A Structural Equation Modelling Approach to Determine Factors of Bone Mineral Density in Korean Women

Background: no studies have assessed the associations of nutrient intake, physical activity, age, and body mass index (BMI) with bone mineral density (BMD) using structural equation modelling (SEM) in Korean women. The aim of this study was to examine the effects of nutrient intakes, physical activity, and body mass index (BMI) on BMD in Korean premenopausal and postmenopausal women, with the SEM approach, based on the fourth and fifth Korea National Health and Nutrition Examination Surveys (KNHANES) 2008–2011. Methods: SEM analysis was performed with 4160 women (2863 premenopausal women and 1297 postmenopausal women) aged 30–75 years in order to investigate total, direct, or mediating effects of nutrient intake, physical activity, age, and BMI on BMD. Model sensitivity to external misspecification and statistical significance of SEM was determined by phantom variables and bootstrapping. Reliability assessment of the SEM was done by Cronbach’s alpha. Results: a direct effect of minerals (potassium, calcium, and phosphorus) on BMD (total femur, femoral neck, lumbar spine, and whole body) was observed in premenopausal and postmenopausal women (p = 0.045 and p = 0.048, respectively). Age and BMI showed a total effect on BMD in premenopausal and postmenopausal women (p = 0.002, respectively). Conclusions: our study suggests that mineral intake (potassium, calcium, and phosphorus), age, and BMI are major contributors to BMD in Korean premenopausal and postmenopausal women aged 30–75 years.


Introduction
The world population is rapidly ageing. The number of persons aged over 60 years was 962 million in 2017 worldwide. This number is expected to double to nearly 2.1 billion in 2050. In 2050, the persons aged over 60 years will account for 35 percent of the population in Europe, 28 percent in Northern America, 25 percent in Latin America [1,2]. The fastest ageing Organization for Economic Cooperation and Development (OECD) countries are Greece, Korea, Poland, Portugal, Slovenia, and Spain, while the fastest ageing non-OECD countries are Brazil, China, and Saudi Arabia [3].
Bone loss occurs as people get older. A reduced bone mineralization caused by disproportion of bone resorption and bone mineralization leads to osteopenia [4,5]. People with osteopenia have a higher risk of osteoporosis [4]. Osteoporosis is characterised by decreased bone mineral density (BMD) and bone strength [6]. People with osteoporosis are more likely to have fracture risk. Global hip fracture is projected to increase from 37 percent in 2025 to 45 percent in 2050 in Asia, as the aging population is rapidly increasing [7].
Data on overall health levels, health-related awareness and behaviours, and food and nutrition intake from a sample population were statistically analysed.

Participants
The participants included in this study were premenopausal and postmenopausal women aged over 30-75 years. The excluded participants were women aged <30 or ≥76 years (n = 7751) and men (n = 17,195). Moreover, we excluded missing data on BMD measurement (n = 4501), disease status (arthritis, pulmonary tuberculosis, asthma, renal failure, diabetes mellitus, thyroid dysfunction, cancer, liver cirrhosis, or hepatitis (type B and C)) (n = 3387), missing data on anthropometric parameters (height, weight, and waist circumference) (n = 18), missing data on nutrition intake survey (n = 367), or missing data on physical activities, income level, education level (n = 71), and oestrogen use and ovariectomy status (n = 303). Finally, 4160 subjects (2863 premenopausal women and 1297 postmenopausal women) were included in the statistical analysis, as shown in Figure 1. bone density and body composition, chest, and knee and hip-joint X-ray. The nutrition survey consisted of components, including dietary behaviour, dietary supplement use, food security, food frequency, and food and dietary intake [18]. A detailed explanation on the KNHANES is available at http://knhanes.kdca.go.kr (accessed on 24 February, 2021). Data on overall health levels, health-related awareness and behaviours, and food and nutrition intake from a sample population were statistically analysed.

