Comparative Analysis of Forecasting Models for Disability Resource Planning in Brazil’s National Textbook Program ^†

Abstract

The accurate forecasting of student disability trends is essential for optimizing educational accessibility and resource distribution in the context of Brazil’s oldest public policy, the National Textbook Program (PNLD). This study applies machine learning (ML) and time series forecasting models (TSF) to predict the number of visually impaired students in Brazil using educational census data from 2021 to 2023, with the aim of estimating the amount of Braille textbooks to be acquired in the PNLD’s context. By performing a comparative analysis on various ML models (e.g, Naive Bayes, ElasticNet, gradient boosting) and TSF techniques (e.g., ARIMA and SARIMA models, as well as exponential smoothing) to predict future enrollment trends, we identify the most effective approaches for school-level and long-term disability enrollment predictions. Results show that ElasticNet and gradient boosting excel in forecasting enrollment estimations over TSF models. Despite challenges related to data inconsistencies and reporting variations, incorporating external demographic and health data could further improve predictive accuracy. This research contributes to AI-driven educational accessibility by demonstrating how predictive analytics can enhance policy decisions and ensure an equitable distribution of resources for students with disabilities.

1. Introduction

Ensuring inclusive education for students with disabilities remains a critical challenge worldwide [1,2,3]. One of the primary barriers to accessibility is the lack of accurate data-driven forecasts to support decision-making in resource allocation. Students with visual impairments, in particular, require specialized learning materials, such as Braille textbooks, to participate fully in the educational system. However, inadequate forecasting models result in an inefficient distribution, leading to shortages in some regions while causing surpluses in others. Addressing this issue requires a proactive and efficient approach that uses predictive analytics [4] to estimate the number of students with disabilities in each school and educational stage.

The National Education Development Fund (FNDE), in collaboration with the National Institute of Educational Studies and Research (INEP) and the Ministry of Education (MEC) in Brazil, collects annual census data on students with disabilities. These datasets provide valuable information on trends in disability enrollment, but they are underutilized in strategic decision-making. Traditional planning methods often rely on historical reports and manual estimates, which do not capture the dynamic nature of student populations. Without predictive models, educational institutions are forced to adopt reactive measures, addressing accessibility gaps only after they have already impacted students. This study aims to bridge this gap by employing machine learning models (ML) and time series forecasting algorithms (TSF) to estimate the number of visually impaired students and optimize the distribution of Braille textbooks and other accessibility resources under the National Textbook Program (PNLD) [5].

The need for data-driven decision-making in education is well documented. Studies such as [6] emphasize the importance of community-based interventions for people with intellectual disabilities, highlighting how predictive analytics can improve the effectiveness of interventions. Similarly, Clemente et al. [7] outline the structural barriers that people with disabilities face in accessing education, including inefficiencies in policy and a lack of customized resources. These studies underscore the urgency of using forecasting methods to improve educational accessibility and resource distribution.

Given this context, the main objective of this study is to develop and evaluate predictive models that can accurately estimate the number of students with visual impairments in Brazilian schools. To achieve this, we analyze educational census datasets from 2021 to 2023 and apply various ML models (e.g., Naive Bayes, ElasticNet, gradient boosting) and TSF techniques (e.g., ARIMA, and SARIMA, exponential smoothing) to predict future enrollment trends, aiming to identify the most effective approaches for enrollment predictions. The findings will inform policy recommendations and help improve the efficiency of the PNLD program in the distribution of Braille textbooks in schools nationwide.

In summary, the novel contributions of this study are as follows: (a) comparisons between machine learning and time series models that are capable of forecasting enrollments of students with disabilities and (b) measurement of the performance of several models and evaluation of their influence on the prediction of the allocation of resources, such as Braille textbooks.

2. Background and Related Work

In this section, we cover the foundations of this study, including background information on Brazil’s National Textbook Program (PNLD), the relevance of ML in public policy [8], and the use of machine learning in the context of predicting relevant educational data (e.g., outcomes, enrollments, accessibility, etc.).

2.1. Background

Educational accessibility [9] for students with disabilities has been a central concern for policymakers, educators, and researchers for decades. Ensuring that students with disabilities have equal access to learning opportunities requires effective resource allocation, particularly for specialized materials such as Braille textbooks for visually impaired students. Governments and educational institutions often struggle to efficiently distribute these resources due to poor forecasting and limited data-driven decision-making processes.

Traditional approaches to disability resource planning often rely on historical records and manual estimates, which are prone to errors and inconsistencies. The National Education Development Fund (FNDE) and the National Institute of Educational Studies and Research (INEP) in Brazil collect census data on disability enrollment, but the lack of predictive analytics integration limits their usefulness for strategic planning. The emergence of ML and artificial intelligence (AI)-driven predictive modeling has opened new avenues to optimize educational resource distribution.

