The Application of Binary Logistic Regression in Modeling the Post-COVID-19 Effects on Food Security: In Search of Policy Recommendations in Promoting Sustainable Livelihoods for Food-Insecure Households

Abstract

COVID-19 has caused global problems with complex ramifications. Vulnerable households worry about disruptions to food security. Mobility restrictions, decreased salaries, and supply chain disruptions have increased food insecurity. This study examined the best food security model and its determinants. The primary research data were collected from 257 respondents via cluster random sampling. Binary logistic regression, using R-Studio, was employed to analyze the data. The study showed that the Minimal Model (MM) was optimal in explaining food security status, with three predictors: the available food stock (AFS), education of the household head (EHH), and household income (HIc). This aligned with studies showing that food purchase ability depends on income and education. Male household heads demonstrated better food security than females, while women’s education influenced consumption through improved nutritional knowledge. Higher income provides more alternatives for meeting needs, while decreased income limits options. Food reserve storage influenced household food security during the pandemic. The Minimal Model effectively influenced food security through the AFS, EHH, and HIc. The findings underline the importance of available food stock, household head education, and household income in developing approaches to assist food-insecure households. The research makes a significant contribution to ensuring food availability and promoting sustainable development post-pandemic.

1. Introduction

The COVID-19 pandemic has profoundly impacted global food security through its effects on the availability and accessibility of food. Several studies have documented the impact of the pandemic on food systems, nutrition, and household food insecurity both during and after the immediate response to the pandemic [1,2,3,4]. In the calendar year 2022, cumulative COVID-19 infections and deaths continued to mount worldwide. As of 29 January 2023, the WHO had recorded over 753 million confirmed cases and more than 6.8 million deaths globally. In Indonesia, UNICEF data show that by December 2021, a total of 4,267,452 cases and 143,969 deaths had been reported; these figures continued to rise through 2022, reflecting persistent community transmission across the archipelago. This health crisis precipitated the deepest global recession in decades: worldwide real GDP fell by 3.4 percent in 2020—the worst contraction since World War II—before rebounding by 5.5 percent in 2021 [5]. Indonesia’s economy mirrored this pattern, contracting by 2.1 percent in 2020, its first annual decline in over two decades, then recovering with 3.7 percent growth in 2021. These macroeconomic shocks critically undermined household incomes and purchasing power, exacerbating food insecurity [6].

There is a need to provide evidence-based policy recommendations that specifically address food security challenges today while supporting sustainable livelihoods among food-insecure households in the long term. This encompasses establishing applicable interventions and backup systems to bolster resilience and sustainability in the food system [7,8]. This study aims to address this gap by using binary logistic regression to identify and model the effect of post-COVID-19 on food security. It is also intended to pinpoint critical determinants of food security during the post-pandemic phase and design policy interventions that foster livelihood sustainability for food-insecure households. Hence, this study aimed to examine the best food security model and its determinants. The results of this study would inform policymakers on practical approaches to support food-insecure households and build more sustainable food systems. In addition, the results of this study would also contribute to efforts toward food security and sustainable development in the post-pandemic context.

2. Literature Review

2.1. Impact of COVID-19 on Food Security

The COVID-19 pandemic affected global food security, particularly among vulnerable households. The paper reviews the literature on applying binary logistic regression in modeling these impacts and aims to draw policy recommendations to foster sustainable livelihoods for households vulnerable to food insecurity. Food security traps are worsening globally with the pandemic in all regions, including developed and developing countries [8,9,10]. In particular, loss of income, food price escalation, and food supply chain disruption are the principal drivers of food security during the pandemic. In the wake of the COVID-19 pandemic, three drivers stand out as reasons for concern. For one, layoffs, reduced working hours, or business closures have diminished income and purchasing power, especially for vulnerable groups. Access to adequate and nutritious food has thus become limited and a challenge. Second, food prices driven up by scarcity, panic buying, and market speculation have worsened the situation by driving staple foods out of reach of many households [11,12,13]. The third major reason, food chain supply disruptions, is a complex but powerful threat. Restrictions on movement, border closures, and logistical bottlenecks are disrupting the flow of food from producers to consumers. Consequently, some stocks have built up in some areas, while others are scarce. Most smallholder farmers and local food producers have difficulties finding a market for their products, and consumers have a limited choice and access to fresh food. These three aspects make food security a challenging issue to sustain through the current pandemic, with the call for rapid, efficacious policy responses at national levels and policies reached through international cooperation to best overcome the crisis [14,15,16].

2.2. Binary Logistic Regression in Food Security Studies

The determinants of food security are commonly estimated using binary logistic regression. This approach facilitates the use of significant predictors, including income, education, household size, and access to technology. Lower educational attainment, larger household size, and lower income were associated with food insecurity in studies that employed binary logistic regression. Binary logistic regression is a convenient statistical method of analyzing food security determinants. This approach enables researchers to assess the influence of multiple independent factors on the likelihood that a household is food secure or food insecure. For example, some significant predictors that these studies found were income level, level of education, size of household, and access to technology [17,18]. Households with lower educational status, larger family sizes, and lower income are consistently characterized by a higher risk of being food insecure. Binary logistic regression is a widely used method for analyzing data in food security research, offering the advantage of processing binary dependent variables (i.e., food secure or food insecure) and producing precise odds ratios. This enables policymakers and researchers to better understand the relative contributions of each factor to a household’s food security status. Moreover, this approach effectively determines such relationships while controlling for multiple variables, thereby yielding a more comprehensive picture of the food security dynamics. Notably, while ordinal and binomial LR are informative, there are other, more diverse analytical approaches, including qualitative methods and longitudinal analysis, that give better insight into the complexities of food security [19,20,21].