Participants
The participants included in this study were premenopausal and postmenopausal women aged over 30-75 years. The excluded participants were women aged < 30 or ≥ 76 years (n = 7751) and men (n = 17,195). Moreover, we excluded missing data on BMD measurement (n = 4501), disease status (arthritis, pulmonary tuberculosis, asthma, renal failure, diabetes mellitus, thyroid dysfunction, cancer, liver cirrhosis, or hepatitis (type B and C)) (n = 3387), missing data on anthropometric parameters (height, weight, and waist circumference) (n = 18), missing data on nutrition intake survey (n = 367), or missing data on physical activities, income level, education level (n = 71), and oestrogen use and ovariectomy status (n = 303). Finally, 4160 subjects (2863 premenopausal women and 1297 postmenopausal women) were included in the statistical analysis, as shown in Figure 1. The ethical review and approval were waived for this study. Written informed consent was obtained from all subjects involved in the Study.

Measurements of Anthropometric Parameters and Bone Mineral Density
For SEM analysis, we obtained data from KNHANES IV-V, including demographic characteristics (age, income level, education level, occupation status, mean daily sleep time, smoking status, alcohol intake), anthropometric characteristics (height, weight, waist circumference, and BMI), physical activities (high-intense physical activity, moderate-intense activity, and regular walking), BMD (total femur, femoral neck, lumbar spine and whole body), and nutrient intakes (energy, water, protein, carbohydrate, calcium, phosphorus, potassium, total vitamin A, retinol only, and vitamin C).
Height (cm) of participants was measured to the nearest 0.1 cm. Body weight (kg) was measured to the nearest 0.1 kg, with the participant wearing light clothing without shoes.
BMI was calculated as weight (kg)/height squared (m 2 ). Waist circumference (WC) was measured according to the World Health Organization (WHO) guideline. The ethical review and approval were waived for this study. Written informed consent was obtained from all subjects involved in the Study.

Measurements of Anthropometric Parameters and Bone Mineral Density
For SEM analysis, we obtained data from KNHANES IV-V, including demographic characteristics (age, income level, education level, occupation status, mean daily sleep time, smoking status, alcohol intake), anthropometric characteristics (height, weight, waist circumference, and BMI), physical activities (high-intense physical activity, moderateintense activity, and regular walking), BMD (total femur, femoral neck, lumbar spine and whole body), and nutrient intakes (energy, water, protein, carbohydrate, calcium, phosphorus, potassium, total vitamin A, retinol only, and vitamin C).
Height (cm) of participants was measured to the nearest 0.1 cm. Body weight (kg) was measured to the nearest 0.1 kg, with the participant wearing light clothing without shoes.
BMI was calculated as weight (kg)/height squared (m 2 ). Waist circumference (WC) was measured according to the World Health Organization (WHO) guideline.
Participants were asked how frequently they exercised weekly for the physical activity assessment with Korean version of the international physical activity questionnaire (IPAQ), categorised into "yes" or "no".
Subjects who exercised vigorously for >20 min, at least three times a week, or moderate exercise, or walking for >30 min, at least five times a week, were considered as doing regular exercise or "yes" subjects.
Participants who did vigorous exercise for >20 min, at least three times a week, were considered as doing high intense physical activity. Participants who did a moderate exercise for >30 min, at least five times a week, were considered as doing moderate intense physical activity. Walking was considered as walking for >30 min at least five times a week.

Nutrient Intakes
Trained dietitians administered a multiple-pass 24-h dietary recall questionnaire for nutrient intake assessment, including food, energy, water, protein, fat, carbohydrate, fibre, ash, calcium, phosphorus, iron, sodium, potassium, total vitamin A, carotene, retinol only, thiamine, riboflavin, niacin, and vitamin C. The food composition table from the Korean National Rural Development Institute was used to estimate nutrient intake [19].
This study used observational variables of nutrient intake (energy, water, protein, carbohydrate, calcium, phosphorus, potassium, total vitamin A, retinol only, and vitamin C) for SEM analysis, using Cronbach's alpha, which is an advantageous method in order to increase reliability, considering the principle of parsimony.

