×5=1 062. The data sets for training and validation were used train parameters to establish the model and were trained through the five-fold cross-validation method, to establish the ResNet-18 cataplexy face recognition model via transfer learning.10% (118 images) of the original non-amplified images were extracted as the test set. The test set data did not participate in data enhancement and model training, and was only used to evaluate the final performance of the model. Finally, ResNet-18 was compared with VGG-16, ResNet-34 and Inception V3 deep learning models, and the receiver operating characteristic curve was used to evaluate the value of ResNet-18 image recognition network in cataplexy face recognition. Results: Among 25 patients with narcolepsy type 1, 15 were males and 10 were females, aged [M (Q1, Q3)] of 14.0(11.0, 20.5) years.Among 25 healthy controls, 14 were males and 11 were females, with a median age of 16.0(14.4, 23.0) years.The overall accuracy of ResNet-18 image recognition network in the test set was 90.9%, the sensitivity was 96.4% and the specificity was 85.2%. The area under the ROC curve was 0.99(95%CI:0.96-1.00). The ResNet-18 model parameter amount was 11.69 M, the floating point operation amount was 1 824.03 M, and the single image recognition time was 5.9 ms. Conclusions: The cataplexy face prediction model built based on the deep learning image recognition network ResNet-18 has a high accuracy in identifying cataplexy faces.

A two‐stage adaptive robust model for designing a reliable blood supply chain network with disruption considerations in disaster situations

AbstractWe consider multi‐period blood supply chain network design in disaster situations that involve blood donor groups, permanent and temporary blood collection facilities, blood banks, and hospitals. We use a discrete scenario set to model the uncertain blood supply and demand, and the unforeseeable disruptions in permanent blood collection facilities, blood banks, and road links arising from a disaster, where instead of complete failure, disrupted permanent blood collection facilities and blood blanks may only lose part of their capacities. To design a reliable blood supply network to mitigate the possible disruptions, we present a two‐stage adaptive robust model that integrates the location, inventory, and allocation decisions incorporating a blood sharing strategy, where blood can be delivered from a disrupted/non‐disrupted blood bank to disrupted blood banks to enhance the flexibility of the relief network. For this novel problem, we devise an exact algorithm that integrates column‐and‐constraint generation and Benders decomposition and introduce several non‐trivial acceleration techniques to speed up the solution generation process. We conduct extensive numerical studies on random data sets to evaluate the algorithmic performance. We also conduct a case study in Tehran to demonstrate its real‐life applicability and examine the impacts of key model parameters on the solutions. The numerical results verify the benefits of our model over typical benchmarks, that is, deterministic and stochastic models, and the superiority of our solution algorithm over the CPLEX solver and two well‐known solution approaches, that is, column‐and‐constraint generation and Benders decomposition. Finally, based on the numerical results, we derive managerial insights from the analytical findings.

Reproducibility analysis of bioimpedance-based self-developed live cell assays

Bioimpedance spectrum (BIS) measurements have a great future in in vitro experiments, meeting all the requirements for non-destructive and label-free methods. Nevertheless, a real basic research can provide the necessary milestones to achieve the success of the method. In this paper a self-developed technology-based approach for in vitro assays is proposed. Authors invented a special graphene-based measuring plate in order to assess the high sensitivity and reproducibility of introduced technique. The design of the self-produced BIS plates maximizes the detection capacity of qualitative changes in cell culture and it is robust against physical effects and artifacts. The plates do not influence the viability and proliferation, however the results are robust, stable and reproducible regardless of when and where the experiments are carried out. In this study, physiological saline concentrations, two cancer and stem cell lines were utilized. All the results were statistically tested and confirmed. The findings of the assays show, that the introduced BIS technology is appropriate to be used in vitro experiments with high efficacy. The experimental results demonstrate high correlation values across the replicates, and the model parameters suggested that the characteristic differences among the various cell lines can be detected using appropriate hypothesis tests.

Green pepper fruits counting based on improved DeepSort and optimized Yolov5s

IntroductionGreen pepper yield estimation is crucial for establishing harvest and storage strategies.MethodThis paper proposes an automatic counting method for green pepper fruits based on object detection and multi-object tracking algorithm. Green pepper fruits have colors similar to leaves and are often occluded by each other, posing challenges for detection. Based on the YOLOv5s, the CS_YOLOv5s model is specifically designed for green pepper fruit detection. In the CS_YOLOv5s model, a Slim-Nick combined with GSConv structure is utilized in the Neck to reduce model parameters while enhancing detection speed. Additionally, the CBAM attention mechanism is integrated into the Neck to enhance the feature perception of green peppers at various locations and enhance the feature extraction capabilities of the model.ResultAccording to the test results, the CS_YOLOv5s model of mAP, Precision and Recall, and Detection time of a single image are 98.96%, 95%, 97.3%, and 6.3 ms respectively. Compared to the YOLOv5s model, the Detection time of a single image is reduced by 34.4%, while Recall and mAP values are improved. Additionally, for green pepper fruit tracking, this paper combines appearance matching algorithms and track optimization algorithms from SportsTrack to optimize the DeepSort algorithm. Considering three different scenarios of tracking, the MOTA and MOTP are stable, but the ID switch is reduced by 29.41%. Based on the CS_YOLOv5s model, the counting performance before and after DeepSort optimization is compared. For green pepper counting in videos, the optimized DeepSort algorithm achieves ACP (Average Counting Precision), MAE (Mean Absolute Error), and RMSE (Root Mean Squared Error) values of 95.33%, 3.33, and 3.74, respectively. Compared to the original algorithm, ACP increases by 7.2%, while MAE and RMSE decrease by 6.67 and 6.94, respectively. Additionally, Based on the optimized DeepSort, the fruit counting results using YOLOv5s model and CS_YOLOv5s model were compared, and the results show that using the better object detector CS_YOLOv5s has better counting accuracy and robustness.

A Mixed-level Factorial Experiment to Elucidate the Impact of Inorganic Fertilizers on Crop Yield

Lack of nutrients in the soil affects soil fertility which can hinder the growth and yield of any crop. Therefore, soil amendment is important to improve soil nutrient either by organic or inorganic technique. In this paper, we considered different inorganic fertilizers to determine the main optimal effect and their interaction on the yield of crop by adoption of mixed-level factorial experiment. Three inorganic fertilizers namely Nitrogen (N), Phosphorous (P) and Potassium (K) were considered each at different levels using tomato crop for investigation. We set up a multiple linear model to match with the design. We estimated the model parameters with the error component and sums of squares. A 2×3×4 design structure for factorial combinations—of factor N at two levels, factor P at three levels, and factor K at four levels using a randomized complete block design with three replications—was developed. Normality of the data was tested and factors visualization for both main and interaction effects were illustrated by the use of graphs. The result revealed that Nitrogen (N) and Potassium (K) concentration are significant while Phosphorous (P) concentration is not, the effect of two-factor interactions for NP and PK are not significant and NK is significant, which signified that the yields do not depend on the levels irrespective of the factor. Based on the results, we concluded that phosphorus is the best inorganic fertilizer compared with Nitrogen and Potassium in terms of soil nutrient for the yield of crops.