2.3. Key Determinants of Food Security

Socio-economic factors heavily influence the food security of a household. Higher levels of education are often associated with a better understanding of nutrition and health practices as well as a greater capacity to manage household resources. Thus, higher incomes lead to better access to quality food and a higher quantity of food. Stable employment status also supports food security by providing a steady income stream. Household characteristics also determine food security, however. Bigger households will face the toughest challenges in providing food for all their members. By contrast, households headed by younger or female heads are likely to have other socio-economic constraints [22,23,24]. Support from outside the home is crucial in combating food insecurity, particularly for at-risk households. Whether in the form of cash transfers, food subsidies, or economic empowerment programs, government assistance can help improve access to and the availability of food and enhance household food access. (Incomes from remittances of family members working outside the region or country also contribute to a significant part of household finance and can reduce the risk of food insecurity.) However, the impact of this support (whether internal or external) is contingent on how it is focused, sustained, and aligned with the community’s particular needs. Policies should aim to build educational and income-generating opportunities, both promoting food security. Targeted programs, such as safety net programs and assistance to the most vulnerable groups, including women, are vital. Encouraging sustainable agricultural practices and home gardening can increase food availability and stability [25,26,27]. The binary logistic regression in the models played a crucial role in determining the post-COVID-19 impact on food security. These insights, drawn from this study, can inform policy recommendations to support sustainable livelihoods and mitigate food insecurity among vulnerable households. Further studies should build on and refine these models while also considering additional drivers of food security in a post-pandemic world.

While existing studies robustly identify common predictors and verify the utility of binary logistic regression, several gaps remain. First, most analyses are cross-sectional, which limits our understanding of the temporal dynamics and long-term effects of interventions. Second, most prior studies of food-security determinants employ multiple regression techniques, with a smaller number using logistic regression, and then report only those predictors that achieve statistical significance. In contrast, our research employs binary logistic regression in R Studio version 2025.05.0+496 to analyze the entire dataset and systematically compare six alternative variable-set models derived from previous empirical work and the authoritative literature. This allows us to both validate existing significant predictors and explore the broader set of candidate variables in a unified modeling framework. Addressing these gaps through longitudinal data analysis and expanded modeling frameworks will be crucial for informing more effective, context-sensitive policies in a post-pandemic world.

Based on the literature review discussed, this study hypothesizes that the education level of the household head, household income, and the availability of food stock are the primary determinants most significantly influencing household food security in the post-COVID-19 period.

3. Materials and Methods

3.1. Study Area

The research was conducted in Pangkajene and Islands Regency (Pangkep), as depicted in Figure 1. The selection of this place considered the fact that Pangkep is a region with diverse topography, encompassing mountains (highlands), oceans (coastal areas), and urban and suburban areas (lowlands), each with distinct characteristics. Pangkep Regency has 13 districts, with an area of 1236 km², 3 of which are located on the outer islands with a total of 115 islands. The total number of households is 96,757, spread across urban, rural, and highland areas.

3.2. Binary Logistic Regression with R-Studio: A Model Design and Its Steps

The research process is represented by a three-stage flowchart (Figure 2), which offers a clear, visual outline of the program’s progression. First, the study began with systematic observation and data collection. Next, the gathered information underwent rigorous analysis to identify patterns and relationships. Finally, the analysis culminated in the formulation of conclusions and the proposal of actionable recommendations. This structured depiction enhances transparency and facilitates comprehension of each procedural step.

• STEP ONE. Step 1 involved gathering data to meet the established criteria for addressing the research questions posed in the study as part of constructing the logistic regression model. Subsequently, the data underwent additional verification to determine its suitability for the study.

3.2.1. Building Binary Logistic Regression

Binary logistic regression requires a binary dependent variable. The factor level 1 of the dependent variable in a binary regression should accurately represent the anticipated outcome. Only the factors that hold significance should be incorporated. The independent variables must exhibit independence from one another. The model should exhibit minimal or negligible multicollinearity. When there are five independent variables in the given scenario, the expected probability of the least frequent event can be determined [28].

3.2.2. Data Collection and Data Verification

Preliminary field observations were subsequently used to identify research problems and objectives. Step 1 also outlines the sampling and data collection processes. This study employed quantitative methodology via a survey-based approach. Households were interviewed using a standardized and pre-designed questionnaire in urban, mountainous, seashore, and suburban locations. Most of the examined population belonged to the lower-middle socio-economic category. All houses in Pangkep District constituted the population for this survey. The research respondents were selected using the cluster random sampling technique. The population comprises 96,757 households, and 257 household samples were obtained using the Cochran formula [29]. The study population comprised household heads—both male and female—aged between 25 and 60 years residing in Pangkep Regency. These individuals were stratified by area of residence: urban inhabitants, predominantly working as civil servants, entrepreneurs, or private-sector employees; peri-urban dwellers, engaged as food-stall proprietors, fruit vendors, or traders of vegetables and side dishes; coastal residents, whose livelihoods included fishing or laboring at the Tonasa cement factory; and rural villagers, primarily employed in agriculture. A cluster sampling technique was employed to select participants, and field observations and interviews were conducted over four months (June–September 2023). Ultimately, face-to-face interviews were completed with 257 respondents using a questionnaire that had undergone validation. The food security instrument was developed under the FAO’s Household Dietary Diversity Score (HDDS) for Measurement of Household Food Access: Indicator Guide (Version 2).

Before data collection, we performed an a priori power analysis using GPower 3.1 for logistic regression with α = 0.05 (two-tailed), a medium effect size (OR = 1.5), and five predictors. The resulting power for a sample of 257 households was 0.82, exceeding the conventional threshold of 0.80 for adequate sensitivity. Furthermore, only adults aged 18–65 years were eligible to participate to target the working-age population primarily responsible for household food management and to minimize recall bias among older respondents, as recommended by Cabal et al. [30].

• STEP TWO. Step 2 was proceeding to the stage of logistic regression analysis. The process began with exploratory data analysis, which created a script using the obtained field data. This script was then used to facilitate logistic regression analysis in R-Studio. In this analysis, six models were derived using patterns and literature studies. The six models were created to promote the comparison of analysis findings based on the lowest AIC and BIC values.