Structural Equation Modelling
We determined the related pathway or relationships between independent and/or dependent (e.g., mediators) variables based on results obtained after a reliability and feasibility analysis, using SEM on the AMOS 27.0 (IBM, Chicago, IL, USA).
The total, direct, and indirect effects of the major variables on BMD variables were investigated after the structural model fit was determined. The statistical significance of the indirect effect was tested with the bootstrapping technique to assess the mediating effect. Phantom variables were used to determine the mediating effects in multiple mediator models.
The reliability of multi-item scale variables was assessed with Cronbach's alpha correlation coefficient. The reliability was elevated by omitting an item with a high value among Cronbach's alpha values.
The full information maximum likelihood method was used for the research model evaluation. Absolute fit indices (X 2 (Chi-square), X 2 /df (relative Chi-square), root mean square error of approximation (RMSEA)), and incremental fit indices (Tucker-Lewis Index (TLI) and comparative fit index (CFI)) were used for the model fit examination.
The bootstrapping technique was applied for the significance. A total of 1000 samples were used for bootstrapping. Percentile confidence intervals were set at 95%. Bias-corrected confidence intervals were set at 95%.

Statistical Analysis
Before performing SEM procedures, missing values were treated through data preprocessing process. The processing of missing data is typically performed by removing or replacing, but in this study, all analyses were performed by removing missing values.
The Kolmogorov-Smirnov test, Q-Q plots, and histograms were used to test for the normality distribution. Variables that were not normally distributed were log-transformed.
To examine variables of general characteristics, education level, income level, occupation status, average sleep duration, alcohol consumption, smoking status, physical activity, and bone health status, the chi-squared test was used for categorical variables. We used two sample t-tests when variables were normally distributed. We used the Mann-Whitney U test when variables were not normally distributed.
Partial correlation coefficient was used to clarify the association between nutritional intake (energy, carbohydrate, protein, water, calcium, phosphorus, potassium, total vitamin A, retinol only, and vitamin C) and BMD (total femur, femoral neck, lumbar spine, and whole body) at each site to control the variables (age, BMI, physical activities, and alcohol consumption). The statistical analysis was performed with SPSS 27.0 (IBM, Chicago, IL, USA).

Participant Characteristics
As shown in Table 1, a total of 4160 subjects aged 30-75 years were analysed in this study. The number of premenopausal women aged 30-39 years was 1515 (52.9%). The number of postmenopausal women aged 50-59 years was 583 (44.9%). The BMI was significantly higher in postmenopausal women than in premenopausal women (postmenopausal women median 23.6, premenopausal women median 22.5, respectively, p < 0.001). Most of the subjects answered that they did not do high intense (vigorous) physical activity (premenopausal women's n = 2431 (84.9%), postmenopausal women n = 1128 (87.0%), respectively) or that they did not do moderate intense physical activity (premenopausal women's n = 2475 (86.4%), postmenopausal women n = 1099 (84.7%), respectively). Walking for 30 min or more and 5 days a week or more comprised 38.5% in premenopausal women (n = 1103) and 44.9% in postmenopausal women (n = 583).