Recent studies have demonstrated the potential of AI to improve accessibility planning. For example, Ref. [1] explored how probabilistic causal modeling can identify barriers to accessibility for students with disabilities, helping policymakers address systemic inequalities. Similarly, Ref. [9] examined how learning analytics techniques can improve the accessibility of students with disabilities in educational environments, reinforcing the importance of integrating predictive models into decision-making processes.

The potential benefits of predictive modeling in disability-focused education extend beyond resource allocation. Research has highlighted that machine learning models can improve the early identification of accessibility needs, enabling institutions to take proactive measures. Ravichandran [10] discussed the role of AI models in identifying learning difficulties at an early stage, ensuring that students receive the necessary support before facing academic setbacks. This underscores the need for AI-enhanced forecasting tools in disability education.

2.2. The PNLD: A Cornerstone of Brazilian Public Education Policy

The National Textbook Program (PNLD), established in 1985, is a foundational policy in Brazil that aims to ensure equitable access to high-quality educational materials. Managed by the National Education Development Fund (FNDE), PNLD distributes didactic and literary resources to millions of students and teachers in more than 178,000 schools throughout the country, encompassing both urban and rural areas [5].

The PNLD workflow (Figure 1) involves several stages, beginning with publishers submitting materials for editorial and pedagogical evaluation to ensure alignment with the national curriculum of Brazil. Once approved, textbooks move into the logistics phase, where FNDE plans printing and distribution.

Currently, textbook distribution relies on projections from historical census data. Although this offers a baseline, it often results in mismatches—either a surplus or shortage—that cause waste or resource gaps [11]. To improve accuracy, this study proposes integrating machine learning and time series models to more precisely forecast enrollments. These predictive tools can inform logistics planning, optimize resource allocation, reduce costs, and improve equitable distribution [5].

Incorporating machine learning forecasting not only addresses current logistical inefficiencies but also exemplifies how data science can support sustainable and equitable public policy at scale [5].

2.3. Related Work

The application of AI-driven predictive analytics using machine learning models in education has been widely explored, particularly in the context of student success prediction [2], accessibility enhancements [1], and resource planning [12,13].

Sobnath and others [14] developed a machine learning approach to predict employment outcomes for students with disabilities using feature selection techniques. Their study underscores the importance of selecting the right features for predictive modeling to ensure the accurate forecasting of educational trajectories. Similarly, Perlow [3] introduced the Hamner Enrollment Prediction Model, which integrates predictive analytics to assist students with access needs in transitioning to college.

AI-driven or machine learning models have also been applied to address structural challenges in disability education. Sullivan and Van Norman [15] investigated the use of predictive analytics to identify patterns in exclusionary disciplinary actions against students with disabilities, highlighting how AI can identify systemic inequalities in educational policies. Their study demonstrates how predictive modeling can be leveraged not only for resource planning but also for improving educational equity.

Singer and others [16] developed an ordinal and interpretable machine learning-based methodology to evaluate the effectiveness of accommodations given to students with learning disabilities. Their study highlights the importance of accurate forecasting to ensure that students receive the accommodations they need at the right time.

Other studies emphasize the role of AI in improving learning environments for students with disabilities. Yamamoto and Alverson [2] explored how predictive analytics can be applied to state education data to identify post-school outcomes for students with disabilities, ensuring that transition programs are evidence-based and proactive. This aligns with our study’s focus on AI-enhanced resource distribution, as both highlight the importance of predictive methodologies in improving educational accessibility.

Although significant progress has been made in applying AI to predictive modeling in education, challenges remain. Zakir, Wolbring and Yanushkevich [1] discuss how bias in predictive models can limit their effectiveness, particularly when data sources are incomplete or reported inconsistently between educational institutions. Addressing these biases requires the incorporation of external data sources, improved feature engineering, and transparent model evaluation metrics. In the context of public policies, extensive discussion has been carried out by [8], including challenges related to bias.

This study builds on the existing literature by integrating ML and TSF to predict disability enrollment trends and optimize resource distribution. Through a comparative approach, our research contributes to the growing body of work in AI-powered accessibility planning, offering a scalable and efficient tool for policy makers.

3. Materials and Methods

3.1. Dataset Overview

The dataset used in this study comprises educational census data from 2021 to 2023, provided by FNDE, INEP, and MEC. These datasets contain information on student demographics, disability classifications, school locations, and administrative details. The primary goal of this analysis is to extract relevant features that can contribute to an accurate prediction of students with visual impairments and optimize the distribution of Braille textbooks under the PNLD program.

The datasets include the following classifications of visual impairments (see

Table 1. Visual impairment categories.