3.2.3. Data Analysis, Exploratory Analysis Data, and Hypothesis

Data analysis using logistic regression with R-Studio tools takes several general steps, as in Figure A1 (Appendix A). The next step was to formulate a research model specification and identify the variables that had a real effect in this study. Several steps were involved, as shown in Figure A1 (Appendix A). Unlike previous studies, the main novelty of this work lies in its thorough examination of the determinants of food security using the R-Studio tool. The previous article [31,32] used IBM SPSS Statistic 25 to analyze household food security factors. Its findings exclusively identify factors that have a significant impact.

The study employed binary logistic regression or the logit model to assess the variables influencing the household food security status during and after the COVID-19 pandemic. The household food security status, the dependent variable, was categorical and ordinal. The binary logistic regression model was employed when the response variable consisted of two categories with values of 0, conforming to the Bernoulli distribution (Equation (1)) [33,34]:

$$\mathrm{f}\left(\mathrm{y}\mathrm{i}\right)={\mathsf{\pi }}_{\mathrm{i}}^{\mathrm{y}\mathrm{i}}(1-{\mathsf{\pi }}_1{)}^{1-\mathrm{y}\mathrm{i}}$$

(1)

where

πi = probability of i-th event;

yi = the first random variable consisting of 0.

One predictor variable represents the formula below for a logistic regression model (Equation (2)) [27]:

$$\mathsf{\pi }\left(\mathrm{x}\right)={\displaystyle \frac{\exp ({\mathsf{\beta }}_0+{\mathsf{\beta }}_1\mathrm{X})}{1+\exp ({\mathsf{\beta }}_0+{\mathsf{\beta }}_1\mathrm{X})}}$$

(2)

In constructing the estimate of the regression parameters easier, the symbol π (x) in the given equation is changed into the logistic form in the following way (Equation (3)) [33,34]:

$$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{I}\mathrm{n}\left[{\displaystyle \frac{\mathsf{\pi }\left(\mathrm{x}\right)}{1-\mathsf{\pi }\left(\mathrm{x}\right)}}\right]=({\mathsf{\beta }}_0+{\mathsf{\beta }}_1\mathrm{X})$$

(3)

Then, the mathematical equation for the empirical logistic regression model is presented in Equation (4).

$$\begin{gathered} \mathrm{g}\left(\mathrm{x}\right)=\ln \left[{\displaystyle \frac{\mathsf{\pi }\left(\mathrm{x}\right)}{1-\mathsf{\pi }\left(\mathrm{x}\right)}}\right]=({\mathsf{\beta }}_0+{\mathsf{\beta }}_1\mathrm{R}\mathrm{A}+{\mathsf{\beta }}_2\mathrm{E}\mathrm{H}\mathrm{H}+{\mathsf{\beta }}_3\mathrm{N}\mathrm{F}\mathrm{D}+{\mathsf{\beta }}_4\mathrm{H}\mathrm{I}\mathrm{c}+{\mathsf{\beta }}_5\mathrm{T}\mathrm{o}\mathrm{H}+{\mathsf{\beta }}_6\mathrm{G}\mathrm{H}\mathrm{H}{+\mathsf{\beta }}_7\mathrm{L}\mathrm{o}\mathrm{R}+{\mathsf{\beta }}_8\mathrm{N}\mathrm{C}\mathrm{F}+{\mathsf{\beta }}_9\mathrm{P}\mathrm{B}\mathrm{W} \\ +{\mathsf{\beta }}_{10}\mathrm{S}\mathrm{I}\mathrm{c}+{\mathsf{\beta }}_{11}\mathrm{C}\mathrm{I}\mathrm{c}+{\mathsf{\beta }}_{12}\mathrm{A}\mathrm{F}\mathrm{S}) \end{gathered}$$

(4)

where

RA = respondent age (year); EHH = education of household head (year); NFD = number of family dependents (number of people); HIc = household income (Rupiah); ToH = type of household (1 = non-farm household, 0 = farm household); GHH = gender of household head (1 = man, 0 = woman); LoR = location of residence (1 = city. 0 = non-city); NCF = number of children under five; PBW = pregnant and breastfeeding woman (1 = yes, 0 = not); Sic = source of income (1 = permanent job, 0 = others); CIc = change in income (1 = change, 0—not change); AFS = available food stock (1 = available, 0 = not available). Then, ${\beta }_0$ = constant, ${\beta }_{1–4}$ = independent variable regression coefficient, ${\beta }_{5–12}$ = dummy coefficient.

3.2.4. Logistic Regression with R-Studio

There is a plethora of model comparison methods that aim to resolve the ever-present dilemma between parsimony and goodness of fit. In this article, three primary categories of related techniques were highlighted: (1) AIC and BIC, the most popular information criteria; (2) minimum description length; and (3) Bayes factors [28,29]. The fundamental principle of model construction is to minimize the number of variables included while ensuring that the model (a parsimonious model) accurately represents the actual outcomes of the data. This article will outline the deliberate selection process in the R programming language. The initial model construction stage involved selecting variables [20]. Figure A1, regarding the steps of logistic regression analysis using R-Studio tools, is in Appendix A.

3.3. Data Analysis with R-Studio

3.3.1. Outliers

Data points that differ significantly from the majority of data in a specific dataset are called outliers. Outliers are atypical observations that deviate considerably from the general patterns and are situated distantly from the central tendency of the data. Anomalies in the data can disrupt the data analysis process, particularly when it involves regression analysis. Outliers can result in consequences [35]. With large residuals from the model, the variance of the data will be larger, and the interval estimate will have a larger range. Furthermore, there are three types of outliers in regression analysis, which are as follows: vertical outlier, good leverage point, and bad leverage point [36]:

a.

Graphical Method or Scatter Plot.

Plotting data with statistical software is the method used at this stage. If one or more piece of data is far from the overall pattern of the data set, this indicates the presence of outliers.

b.

Box Plot.