Nutrient Intakes
As shown in Table 1, the median energy intake of postmenopausal women (median: 1510.9 Kcal/day) was higher than those of premenopausal women (median: 1210.9 Kcal/day) (p < 0.001). The energy intakes of premenopausal and postmenopausal women were lower than the 2020 Korean energy requirement. For reference, the average estimated energy requirement for the 2020 dietary reference intakes for Koreans (KDRIs) [20] was 1900 Kcal/day for women aged 30-49 years, 1700 Kcal/day for women aged 50-64 years, 1600 Kcal/day for women aged 65-74 years, and 1500 Kcal/day for women aged over 75 years. The recommended carbohydrates intake for the 2020 KDRIs [20] was 130 g/day for Korean women aged 30-75 years. In this study, recommended intakes of carbohydrates were 274.0 g/day in premenopausal women and 284.0 g/day in postmenopausal women (p = 0.014). Premenopausal and postmenopausal women consumed in excess of the recommended carbohydrate amounts. In this study, recommended intakes of protein was 62.4 ± 0.54 g/day in premenopausal women and 47.4 g/day (median) in postmenopausal women (p < 0.001). These amounts were higher than the recommended protein intake for premenopausal women (50 g/day) aged 30-75 years. However, the protein intake for postmenopausal women was lower than the recommended protein intake (50 g/day for women aged 30-75 years).
Water intake refers to the water content in food. In this study, recommended intakes of water were 796.6 mL/day (median) in premenopausal women and 639.4 mL/day (median) in postmenopausal women (p < 0.001). The water intake amounts were lower than recommended water intake (1000 mL/day for women aged 30-49 years, 900 mL/day for women aged 50-74 years and 800 mL/day for women aged over 75 years).
In the 2020 KDRIs [21], retinol activity equivalents (RAEs) were used as the unit of total vitamin A, but in fourth and fifth KNHANES, the unit of the total vitamin A was used as the retinol equivalent (RE). Therefore, this study used the 2010 KDRIs for only the total vitamin A among nutrients. Premenopausal women 581.7 µgRE/day (median) and postmenopausal women 491.7 µgRE/day (median) were found to be lower than the recommended total vitamin A intake (650 µgRE/day for women aged 30-49 years and 600 µgRE/day for women aged 50-75 years) (p < 0.001). Vitamin C intakes were 82.0 mg/day (median) for premenopausal women and 77.3 mg/day (median) for postmenopausal women. The recommended vitamin C intake for the 2020 KDRIs was 100 mg/day for Korean women aged 30-75 years. In this study, vitamin C intakes were lower than recommended vitamin C intakes [21].
Calcium intakes were 473.3 ± 5.8 mg/day for premenopausal women and 424.6 ± 8.3 mg/day for postmenopausal women. The calcium intake was lower than recommended calcium intake (550 mg/day for women aged 30-49 years and 600 mg/day for women aged 50-75 years). Phosphorus intakes were found in premenopausal women (median: 1002.4 mg/day) and postmenopausal women (median 894.6 mg/day) (p < 0.001). These intakes were higher than the recommended phosphorus intakes for women (700 mg/day) aged 30-75 years. The sufficient potassium intakes were 2847.2 ± 25.7 mg/day in premenopausal women and 2389.5 mg/day (median) in postmenopausal women (p < 0.001). Sufficient potassium intake for the 2020 KDRIs was 3500 mg/day for Korean women aged 30-75 years [22]. In this study, potassium intake was lower than sufficient potassium intake (Table 1).

Bone Health Status
The proportions of postmenopausal women with osteopenia at the total femur, femoral neck, and lumbar spine were 29.8%, 57.5%, and 45.0%, respectively. Moreover, 1.5%, 14.0%, and 27.8% of postmenopausal women had osteoporosis at the total femur, femoral neck, and lumbar spine, respectively. The proportions of premenopausal women with osteoporosis at the total femur, femoral neck, and lumbar spine were only 0.0%, 0.7%, and 0.8%, respectively ( Table 1). Table 2 presents variable selection with Cronbach's alpha. Nineteen variables were analysed with the reliability coefficient of Cronbach's alpha, and were 0.755 for premenopausal women and 0.749 for postmenopausal women.  Table 3 presents the model fit evaluation results for BMDs in premenopausal and postmenopausal women. The model fit of premenopausal women was X 2 = 1193.239 (df = 110; p < 0.001), which indicated the statistical significance of the X 2 /df. The model fitted the data (TLI = 0.949; CFI = 0.967; RMSEA = 0.059). Moreover, the model fit of postmenopausal women was X 2 = 1123.090 (df = 124; p < 0.001), which indicated the statistical significance of the X 2 /df. The model fitted the data (TLI = 0.924; CFI = 0.945; RMSEA = 0.079).  Table 4 presents the standard regression weights of independent variables. The effects between the variables were compared with the absolute value if a value ranged from −1 to 1.