Variable	Description
QT_BAIXA_VISAO	Low Vision
QT_CEGUEIRA	Blindness
QT_SURDOCEGUEIRA	Deafblindness
QT_DEF_MULTIPLA	Multiple Disabilities

):

Additionally, datasets contain variables related to school-level data (see

Table 2. School-level data variables.

Variable	Description
NU_YEAR_CENSO	Census Year
COD_ESCOLA	School Code
NO_ENTITY	School Name
SG_UF	State
NO_MUNICIPIO	Municipality
Location	Urban or Rural
DS_ETAPA_ENSINO	Teaching Stage Description
Administrative Dependence	Federal, State, Municipal

).

These attributes enable trend analysis, ensuring that predictions factor in geographic, administrative, and demographic variations in disability reporting.

Descriptive statistics (count, average, standard deviation, minimum, maximum, and sum) from the 2021, 2022, and 2023 censuses are shown in

Table 3. Statistical description of the 2021 disability school census.

	Count	Mean	Std	Min	Max	Sum
QT_LOW_VISION	367,633	0.209937	0.646371	0.0	65.0	77,180
QT_BLINDNESS	367,633	0.193508	0.253293	0.0	84.0	7114
QT_SURDOCEGUEIRA	367,633	0.157222	0.432944	0.0	5.0	578
QT_DEF_MULTIPLE	367,633	0.234097	0.101870	0.0	92.0	86,062

,

Table 4. Statistical description of the 2022 disability school census.

	Count	Mean	Std	Min	Max	Sum
T_LOW_VISION	331,872	0.193116	0.581369	0.0	62.0	64,090
QT_BLINDNESS	331,872	0.017265	0.189956	0.0	35.0	5730
QT_SURDOCEGUEIRA	331,872	0.001428	0.039785	0.0	4.0	474
QT_DEF_MULTIPLE	331,872	0.222299	0.972400	0.0	91.0	73,775

and

Table 5. Statistical description of the 2023 disability school census.

	Count	Mean	Std	Min	Max	Sum
QT_LOW_VISION	302,703	0.182221	0.550967	0.0	59.0	55,159
QT_BLINDNESS	302,703	0.016336	0.182611	0.0	47.0	4945
QT_SURDOCEGUEIRA	302,703	0.001344	0.039170	0.0	5.0	407
QT_DEF_MULTIPLE	302,703	0.215306	0.958152	0.0	101.0	65,174

, respectively.

3.2. Data Cleaning and Preprocessing

Prior to analysis, the datasets required preprocessing to handle missing values, inconsistencies, and redundant information. Some of the key preprocessing steps included in this study were (a) handling missing data: certain columns, such as EMAIL, NO_FAX, and TEL_NUM, contained a large proportion of null values and were either removed or imputed based on school attributes; (b) standardizing disability classification: since some disability types overlap (e.g., students with multiple disabilities could be classified under both QT_CEGUEIRA and QT_DEF_MULTIPLA), we ensured that all records were aggregated logically to avoid double-counting; (c) encoding categorical variables: features such as state codes (SG_UF), administrative dependence (DEPEN_ADM), and location type (Urban/Rural) were converted into numerical representations using label encoding; (d) feature selection: after exploratory data analysis, non-informative variables were dropped, ensuring that the models focused on the most relevant predictors.

3.3. Statistical Analysis of Disability Trends

Initial statistical analysis revealed the following key trends in disability prevalence: (a) students with blindness (QT_CEGUEIRA) were concentrated in specific urban schools specialized in disability education; (b) the standard deviation in student counts was often higher than the mean, indicating high data dispersion and possible inconsistencies in disability reporting; and (c) the number of students classified with multiple disabilities (QT_DEF_MULTIPLA) increased over the years, suggesting that diagnostic processes may be improving.

These insights were critical in shaping the feature engineering process for predictive modeling, as detailed in the next section.

4. Implementation of Forecasting Methods

To predict the number of visually impaired students per school year, we implemented two types of predictive modeling approaches. We selected time series forecasting (TSF) models and supervised machine learning (ML) trained on historical census data to learn patterns from the merged datasets. The choice of these models was based on previous empirical studies [12,17,18]. In addition, both TSF and ML models have widely available open-source libraries, such as scikit-learn. (https://scikit-learn.org/) and statsmodels (https://www.statsmodels.org/stable/index.html (accessed on 09 February 2025)). Such implementations ensure the reproducibility of this research and experimentation with a considerable number of models.

For time series forecasting, we have considered the following models: (a) autoregressive integrated moving average (ARIMA), (b) seasonal ARIMA (SARIMA), and (c) exponential smoothing (ETS).

For ML models, we selected the following ML models: (a) decision tree regressor (DT), (b) extra trees regressor (ET), (c) Gaussian NB (GNB), (d) passive aggressive regressor (PA), (e) ridge, bagging, (f) hist tests gradient boosting regressor (HGB), (g) gradient boosting regressor (GB), (h) complement NB (CNB), (i) multinomial NB (MNB), (j) ElasticNet (EN), and (k) XGB regressor (XGB).

