Table 1 Description of variables

Concurrent anemia and stunting (CAS)

Defined when a child was both anemic and stunted. Anemia status was measured by hemoglobin level < 11 g/dL and categorized as anemic and non-anemic [3]. Stunting was measured by length-for-age < − 2 z-score and categorized as stunted and non-stunted.

 Residence place

Categorized as urban and rural.

 Region

Categorized as mainly agrarian and mainly pastoral.

 Household wealth category

First, household wealth index was developed by principal component analysis, using asset variables collected during the survey [19]. Then, the index was used to rank the households into low, middle and high wealth categories.

 Caregiver’s education status

Categorized as illiterate/none, primary, and secondary and above.

 Water source

Categorized as improved and unimproved.

 Toilet facility

Categorized as improved and unimproved.

 Child sex

Categorized as boy and girl.

 Child age

Categorized into < 12 and 12–23 months of age.

 Birth size

Assessed by the subjective reporting of the mother about the size of the child at birth and categorized as large, average and small. Birth size was used as a proxy measure of birth weight.

 History of infection

Assessed by whether the child had fever, diarrhea, or cough in the last two weeks preceding the survey. Categorized as yes and no.

 Breastfeeding duration

Categorized as < 12 and 12–23 months.

 Early breastfeeding initiation

Assessed by initiation of breastfeeding within the first hour after birth. Categorized as yes and no.

 Deworming tablet use

Assessed by whether the child received deworming table within the previous 6 months. Categorized as yes and no.

 Vitamin A supplement use

Assessed by whether the child received vitamin A supplement within in the previous 6 months. Categorized as yes and no.

 Iron supplement use

Assessed by whether the child received iron supplement within the previous 7 days. Categorized as yes and no.

 Complementary food groups

During the survey, caregivers were asked to recall the type of food the child was fed in the 24 h (one day) prior to the survey. The frequency of feeding during the same period was also assessed. The data were collected by trained interviewers, following the 5-Step Multiple-Pass Method. Using the WHO/UNICEF [39] and the DHS guidelines [19] for the assessment of infant and young child feeding practices, the food items were further categorized into 7 food groups: (1) meat, (2) egg, (3) milk, (4) grains, roots, and tubers, (5) legumes and nuts, (6) vitamin-A rich fruits and vegetables (VARFV), and (7) other fruits and vegetables (OFV). Using the 7 food groups above and following the WHO/UNICEF [39] and the DHS guidelines [19], dietary diversity and meal frequency indexes were determined for each child. The diversity and frequency indexes were used to determine whether the child met the WHO/UNICEF recommendations for dietary diversity and meal frequency.

 Minimum dietary diversity (MDD)

Assessed by whether the child received ≥4 complementary food items from the 7 food groups within the previous 24 h. Categorized as yes and no [39].

 Minimum meal frequency (MMF)

Assessed by whether the child was fed with complementary food ≥3 times if on breastfeeding, or ≥ 4 times if not on breastfeeding, within the previous 24 h. Categorized as yes and no [39].