The role of social brand engagement on brand equity and purchase intention for fashion brands

Abstract This study aims to determine how social brand engagement via social media platforms will have an impact on brand equity and purchase intention towards brands in the field of fashion in the Vietnamese market. The study was carried out a quantitative method, primary data was collected on 637 Vietnamese people aged 18–50 years old. Research results have recognized the direct positive impact of social brand engagement on brand equity and indirect effect on purchase intention. In addition, as a moderator variable, social brand engagement has a positive effect on brand awareness and purchase intention relationship, but this variable is not statistically significant when considering its impact on brand association and purchase intention relationship. These findings contribute to providing information confirming the role of social brand engagement in communication, making a great contribution to brand awareness, but not enough evidence to show the direct impact of social brand engagement on purchase intention. In addition, this study has also established four target customer segments by age in the field of fashion business in Vietnam market with different social brand engagement, perceived brand equity, as well as the intention to purchase different brands are significant. The results help to provide information to identify the target markets for the fashion industry in Vietnam, so that brands have strategic orientations in marketing, selection of target markets, as well as communication strategies and targeting the authentic of social media marketing programs.


Introduction
In recent years, Vietnam's fashion market has made great progress in both quantity and quality. There have been a series of fashion brands born to provide products and services with different segments from affordable to high-end to meet the fashion shopping needs of customers. Besides, the Vietnamese fashion market has recorded the landing of fashion brands in the world and is increasingly dominant such as H&M, Zara, Uniqlo and so on. There are currently more than 200 foreign fashion brands from mid-range to high-end products that have official stores in Vietnam. This "landing" has made the domestic fashion industry, which only has a small market share, narrower now. This means that the competition between fashion brands is getting more and more fierce. Besides, although fashion market revenue in 2020 decreased by more than 10% compared to 2019 under the impact of the COVID-19 epidemic. However, this has made media shopping channels, online shopping receive outstanding growth when consumers begin to have shopping habits and interact with brands through social media platforms, namely, online fashion shopping channels such as Lazada, Sendo, Tiki, Facebook and so on are increasing. By early 2022, the world's population has reached 7.91 billion people, of which, global social network users are 4.62 billion people, accounting for 58.4%, showing that social networks, where more than 58% of the world's population is concentrated, are an ideal environment for brands to implement communication strategies, through social networks, users post, share, interact with each other and engage with the brand, which will create a widespread effect in the community of users and customers. In the inevitable development trend, to implement digital communication, especially via social networks, brands are trying to maximize communication effectiveness, increase brand awareness, brand association and purchase intentions towards the brand. So, the social network platform is a space, a digital platform, that brands have been investing in, implementing communication programs to communicate, attract customers, build and develop equity brand, as well as driving consumer intention.
The studies have been conducted to evaluate the impact of social media marketing on brand equity, brand authenticity and purchase intention (Chahal & Rani, 2017;Chahal et al., 2020;Filo et al., 2015;Mangold & David, 2009). In particular, many studies have focused on communication marketing content, interaction, and brand engagement via social networks as important factors affecting, are the main components in many research models performed. Social media is an interactive platform for customers to interact and engage with others and brands during multiple stages of the consumption process (Chahal et al., 2020;Filo et al., 2015). The ways that information is delivered and used in customer-brand interactions and engagement activities in this media are essential to understand clearly the concept of social media brand engagement (Chahal & Rani, 2017;Mangold & David, 2009). Social brand engagement is considered as a preferred brand performance indicator and an increasingly important strategy by brand. It contributes to brand communication, increased interaction, and increased experience for the brand. It also contributes to increase brand equity and purchase intention of customers. Therefore, brands need to have active communication strategies and activities via social sites to increase interaction, maximize brand engagement, thereby increasing brand equity and purchase intention with brands via social networking platforms.
The studies have mentioned the positive impact of brand authenticity, brand trust, relationship quality, brand equity, etc., on purchase intention of customers (Morhart et al., 2015;Fritz et al., 2017;Lee & Chung, 2019;Cinelli & LeBoeuf, 2019;Stuppy et al., 2019;and Jing;Yang et al., 2021). As many previous studies that have identified a positive correlation of social brand engagement to purchase intention (Kim et al., 2008;Dehghani & Tumer, 2015;Aji et al., 2020;Algesheimer et al., 2010). Most of the results show an indirect impact of social brand engagement on purchase intention through brand equity, brand authenticity or brand loyalty. On that basis, this study aims to inherit the previous studies, to determine the correlation of social brand engagement with brand equity and purchase intention. In addition, this study also aims to analyze the role of social brand engagement as a moderator factor effect on brand equity and purchase intention relationship, thereby fully assessing the role of social brand engagement on the brand equity and purchase intention of customers in the fashion business in Vietnam market has not been studied by many studies related to this field.