Goodness of Fit Structural Equation Models and Variable Weights
In premenopausal women, the most influential degree of physical activities was in the order of high intense physical activity (estimate = 0.501), moderate intense activity (estimate = 0.483), and regular walking (estimate = 0.323).
The most influential degree of energy, carbohydrate, and protein (E.C.P) was in the order of energy (estimate = 1.099), carbohydrate (estimate = 0.795), and protein (estimate = 0.727). The most influential degree of minerals was in the order of phosphorus (estimate = 0.990), potassium (estimate = 0.807), and calcium (estimate = 0.732). The most influential degree of vitamins was in the order of vitamin C (estimate = 0.503), total vitamin A (estimate = 0.390), and retinol only (estimate = 0.258). In postmenopausal women, the most influential degree of physical activities was in the order of moderate intense physical activity (estimate = 0.645), regular walking (estimate = 0.258), and high moderate intense activity (estimate = 0.218).
The most influential degree of energy, carbohydrates, and protein (E.C.P.) was in the order of protein (estimate = 0.955), energy (estimate = 0.865), and carbohydrate (estimate = 0.606). The most influential degree of minerals was in the order of potassium (estimate = 0.907), phosphorus (estimate = 0.787), and calcium (estimate = 0.563). The most influential degree of vitamins was in the order of vitamin C (estimate = 0.896), vitamin A (estimate = 0.490), and retinol (estimate = 0.088). Figure 2 presents results of the direct and total pathways of variables between each component and BMD in premenopausal women using a SEM. Table 5 presents a summary of the direct and total pathways among major variables in premenopausal women based on findings from Figure 2. A direct association between minerals (potassium, calcium, and phosphorus) and BMD (total femur, femoral neck, lumbar spine, and whole body) was observed (p = 0.045). The direct association between vitamins (total vitamin A, retinol only and vitamin C) and BMD was observed (p = 0.016). The direct association between E.C.P. and BMD was also observed (p = 0.013). Moreover, the direct association between water intake and BMD was observed (p = 0.013). There were total effect associations between age and BMD (p = 0.002). It was observed that age and BMD not only had a direct effect, but also a total effect (p < 0.001 and p = 0.002, respectively). Moreover, there was a total effect of BMI on BMD (p = 0.002). It was observed that BMI and BMD not only had a direct effect, but also a total effect (p < 0.001 and p = 0.002, respectively). and vitamin C) and BMD was observed (p = 0.016). The direct association between E.C.P. and BMD was also observed (p = 0.013). Moreover, the direct association between water intake and BMD was observed (p = 0.013). There were total effect associations between age and BMD (p = 0.002). It was observed that age and BMD not only had a direct effect, but also a total effect (p < 0.001 and p = 0.002, respectively). Moreover, there was a total effect of BMI on BMD (p = 0.002). It was observed that BMI and BMD not only had a direct effect, but also a total effect (p < 0.001 and p = 0.002, respectively).

Analysis of Mediating Pathways among Component in Premenopausal Women
HE_BMI, body mass index; BMD, bone mineral density; C.R., critical ratio; E.C.P., energy, carbohydrates, and protein; β, standard regression coefficient; S.E., standard error; N_WATER, water.  Table 6 presents a summary of the mediating effect among major variables in premenopausal women based on findings from Figure 3.

Analysis of Partial Correlation Coefficients between Bone Mineral Density and Nutrient Intake in Premenopausal Women
In the premenopausal women, minerals, vitamins, and E.C.P. had a direct effect on BMD. Moreover, the mediating effect of vitamins and E.C.P. on the association between age and BMD was statistically significant. Table 9 presents partial correlation coefficients to clarify the correlation between nutrient intake and BMD at each site. Total femur BMD was positively associated with carbohydrate after adjustment for age, BMI, physical activity, and alcohol consumption. In addition, total femur BMD was positively associated with potassium after adjustment for age, BMI, physical activity and alcohol consumption. Femoral neck BMD was positively associated with carbohydrate and energy after adjustment for age, BMI, physical activity, and alcohol consumption. Femoral neck BMD was positively associated with minerals (potassium and calcium) after adjustment for age, BMI, physical activity, and alcohol consumption. Lumbar spine BMD was not statistically significant in E.C.P., minerals (potassium, calcium, and phosphorus), vitamins (total vitamin A, retinol only, and vitamin C) and water after adjustment for age. In addition, whole body BMD was not statistically significant in E.C.P., minerals (potassium, calcium, and phosphorus), vitamins (total vitamin A, retinol only, and vitamin C), and water after adjustment for age. Table 9. Partial correlation coefficients between nutrient intake and bone mineral density in premenopausal women.

