Study setting, period, and time frame

The data were obtained from the most recent standard DHS dataset of East African countries (2015/16–2022) (Table 1). A standardized dataset was used [22] to obtain all parameters and a large sample size that is representative of the population source. DHS collects data that is cross-nationally comparable. The surveys are population-based and nationally representative of each country, with large sample sizes [22]. Eastern Africa comprises 14 countries located in the Great Lakes region, the Horn of Africa, and the Indian Ocean Islands.

Table 1 Countries, sample size, and survey year of Demographic and Health Surveys included in the analysis for 10 East African countriesData source and population

DHS databases for children’s records or child records were utilized. Before using the DHS dataset, weighted values were employed to restore the representativeness of the sample data. The source population included all children aged 0–23 months over the five years before the survey period in East Africa. Mothers who had more than one child within the previous two years were asked about the most recent or younger child. However, mothers who had twins in the previous birth were asked about both children [22]. This study covered all children aged 0–23 months in the five years preceding the survey in the selected enumeration areas (EAs) in each country. Children born recently and who died were excluded from the study. According to the DHS recode manual for the treatment of missing values, missing and “don’t know” replies on whether the child drank from a bottle with a nipple yesterday throughout the day or night were included in the study but were regarded as not using bottle feeding [22]. Finally, weighted 43,150 samples were analyzed.

Sample size determination and sampling technique

Demographic and Health Survey (DHS) samples are frequently stratified by administrative geographic region and within each region by urban/rural areas. In the first round of sampling, the EAs were chosen with a probability proportional to their size within each stratum. The systematic sampling approach selected a predetermined number of households in the specified EAs in the second sampling step. Following the listing of the households, a fixed number of households were chosen in the designated cluster using equal-probability systematic sampling [22].

Study variables

The bottle feeding practice of children aged 0–23 months was the outcome variable. Factors such as the mother’s age, work status, marital status, family size, maternal education, age at first birth, number of health facility visits, media exposure, household wealth status, child’s age, birth weight, breastfeeding status, sex, twins, place of delivery, pregnancy preference, birth order, preceding birth interval, distance to the health facility, Postnatal Care (PNC), and Antenatal Care (ANC), community-level factors, such as distance from health facilities, ANC, women’s education, mass media exposure, place of living, and community wealth level, were all assessed at the community level.

Data processing and analysis

The DHS files for child record were downloaded in the STATA format. Following access to the data, they were cleaned, coded, and merged to provide suitable variables for analysis. The data were then weighted using sample weights for probability sampling and non-response to restore representativeness before statistical analysis. To define the variables in the study using statistical measurements, Microsoft Excel 2019 and STATA 17 software were used to provide both descriptive and analytic statistics.

Model building for multi-level analysis

The usual logistic regression model assumptions may be violated due to the hierarchical nature of the DHS data. Consequently, a multilevel logistic regression with four models was fitted. The null model was used to evaluate variability in bottle feeding across clusters. The second model contained factors at the individual level, whereas the third model incorporated variables at the community level. In the final model (Model 4), both individual- and community-level variables were fitted simultaneously with the prevalence of bottle feeding. For model comparisons, the log-likelihood hood and deviation tests were utilized, and the model with the highest log-likelihood hood and lowest deviance value was chosen as the best-matched model. Variance inflation factor (VIF) was used to detect multicollinearity. All variables had VIF values of less than 10, with the final model’s mean VIF value being 1.46.

Parameter estimation method

Furthermore, this model served as a litmus test to determine whether multilevel or conventional logistic regression should be used, justifying the employment of such a framework. It was assessed using the log-likelihood ratio test (LLR), median odds ratio (MOR), intraclass correlation coefficient (ICC), and proportional change of variance (PCV). Moreover, the model comparison was made using model deviance, with the model with the lowest deviance selected for reporting and interpreting results.

Null model. For individual i in community j, the model can be represented as [23, 24]:

$$} + }\Upsilon 00 + } + \varepsilon ij...........nullmodel $$

Where: Yij is the bottle feeding status of ith child in the jth cluster, µ00 = is the intercept; that is the probability of having bottle feeding in the absence of explanatory variables, µ0j = community-level effect; εij error at the individual level.

Mixed model: This model was derived by mixing both individual and community-level factors simultaneously [25].

$$} + \Upsilon 00 + \Upsilon k0} + }\Upsilon 0p} + }} + \varepsilon ij.}.}.}.}.}. $$

Where: The term γk0 is the regression coefficient of the individual-level variable Xk and γ0p is the regression coefficient of the community-level variable Zp. Xk and Zp were individual and community-level explanatory variables respectively. The subscripts i and j represent the individual level and cluster number respectively.