The box plot is the most prevalent approach for calculating quartile and range values. The first three quartiles partition a sequence of data into four segments. R, which stands for “interquartile range,” is the difference between the first and third quartiles (Q3 and Q1) and is used to denote the range. Outlier data are values falling below the 1.5th percentile of the range from the first to the third quartile. The formula for quartiles is in Equation (5) [35]:

$${\mathrm{Q}}_1={\displaystyle \frac{\left(i\ast n\right)+2}{4}}$$

(5)

with

i = quartile: 1 for the lower quartile, 2 for the median, 3 for upper quartile; n = number of data.

A single step, on the other hand, is equal to 1.5 times the dispersion between the two quartiles. Below is the outlier identification scheme using a boxplot.

Standardized residual is shown below.

The i-th residual is defined (Equation (6)).

$$\widehat{\mathrm{e}}={\widehat{\mathrm{y}}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}$$

(6)

c.

Standardized residual to-i (Equation (7)).

$$\widehat{\mathrm{e}}={\displaystyle \frac{{\mathrm{e}}_{\mathrm{i}}}{\sqrt{\mathrm{M}\mathrm{S}\mathrm{E} }}}\mathrm{M}\mathrm{S}\mathrm{E}={\displaystyle \frac{\sum _{\mathrm{i}=1}^n\widehat{\mathrm{e}}}{n-k}}$$

(7)

Averaging the squared discrepancies between the actual and anticipated values yields the Mean Squared Error (MSE), sometimes called the standard error. One popular metric for evaluating regression models is the standard error, commonly used when comparing several models. The standard error quantifies the level of dispersion inside the regression model. A regression model is considered better when it has a smaller value.

d.

Cook’s Distance.

Cook introduced this method with the following formula in Equation (8).

$$\mathrm{D}\mathrm{i}=\left({\displaystyle \frac{h_{ii}}{(1-h_{ii})2}}\right)\left({\displaystyle \frac{{\mathrm{e}}_{\mathrm{i}}^2}{k\mathrm{M}\mathrm{S}\mathrm{E}}}\right)$$

(8)

where h_ii are the diagonal elements of the matrix H, and k is the number of response variables, as shown in the formula in Equation (9) [36]:

$$\begin{gathered} \begin{array}{cc}\hfill \widehat{\mathrm{Y}}& =\mathrm{X}\widehat{\mathsf{\beta }}\hfill \\ & =\mathrm{X}\left[{\left({\mathrm{X}}^{\mathrm{\prime }}\mathrm{X}\right)}^{-1}{\mathrm{X}}^{\mathrm{\prime }}\mathrm{Y}\right]\hfill \\ & =\mathrm{X}{\left({\mathrm{X}}^{\mathrm{\prime }}\mathrm{X}\right)}^{-1}{\mathrm{X}}^{\mathrm{\prime }}\mathrm{Y}\hfill \\ & =\mathrm{H}\mathrm{Y}\hfill \end{array} \\ \mathrm{with}\mathrm{H}=\mathrm{X}{\left({\mathrm{X}}^{\mathrm{\prime }}\mathrm{X}\right)}^{-1}{\mathrm{X}}^{\mathrm{\prime }}. \end{gathered}$$

(9)

Multicollinearity may also be detected by utilizing the tolerance value and its corresponding variable, the Variance Inflation Factor (VIF). These two metrics represent the extent to which mutual explanations exist between independent variables. Following the relationship between tolerance and VIF, a low tolerance value signifies a high VIF value (VIF = 1/tolerance). To detect multicollinearity, a tolerance value of 0.10 or a VIF value greater than 10 is generally accepted [35,36]:

3.3.2. The Concept of Akaike Information Criterion (AIC)

The Kullback–Leibler measure, devised in 1951, aims to quantify the information loss that occurs during approximations of reality. In other words, it serves as an evaluative criterion for models that effectively reduce information loss. After twenty years, Akaike derived a formula for model selection by establishing a correlation between the Kullback–Leibler measure and the maximum likelihood estimation method, a widely used estimation technique in statistical analyses. In practice, this criterion, known as the Akaike information criterion (AIC), is widely regarded as the initial criterion for model selection. ICT (AIC) is in Equation (10) [37]:

$$\mathrm{AIC}=-2\log \mathrm{L}\left(\hat{\mathsf{\theta }}\right)+2k$$

(10)

where θ = the vector representing the set of model parameters.

L($\widehat{\mathsf{\theta }}$) = the probability that the candidate model, given the data, is accurate when the maximal likelihood estimate (θ) is utilized.

k = the number of estimated parameters in the candidate model.

When dealing with tiny sample sizes, utilizing the second-order Akaike information criterion (AICc) instead of the previously described AIC is recommended. The AICc in Equation (11) is as follows:

$${\mathrm{AIC}}_{\mathrm{C}}=-2\log \mathrm{L}\left(\widehat{\mathsf{\theta }}\right)+2k+(2k+1)/(n-k-1)$$

(11)

In general, when evaluating the robustness of evidence for each potential model, two metrics may be employed:

• The delta AIC;
• The Akaike weights.

Determining and displaying AICm on each potential model can be seen with the AIC delta metric, with M. AIC assumed to be a possible model. The symbol m is interpreted as a variable that represents an integer (value 1 to M). Therefore, the minimum value of the AIC model is said to be effective and efficient. To determine the delta AIC for the $w_m$ model, subtract the AICm from the AIC. This difference is used to determine the level of support each possible model receives:

• A value below 2 signifies that the candidate model is nearly as excellent as the best model, where substantial evidence exists to support it.
• There is a marked decrease in the support for the candidate model between 4 and 7.
• When the candidate model receives a score greater than 10, it implies it has very little support, making it highly improbable that it is the best model.