Analysis of Partial Correlation Coefficients between Bone Mineral Density and Nutrient Intake in Postmenopausal Women
In postmenopausal women, minerals had a direct effect on BMD in a SEM. Table 10 presents an analysis of partial correlation coefficients to clarify correlation between nutrient intake and BMD at each site in postmenopausal women. Total femur BMD was positively associated with minerals (potassium and calcium) after adjustment for age, BMI, physical activity, and alcohol consumption. In addition, total femur BMD was positively associated with water for age, BMI, physical activity, and alcohol consumption. Femoral neck BMD was positively associated with minerals (potassium, calcium, and phosphorus) after adjustment for age, BMI, physical activity, and alcohol consumption. Each of intake of total vitamin A, vitamin C, and water was positively associated with femoral neck BMD. Lumbar spine BMD was positively associated with calcium after adjustment for age. Lumbar spine BMD was positively associated with water after adjustment for age. Whole body BMD was positively associated with calcium after adjustment for age. In addition, whole body BMD was positively associated with water after adjustment for age.

Discussion
This study examined the major determinants of BMD investigating total, direct, and mediating effects of nutrient intake, physical activity, age, and BMI, on BMD in Korean premenopausal and postmenopausal women, aged 30-75 years, using a SEM based on the fourth and fifth KNHANES 2008-2011. This present study found that age, BMI, E.C.P., minerals (potassium, calcium, and phosphorus), vitamins (total vitamin A, retinol only, and vitamin C) and water had direct effects on BMD in premenopausal women. This study also found that energy, carbohydrates, and protein mediated in the relationship between age and BMD, and in relationship between BMI and BMD in premenopausal women. Fung et al., 2017 [23], observed no association between higher protein and fracture risk in postmenopausal women [23], while Rapuri et al., 2003 [24] observed a positive association between 3-year dietary protein intake as a percentage of energy and BMD in postmenopausal women aged 65-77 with calcium intakes > 408 mg/day [24].
Consistent with our results, a cross-sectional study of 994 healthy premenopausal women aged 45-49 years showed an increase in lumbar spine BMD after the highest consumption of zinc, magnesium, potassium, vitamin C, and fibre compared with the lowest consumption [25]. Premenopausal women who consumed higher amounts of fruit and milk in early adulthood had higher BMD compared to premenopausal women who consumed lower amounts of fruit and milk [25]. Vitamins mediated in the relationship between age and BMD.
Vitamin C is known to promote collagen matrix formation and osteoblast activity and inhibit osteoclast activity [26,27]. A meta-analysis showed higher dietary vitamin C intake was associated with increased BMD at femoral neck and lumbar spine [28]. On the other hand, other studies showed dietary vitamin C intake was not associated with BMD at the femoral neck and lumbar spine [29][30][31].
In the present study, we found a direct effect of vitamins (total vitamin A, retinol only, and vitamin C) on BMD only in premenopausal women, not in postmenopausal women. Partially consistent with this finding, the Iowa Women's Health Study and the Women's Health Initiative Observational Study showed little or no association between vitamin A or retinol intake and fracture risk in postmenopausal women [32,33]. On the other hand, several studies showed that higher vitamin A or retinol intake was positively associated with lower BMD fracture [34][35][36]. A meta-analysis of cohort studies showed vitamin A or retinol intake appeared to reduce total fracture risk, whereas hip fracture risk was elevated with vitamin A or retinol intake, indicating different influences on total fracture and hip fracture [37].
We found that mineral intake showed a direct effect on BMD in postmenopausal women. Consistent with our finding, Kong et al., 2017 [38] reported the highest potassium consumption favourably affected BMD at lumbar, total hip, and femur neck compared with the lowest potassium consumption in 4052 Korean postmenopausal women [38]. Studies of in vitro showed that acidosis promoted osteoclast activity and bone resorption [39][40][41]. Dietary potassium can play a key role in acid-base balance as an alkaline source, leading to calcium loss prevention from bone [42][43][44]. Potassium is rich in vegetables and fruits, dairy products, and nuts. Liu et al., 2015 [45], reported 6.4% and 4.8% BMD improvement for the whole body and the femoral neck with elevated daily consumption of 100 g/1000 kcal fruits in Chinese women aged over 60 years, indicating a 14.4% reduction in fracture in women [45]. A meta-analysis of cohort studies and randomised controlled trials showed reduced fracture risk with elevated consumption of more than 1 serving/day of fruits and vegetables in adults aged over 50 years [46]. Moreover, a cohort prospective study of Europe and the USA in adults aged over 60 years showed that fruit and vegetable consumption ranging from three to five servings/day lowered hip fracture risk by 39% compared with less than one serving/day of fruits and vegetables [47].