In addition, we have considered indicators (QTs) associated with vision problems, including blindness, deafblindness, def. multiple, low vision, and a variation of the sum of the QTs (QT_VISAO1 = Blindness + DeafBlindness + Multiple Def. + Low Vision; QT_VISAO2 = Blindness + DeafBlindness + Low Vision), which we will detail in the next subsections.

Performance Evaluation

To conceive and validate the models, we used the holdout method, splitting the data into training (80%) and testing (20%) subsets. The mean absolute error (MAE) and root mean squared error (RMSE) were used to measure the forecasting performance of the models. We compared the prediction values with the actual disability counts in the 2023 census.

We show the performance of the experimental models in Figure 2.

Table 6. Performance comparison of the top three models by category.

Scenario	Category	Model	MAE	RMSE
Blindness	ML	CNB and MNB	0.0139	0.1541
		EN	0.0170	0.1583
	TSF	ARIMA and SARIMAX	0.0270	0.1929
		ETS	0.0368	0.2388
Deafblindness	ML	CNB and MNB	0.0011	0.0350
		EN	0.0013	0.0378
	TSF	ARIMA and SARIMAX	0.0024	0.0502
		ETS	0.0033	0.0584

presents the results of the MAE and RMSE metrics for the models with the best performance for the blindness and deafblindness scenarios. These results lead us to conclude that ML models, particularly those based on the naive Bayes algorithm, outperformed time series models such as ARIMA and SARIMAX.

Overall, machine learning methods performed better than time series methods, and among the machine learning methods, the naive Bayes-based methods—complementary naive Bayes (CNB), multinomial naive Bayes (MNB), and Gaussian naive Bayes (GNB)—appeared in the top five (CNB and MNB tied for first place and GNB for fourth). This was complemented by ElasticNet (EN) in second place, hist. gradient boosting regressor (HGB) in third, and decision tree regressor (DT), extra trees regressor (ET), and ridge tied for fifth place. The best time series methods appear only in the ninth and tenth places. In general, when comparing both ML models and TSF techniques it is clear that CNB, NMB, and EN outperform for the dataset considered in this study.

5. Final Considerations and Future Directions

This study demonstrates the potential of AI-driven predictive models to improve disability resource planning within the Brazilian educational system. By analyzing educational census data from 2021 to 2023, we successfully implemented machine learning and time series forecasting models to predict the number of visually impaired students and ensure the optimal distribution of Braille textbooks and accessibility resources under the PNLD program. Our results highlight the benefits of data-driven methodologies in improving decision-making processes for educational policymakers, school administrators, and accessibility advocates.

The findings of this study emphasize the effectiveness of different ML and TSF methods to predict future enrollments, which will be used by PNLD administrative staff to make a decision on the amount of textbooks to acquire for each Brazilian school. Considering all the compared models, it was clear that for the dataset considered, naive Bayes (CNB, NMB) and ElasticNet performed the best and can be chosen to perform more accurate predictions in the future.

Despite these promising results, certain limitations should be acknowledged. The limited sample size for specific disabilities, particularly those with low national prevalence, made it difficult to build robust predictive models for all disability categories. Furthermore, significant variance in disability reporting between schools posed a challenge, as inconsistent data collection methodologies affected the precision of the model. Furthermore, the study relied primarily on educational census data, which, although valuable, lacked integration with external factors such as socioeconomic conditions, regional access to healthcare, and availability of infrastructure variables that could further refine predictive capabilities. Addressing these challenges in future research would improve the robustness and applicability of predictive models in the field of educational accessibility planning.

To overcome these limitations, future studies should focus on expanding datasets and incorporating external data sources. Integrating demographic data, health records, and socioeconomic indicators from IBGE could improve the predictive accuracy of the models by providing a more holistic view of disability trends. Furthermore, developing a real-time monitoring system for disability tracking, potentially using automated data collection from schools and government agencies, could provide more up-to-date information, improving the responsiveness of policymakers to changing accessibility needs. In addition, advances in deep learning, particularly recurrent neural networks (RNNs) [19,20] and transformer-based architectures [21], hold promise to improve predictive accuracy by capturing more intricate patterns in trends in disability reporting over time.

Ultimately, this research contributes to the field of AI-driven accessibility planning by demonstrating that data-driven methodologies can revolutionize education policy decisions. The models developed in this study provide a foundation for future predictive systems, paving the way for more adaptive, efficient, and inclusive educational environments. Using AI for strategic planning, policy makers and educational institutions can ensure that students with disabilities are provided with equitable learning opportunities, strengthening broader commitment to inclusive education and social equity.