The values listed above for the calculated delta AICs are solely approximations. $w_m$ is a representation of the probability value ascribed to the weight of the Akaike value, as the absolute value of the delta AIC is rendered useless in assessing the strength of evidence for a potential model. These are the ratios in question: the relative AIC of each candidate model as expressed in Equation (12) divided by the total AIC of all candidate models [37]:

$${\mathrm{w}}_{\mathrm{m}}={\displaystyle \frac{\exp \left(-0.5{\mathsf{\Delta }}_{\mathrm{m}}\right)}{\sum _{\mathrm{j}=1}^{\mathrm{M}}\mathrm{e}\mathrm{x}\mathrm{p}\left(-0.5\mathrm{j}\right)}}$$

(12)

Considering the available data, this strength metric for each candidate model can be interpreted as follows: One candidate model’s Akaike weight measures how likely it is to outperform all other candidates. With an Akaike weight of 0.60, for example, a candidate model has a 60% chance of being the best given the currently available data.

3.3.3. The Concept of Bayesian Information Criterion (BIC)

Schwarz [33] initially proposed another criterion for selecting an information theory model in a Bayesian structure called the Bayesian information criterion (BIC). It is thus also called the Schwarz information criterion or Schwarz Bayesian information criterion. Comparing AIC values is used to distinguish BIC, where the fact is that this method imposes severity penalties for more and more factors. This is conducted to differentiate itself from the AIC. In contrast to the BIC, Burnham and Anderson provide theoretical arguments in favor of the AIC, especially the AICc. Yang goes on to say that when selecting a model for a multivariate regression analysis, AIC outperforms BIC. As shown in Equation (13), the BIC is as follows:

$$\mathrm{BIC}=-2\log \mathrm{L}\left(\widehat{\mathsf{\theta }}\right)+k\log n$$

(13)

where the terms are identical to those defined in our AIC description, BIC indicates the optimal model*, as it is the one that yields the minimal BIC. Like delta AIC, delta BIC can be calculated as BIC minus BIC* for each candidate model. The interpretation of the magnitude of the delta BIC against a candidate model is possible as evidence that it is not the best model given M models [37].

• STEP THREE. Step 3 was the final step. The research findings were compared to past research to draw conclusions and offer recommendations for future researchers, as discussed below, to inform future research on food security.

4. Results

Figure 3 presents the correlations between the dependent variable (household food security) and the twelve independent variables. Correlation coefficients fall within the range of 0.40 < r ≤ 0.70 (moderately strong) and 0.70 < r ≤ 0.90 (strong). Notably, household income (HIc), type of household (ToH), and educational attainment of the household head (EHH) demonstrate consistent moderate to strong associations with food security. The asterisks (*, **, ***) on the Figure 3 typically represent the levels of statistical significance for the correlation coefficients shown in the upper triangle of the matrix plot.

*: p-value < 0.05 (statistically significant)

**: p-value < 0.01 (highly significant)

***: p-value < 0.001 (very highly significant)

Figure 4 confirms robust associations (r = 0.60–0.79) among key predictors such as the HIc with the AFS, NFD, EHH, and ToH. The EHH and ToH show particularly high correlation (r = 0.80–1.00). Figure 5 illustrates that all variables exhibit a normal distribution.

4.1. Exploratory Data Analysis

Variables 1–5 utilize box plots depicted in Figure 6; the data being analyzed are numerical. The relationship between age and food security is not statistically significant since there is no substantial difference in age between those who are food insecure and those who are food secure.

The box plot analysis (Figure 6) shows no significant difference in food security status based on age or number of dependents. However, households with less than 10 years of education are notably more food insecure. These findings reinforce the critical role of education and income in ensuring nutritional adequacy. Education and income emerge early as influential differentiators in food security status, supporting their inclusion in predictive models.

4.2. Outlier Analysis

4.2.1. The Cook’s Distance Method

Cook’s distance is a technique used to identify outliers by quantifying the impact of outlier data on regression coefficient estimators. It accomplishes this by calculating the value of Cook’s distance, which represents the size of this influence. Based on Figure 7, generated using Cook’s distance method, three rows (106, 141, and 223) exhibit distinct values from other variables and impact the logistic regression outcomes. A Cook’s distance value exceeding three is considered to indicate biased data. Household values 106, 141, and 223 do not exceed 3. Hence, it does not introduce bias into the data. These three households exert an impact, although it is not significant. Based on Cook’s distance analysis, the values for each variable do not exceed 3, indicating no need to eliminate any data.

4.2.2. Multicollinearity

Multicollinearity refers to the presence of substantial correlations among the independent variables in a regression model. To detect multicollinearity, we examine the Variance Inflation Factor (VIF) for each predictor. While some authors suggest that VIF values above 10 indicate problematic multicollinearity, others recommend a more conservative threshold, considering VIF values between 1 and 5 as indicating moderate correlation and values above five as suggesting high correlation. In our analysis (

Table 1. The collinearity value of the independent variables of household food security status.

Variable	Collinearity Statistic	Variables	Collinearity Statistic
RA	2.583	GHH	1.121
EHH	3.674	NCF	2.141
NFD	1.465	PBW	1.535
HIc	2.632	SIc	1.155
ToH	3.125	CIc	1.229
LoR	3.229	AFS	2.074

), all VIF values fall well below 5, which implies that although there may be moderate interrelations among some variables, none exhibit a level of collinearity that would seriously distort the regression estimates [38].

4.3. Results of the Logistic Regression Analysis

4.3.1. Full Model

The Full Model [28] is the initial modeling approach that incorporates 13 variables that impact family food security. The Full Model (FM) includes thirteen variables: respondent age (RA), education of household head (EHH), number of family dependents (NFD), household income (HIc), location of residence (LoR), type of household (ToH), gender of the household head (GHH), number of children under five (NCF), pregnant and breastfeeding women (PBW), source of income (SIc), change in income (CIc), and available food stock (AFS). This study examines the impact of thirteen predictor variables on household food security (HFS) in Pangkep Regency. The findings of the logistic regression analysis are displayed in

Table 2. The Full Model logistic regression analysis results.