In this study, water showed direct effects on BMD in premenopausal women. Consistently, Vannucci et al., 2018 [48], reviewed the impact of mineral water high in calcium on bone health. They suggested drinking water high in calcium could be a good way to improve calcium bioavailability, leading to beneficial influence on bone health [48].
This present study found BMI had direct effects on BMD in premenopausal women. A study showed weight loss did not affect bone loss in overweight premenopausal women at either 1 g or 1.8 g/d of calcium intake [49].
The present study of models indicated a high goodness of fit with a TLI of 0.949, a CFI of 0.967, and a RMSEA of 0.059 for premenopausal and postmenopausal women, with a TLI of 0.924, a CFI of 0.945, and a RMSEA of 0.079 for postmenopausal women. This stable and appropriate model fit strongly supported our research hypotheses that nutrient intake, physical activity, age, and BMI would exert total, direct, and mediating effects on BMD in Korean premenopausal and postmenopausal women aged between 30 and 75 years. In summary of our findings, a direct effect of minerals (potassium, calcium, and phosphorus) on BMD (total femur, femoral neck, lumbar spine, and whole body) was observed in premenopausal and postmenopausal women. A direct effect and a total effect of age and BMI on BMD was observed in premenopausal and postmenopausal women. In premenopausal women, vitamin intake (total vitamin A, retinol only, and vitamin C), water intake, and E.C.P. intake showed a direct effect on BMD. E.C.P. intake and vitamin intake exerted a mediating effect on the association between age and BMD. E.C.P. intake showed a mediating effect on the association between BMI and BMD. Our findings support the results of previous studies [25,38,48], which showed the favourable influence of minerals on bone health. Moreover, our findings indicate that age, BMI, and mineral intake, which are major factors, can interact with each other, leading to influence on bone health. The findings of this study can aid the development of nutrition education and lifestyle modification strategies for the prevention of osteoporosis and fractures in aging women.
This study has some strengths. Thus far, no other study exist that have examined the determinants of BMD, with a SEM approach, in Korean women. The advantage of SEM allows us to powerfully assess measurement errors compared to a regression analysis. Examination of latent (unobserved) variables are enabled through observed variables [17].
This present study was the first study to investigate the effects of factors (nutrients, physical activity, BMI, and age) on BMD using the SEM approach in Korean women. The large sample size of the KNHANES was enough to determine the contributors to BMD with the model's goodness-of-fit. Determinants of BMD were specifically examined by dividing premenopausal and postmenopausal women.
The limitation needs to be acknowledged. This present study was analysed based on a cross-sectional study of the KNHANES, limiting cause-effect association. It was hard to clarify the extent to which determinants affected BMD. In this study, the observed variables of the SEM were connected with endogenous latent variables (e.g., BMD) and exogenous latent variables (e.g., physical activity, E.C.P., minerals (potassium, calcium, and phosphorus), and vitamins (total vitamin A, retinol only and vitamin C), water, age, and BMI), which is hard to fully identify the causation of each observed variables.
Bias for non-response or measurement or information was not ruled out because this study was based on a cross-sectional study. The 24-h dietary recall for nutrient intake assessment might not be representative of general dietary habits of an individual. Residual confounding could be a limitation. However, a SEM analysis considers the measurement error of the measured variable and the perturbation error of the latent variable, so that the reflected value can be analysed. In this aspect, a SEM has the advantage of analysing values, considering errors compared with a logistic regression analysis.
Since this study used cross-sectional survey data, there is a limit on explaining the relationship between BMD and variables. Longitudinal and intervention studies, including the variables covered in this study, should be conducted in the future.

Conclusions
In conclusion, the present study showed that age, BMI, mineral intake (potassium, calcium, and phosphorus) were major determinants of BMD in Korean premenopausal and postmenopausal women. This result may have critical implications for bone health in Korean women. Further studies are warranted to verify the results.