Predictor Variables	Estimate	Standard Error	Z Value	Pr (>|z|)
(intercept)	−7.050	2.742	−2.571	0.010
RA	−6.591 × 10−2	4.679 × 10−2	−1.409	0.158
EHH	7.085 × 10−1	1.768 × 10−1	4.008	6.13 × 10–5 ***
NFD	−5.351 × 10−2	2.637 × 10−1	−0.203	0.839
HIc	1.821 × 10−6	3.866 × 10−7	4.711	2.47 × 10–6 ***
ToH	−1.712	1.134	−1.509	0.131
LoR	−1.807	1.212	−1.491	0.136
GHH	9.591 × 10−1	9.181 × 10−1	1.045	0.296
NFD	−4.523 × 10−1	8.446 × 10−1	−0.536	0.592
PBW	−6.562 × 10−1	8.325 × 10−1	−0.788	0.430
SIc	−1.231 × 10−1	5.691 × 10−1	−0.216	0.828
CIc	8.934 × 10−1	6.017 × 10−1	1.485	0.137
AFS	−1.399 × 10−2	8.636 × 10−1	−0.016	0.987
Predicted variable: household food security (HFS) AIC value = 121.84; BIC value = 167.97

*** = significant (p-value < 0.001).

. Table 2 indicates that the EHH and HIc variables have p-values less than α, precisely 6.13 × 10⁻⁵ < 0.001 and 2.47 × 10⁻⁶ < 0.001, respectively. Additionally, the AIC value is 121.84, and the BIC value is 167.97. When the p-value is below a certain level of significance (e.g., α = 0.001), it means that the model’s predictor and responder variables are significantly associated with each other [36,39]. Thus, it can be inferred that this study’s EHH and HIc variables impacted the statistically significant household food security (HFS) at a 90% significance level. The results of this investigation agree with prior research [40,41]. These studies collectively demonstrate that the household head’s education level and household income have a notable influence on the current state of food security within the household. The conclusion is as follows: these studies collectively demonstrate that the household head’s education level and household income notably influence the current state of food security within the household

Higher education may also affect household spending. Education boosts a person’s income potential. This provides a broader selection of nutritious foods. Lower education levels are associated with lower salaries, which affect their ability to meet their consumption needs in terms of quantity and diversity. Higher education and knowledge seem to make people more conscious of the need for balanced consumption [42,43].

4.3.2. Forward Stepwise Model

The Forward Stepwise Model [36] is a model in which researchers incrementally include predictor variables based on the most significant partial correlation. The process was stopped when the new predictors could no longer significantly increase the effective contribution below the 0.05 significance level. In the logistic regression results with the Forward Stepwise Model (FSM) (

Table 3. The results of logistic regression and Forward Stepwise Model analysis.

	Estimate	Standard Error	Z Value	Pr (>|z|)
(intercept)	−8.151	1.247	−6.534	6.39 × 10−11
HIc	1.491 × 10−6	2.575 × 10−7	5.793	6.91 × 10−9 ***
EHH	5.918 × 10−1	1.353 × 10−1	4.375	1.21 × 10–5 ***
ToH	−1729	1.010	−1.711	0.087
Predicted variable: household food security (HFS) AIC value = 112.03; BIC value = 129.30

*** = significant (p-value < 0.001)

), two factors were found to have a significant effect (p-value < 0.001) on household food security (HFS). The two factors are the HIc and EHH variables. The results of this FSM, as listed in Section 4.3.5, are consistent with the findings of the regression analysis in the FM, namely that the HIc and EHH variables significantly affect household food security. This result is visible from the respective p-values of HIc = 6.91 × 10⁻⁹ and EHH = 1.21 × 10⁻⁵, whose values are <0.001. Meanwhile, in this FSM, the ToH variable has no significant effect. Based on the available evidence, it is possible to infer that the EHH and HIC variables statistically affect household food security (HFS) significantly at a significant level of 90%. This study’s results align with previous research [40,44], which all showed that household head education and household income have a significant effect on household food security status. The conclusion is as follows: this study’s results align with previous research, which all showed that household head education and household income have a significant effect on household food security status.

4.3.3. Backward Stepwise Model

The Backward Stepwise Model [36] is a model conducted by researchers that includes all 13 variables, which are then eliminated one by one until only significant variables remain. Consistent with the findings of the regression analysis with the Backward Stepwise Model (BSM) (

Table 4. The results of logistic regression and Backward Stepwise Model analysis.

	Estimate	Standard Error	Z Value	Pr (>|z|)
(intercept)	−8.657	1.401	−6.180	6.43 × 10−10
EHH	6.095 × 10−1	1.481 × 10−1	4.116	3.86 × 10−5 ***
Hic	1.526 × 10−6	2.741 × 10−7	5.568	2.58 × 10−8 ***
LoR	−2.220	1.161	−1.912	0.0559
CIc	8.434 × 10−1	5.623 × 10−1	1.500	0.1337
Predicted variable: household food security (HFS) AIC value = 111.96; BIC value = 126.22

*** = significant (p-value < 0.001)

), two factors were found to have a significant effect (p-value <0.001) on household food security (HFS). The two factors are the EHH and HIc variables. The results of this BSM, as listed in Table 3, align with the regression results in the FM and FSM, namely that the HIc and EHH variables significantly affect household food security. This result is evident from the respective p-values of HIc = 2.58 × 10⁻⁸ and EHH = 3.86 × 10⁻⁵. Both values are <0.001 with this BSM’s AIC and BIC values of 111.96 and 126.22, respectively.

The conclusion is as follows: the EHH and HIc variables are explained in the previous two models (FM and FSM), which state that there is a considerable relationship between these two factors and the level of food security in households.

4.3.4. Minimal Model

This study tests the EHH and HIc variables, which have been shown to significantly impact the FSM, along with the AFS variable in the Minimal Model (MM) [36]. The EHH and HIc variables have also been investigated [9,45], which revealed that household head education and income determine food security. Based on scholarly studies [46,47] showing continuous food supply affects household food security, we added the AFS variable into linear logistic modeling with R-Studio. Moreover, the EHH, HIc, and AFS have a substantial effect at a 99% significance level (p-value < 0.01) (

Table 5. The results of Minimum Model analysis.

	Estimate	Standard Error	Z Value	Pr (>|z|)
(intercept)	−2.471 × 10−1	4.242 × 10−2	−5.825	1.72 × 10−8
AFS	1.829 × 10−1	5.962 × 10−2	3.068	0.00239 ***
EHH	4.648 × 10−2	5.524 × 10−3	8.413	2.96 × 10–15 ***
HIc	8.467 × 10−8	1.374 × 10−8	6.162	2.81 × 10–9 ***
Predicted variable: household food security (HFS) AIC value = 76.04; BIC value = 93.79

*** = significant (p-value < 0.001)

). The logistic regression analysis in Section 5 shows that the p-values of the AFS, EHH, and HIc are less than 0.001, 2.96 × 10⁻¹⁵; 2.81 × 10⁻⁹, 0.00239. These MMs have AIC and BIC values of 76.04 and 93.79, respectively. These findings show that the three factors significantly affect household food security. As noted, our findings empirically support earlier research. The conclusion is as follows: the MM is the best model, with the lowest AIC/BIC and the inclusion of a meaningful third variable—food stock availability.

In the COVID-19 pandemic, good food stock management and consumption patterns are needed. This strategy is essential so that the food stock that has been purchased can meet the needs according to the schedule that has been made and ensure that food ingredients are not easily damaged or rotten, which causes food waste [48,49,50,51].

4.3.5. Ethiopia Model

The naming of the Ethiopian Model is based on the location of the research [48], which was in Ethiopia. In this study, the AFS, NFD, ToH, and EHH were used as predictor variables that impact the ability of households to maintain food security. Our study pursued this Ethiopian Model (ME) by testing the four predictor variables [52,53] used with a binary logistic regression approach with R-Studio. This Ethiopian Model is selected based on the research focus, and the variables used are similar to those of the researcher, who compares the outcomes of the logistic regression analysis. The results of our study show that the ME we tested in Pangkep District showed slightly different things from those of [54,55]. This study discovered that only the variable ToH substantially impacts household food security (HFS). This conclusion is based on

Table 6. The results of the Ethiopia model analysis.

	Estimate	Standard Error	Z Value	Pr (>|z|)
(intercept)	−6.530	1.171	−5.576	2.46 × 10−8
AFS	−2.290 × 10−1	8.084 × 10−1	−0.283	0.777
NFD	−1.381 × 10−1	2.235 × 10−1	−0.618	0.537
ToH	1.420 × 10−6	3.015 × 10−7	4.710	2.48 × 10–6 ***
CIc	8.434 × 10−1	5.623 × 10−1	1.500	0.1337
Predicted variable: household food security (HFS) AIC value = 116.71; BIC value = 134.46.

*** = significant (p value < 0.001)

, where the p-value 2.48 × 10⁶ < 0.001 of the ToH Variable with AIC and BIC values in Ethiopia is 116.71 and 134.46, respectively. Meanwhile, the AFS, NFD, and CIc variables all have a p-value > 0.001, which means they do not significantly affect the HFS variable.

This result found that the AFS, NFD, ToH, and EHH variables significantly affect household food security [48]. However, our findings align with those of the household type that affects household income levels, affecting food consumption patterns [56,57,58].

4.3.6. Luwu Model

The name of the Luwu Model (LM) in this study is based on an article [59]. They conducted their research in the Luwu District, South Sulawesi Province, Indonesia, and published it in 2015. We adopted their model in this study, using the term LM. In their study, they used three predictor variables (EHH, HIc, AFS) to test their influence on household food security in the Luwu Regency. In this study, we employ the LM method by testing the three predictor variables mentioned above in Pangkep Regency. Luwu and Pangkep Regencies are in the same province in Indonesia (South Sulawesi Province). The similarity of demographic conditions and socio-economic and cultural characteristics is one of our considerations in adopting this LM and making it the primary literature in this model. Based on the results of our logistic regression analysis with R-Studio, we found that (

Table 7. The regression results of the Luwu Model.

	Estimate	Standard Error	Z Value	Pr (>|z|)
(intercept)	−6.973	9.562 × 10−1	−7.293	3.04 × 10−13
EHH	4.335 × 10−1	9.068 × 10−2	4.780	1.75 × 10–6 ***
HIc	1.391 × 10−6	2.952 × 10−7	4.713	2.45 × 10–6 ***
AFS	−2.874 × 10−1	8.094 × 10−1	−0.355	0.722
Predicted variable: household food security (HFS) AIC value = 115.10; BIC value = 129.71

*** = significant (p value < 0.001)

) the EHH and HIc variables have a p-value of 1.75 × 10⁻⁶ < 0.05 and 2.45 × 10⁻⁶ < 0.05, respectively, with AIC and BIC values of 115.10 and 129.71, respectively (Table 7). These figures indicate that the EHH and HIc variables have a significant impact on the household food security (HFS) variable in Pangkep Regency.

The research results of [59] were slightly different from our findings. They found that in addition to the EHH and HIc variables that had a significant effect, the AFS variable had a significant impact on household food security. In conclusion, the findings of this research are consistent with the research [60,61,62] that the higher the education of the household head is, the better the opportunity for an increase in household income is, and education on nutritious food consumption patterns of family members tends to be given more attention.

5. Discussions

The best model selection is based on the AIC (Akaike information criterion) and BIC (Bayesian information criterion) values for the six models previously described. Then, the best model criteria are determined based on the principle of parsimony, namely the model that has the smallest AIC and BIC values [56,57]. Furthermore, the selected best model serves as the basis for analyzing the factors affecting household food security status, and also provides recommendations for policymaking in overcoming household food insecurity.

Table 8. The summary of AIC and BIC values and the significant variables for the six models were examined.

No.	Types of Models	AIC	BIC	Significant Variable
1.	Full Model (FM)	121.84	167.97	EHH (6.13 × 10–5 ***) HIc (2.47 × 10–6 ***)
2.	Forward Stepwise Model (FSM)	112.03	129.30	HIc (6.91 × 10−9 ***) EHH (1.21 × 10–5 ***)
3.	Backward Stepwise Model (BSM)	111.96	126.22	EHH (3.86 × 10−5 ***) HIc (2.58 × 10−8 ***)
4.	Minimal Model (MM)	76.04	93.79	AFS (0.00239 ***) EHH (2.96 × 10–15 ***) HIc (2.81 × 10–9 ***)
5.	Ethiopian Model (EM)	116.71	134.46	ToH (2.48 × 10–6 ***)
6.	Luwu Model (LM)	115.10	129.71	EHH (1.75 × 10–6 ***) HIc (2.45 × 10–6 ***)

*** = significant (p value < 0.001)

summarizes the AIC and BIC values and significant variables from the logistic regression analysis with R-Studio for each previously described model.

Table 8 shows that the most optimal model in terms of AIC and BIC is the Minimal Model (MM), with values of 76.04 and 93.79, respectively. Thus, the MM is considered the best and most effective model in explaining household food security status in this study. In the MM, all predictor variables, namely the AFS, EHH, and HIc, play a key role in determining the safety of food supplies for families. Testing the Full Model, Forward Stepwise Model, Backward Stepwise Model, and Luwu Model, two predictor variables (EHH and HIc variables) out of three variables in the MM additionally impact family food security significantly. The Ethiopian Model has no substantial relationship between the two factors. Then, the AFS variable has no significant effect on all models tested except in the MM. This study’s findings are consistent with the results that the relationship between what a family can afford to eat depends on their income and the degree of education of the breadwinner. This study illustrates a stronger relationship between income and the education level of the household head. Households headed by men tend to have better food security than women, as men face fewer obstacles than women. However, it cannot be denied that women’s education level is also significant and has a major impact on household food consumption patterns, as it correlates with their nutritional knowledge [63,64].

Furthermore, the results of this study are also consistent with the idea that as the breadwinner’s salary rises, more alternatives are available to him/her to fulfill his/her family’s needs. In general, an increase in income is associated with a shift in food consumption patterns, particularly towards more diverse foods. Conversely, as income decreases, the choice of alternatives to meet family needs becomes more limited. According to Uyanga’s research [62], the inability to meet the family’s and its members’ needs may result from low income. When a family’s income is higher but its expenditure to meet needs does not change, the proportion of income allocated to needs will decrease, so the family can be said to be prosperous. Additionally, research by Bhattacharjee [18] supports the results of this study, indicating that available food stocks impact household food security. The storage of food reserves is necessary during a pandemic like the COVID-19 pandemic, where mobility restrictions lead to disruptions in the food supply. Every household should store food reserves so that each family member can meet their needs. Long-term food storage management is necessary to prevent food loss and waste.

6. Conclusions

This study aimed to examine the best food security model and its determinants of household food security. To achieve the objective of the study, the BLR-R uses six R-Studio models (Full Model, Forward Stepwise Model, Backward Stepwise Model, Minimal Model, Ethiopian Model, and Luwu Model). The result showed that the Minimal Model had the lowest Akaike information criterion (AIC) value of 76.04 and the lowest Bayesian information criterion (BIC) value of 93.79. As a result, by applying the principle of parsimony in the R-Studio model, the Minimal Model emerged as the best model and was deemed the most effective model in this study. Next, based on the BLR-R model, we found that three essential variables had a statistically significant influence on household food security for the best model. The three variables were the available food stock, the education of household heads, and the household income. These three influential and significant variables can serve as a roadmap for the government to formulate strategies/programs to address food insecurity during the COVID-19 pandemic and promote sustainable livelihoods for food-insecure households.

Applying the Minimal Model to our dataset revealed three statistically significant predictors of household food security: the available food stock, household head’s educational attainment, and household income. Each predictor’s effect size and direction were estimated with high precision, thereby establishing a robust empirical foundation for targeted intervention. Building on these results, we propose three policy initiatives directly derived from the Minimal Model’s insights: (a) social safety net program: since available food stock emerged as the strongest determinant, emergency cash transfers and in-kind food distributions should be prioritized to stabilize short-term consumption, (b) educational access program: given the positive association between household head education and food security, investments in adult literacy and skills training—complemented by school meal and health services—will address both immediate nutritional needs and longer-term human capital development, and (c) income-generation program: recognizing the critical role of household income, microenterprise support and vocational training should be tailored to local resource endowments to enhance sustainable livelihood opportunities. By explicitly linking each recommendation to a key model coefficient, this study not only demonstrates the practical applicability of a parsimonious logistic regression framework but also provides policymakers with clear, evidence-based strategies to mitigate household food insecurity in the wake of COVID-19 and beyond.

Despite its contributions, this study has several limitations. First, its cross-sectional design precludes causal inference, as associations between predictors and food security status cannot establish directionality. Second, the sample was restricted to 257 households aged 18–65 in Pangkajene and Islands Regency, which may limit the generalizability of the findings to other regions, age groups, or socio-cultural contexts. Third, data on income, food stock, and security status were self-reported and thus susceptible to recall and social desirability biases. Fourth, we examined only three socio-economic determinants—the available food stock, education of the household head, and income—while other factors such as health status, market access, and psychosocial resilience were not assessed. Finally, our survey was conducted during the early post-pandemic recovery phase (August–September 2023), and food security dynamics may have shifted subsequently.

Future studies should consider a longitudinal design to observe household food security over time and under evolving conditions. Expanding the geographic scope to include urban, peri-urban, and other rural regions would allow for broader generalization. Moreover, incorporating qualitative approaches can capture behavioral and cultural nuances that affect food management practices, which are not reflected in quantitative indicators. This study confirms that strategic factors, such as education, income, and food stockpiling, interact significantly to shape household food security outcomes. By identifying a parsimonious and statistically robust model, this study contributes empirical evidence for targeting interventions that improve livelihoods and food access during and beyond public health crises.