Social brand engagement
Social brand engagement is the feelings and emotional attachment of customers to a brand via social sites. Social brand engagement is considered a co-creative customer experience in which a consumer interacts with a focus agent/object (e.g., a brand), which then reflects the nature of the interacting brand relationships specific to consumers (Hollebeek et al., 2014). Social brand engagement acts as a channel through which customers develop passion and attachment to the brand, building commitment to the brand relationship on social media. When customers are involved, their role in brand or product development becomes prominent (Hoyer et al., 2010). Collectively, brand attachment can be seen as a multidimensional psychological state, the consequence of focusing on interacting with a brand in addition to purchasing, stemming from motivation. It includes aspects of emotional, cognitive, and social engagement. Social media facilitates brand engagement, it allows participants to interact socially with other brands and consumers without boundaries. Drawing from Kozinets (2014) and Laroche et al. (2012), brand engagement on social sites platforms can be defined that the connection, creation, and communication of the brand's story between the firm and consumers (both existing and prospects) using the brand or brand-related language, images, and meanings via the firm's social networking site. This allows them to share their experience with the brand, integrate it into their expression, and to some extent represent the brand as part of themselves (Hammedi et al., 2015). When customers actively engage with a brand in a social-based context, they not only consider any information about the brand, but also recommend the brand to others via social sites, increase brand equity and have a higher purchase intention.
Research by Dwivedi & McDonald (2018)) confirmed a positive correlation between social media communication marketing and brand equity or brand authenticity. Sohaib et al. (2022) showed the role of social media marketing activities on customer response. The research results recognize the direct impact of social media marketing activities on relationship quality and the mediating role that positively affects the relationship between relationship quality and customer repurchase intention. Research by Jing Yang et al. (2021) also showed that advertising model genuineness and trustworthiness on Instagram has a direct positive impact on customer loyalty and behavioral intention. In which, the model trustworthiness has a direct and positive impact on both brand authenticity, brand attitude and customer behavioral intention. Model genuineness has a direct impact on brand authenticity, brand attitude and an indirect positive impact on customer behavioral intention through brand authenticity and brand attitude. Thanasi-Boçe et al. (2022) confirmed that the relationship between fashion brand attachment and social brand engagement was significantly moderated by social media usage. But there were not significant moderating effects of social media usage on the relationship between fashion brand attachment and purchase intention. Building on previous studies, this study aims to explore the impact of social brand engagement on brand equity and purchase intention. In addition, this study hopes to confirm the moderating impact of social brand engagement on the relationship between brand equity and purchase intention for fashion brands in Vietnam. Thereby to evaluate the role of social brand engagement to brand equity and purchase intention in many different ways, both in terms of direct and indirect impact on the brand equity, purchase intention, and brand equity and purchase intention relationship.

Brand equity
Brand equity in customer evaluation is the difference in product value between brands (Yoo et al., 2000). Brand equity is the value of a brand from the customer's perception, which is shaped by components such as brand awareness, quality perception, and brand image (Aaker, 2014). Brand equity is a social cultural phenomenon that goes beyond a mere product name; it is a symbolic meaning that brands seek (Keller, 2013.). It can be considered as one of the most core pieces of intangible assets a company has, and this can provide a competitive advantage. Brand equity is defined that consumers' different response between a local brand and an unbranded product when both have the same level of marketing stimuli and product attributes. Brand equity can be operated as a propensity to choose branded products over similar unbranded products, customerbased branding consists of four components: loyalty, brand awareness, perceived quality, and brand association (Yoo et al., 2000). The previous studies examined the factors that impact brand equity, which were brand awareness, brand association, perceived quality, brand loyalty (Faircloth et al., 2001;Majid et al., 2016;Sasmita & Mohd Suki, 2015;Singh & Pattanayak, 2016;Tolba, 2011). Brand equity is associated with situations in which customers hold favorable, strong, and unique brand association in memory. Brand equity is inculcated in the consumer's memory as a unique value that differentiates it from other brands by combining different brand attributes. In this study, we focus on brand equity including brand awareness and brand association from the perspective of individual consumers.

Brand awareness
Brand awareness is related to the strength of the brand button or memory footprint, and it is an important component of brand equity. According to Seo and Woo Park (2018), brand awareness refers to the ability of consumers to recognize a brand in a certain situation or to be able to remember the brand. Brand awareness has a significant impact on consumer decision-making, with consumers often using it as a decision-making tool that benefits brand equity management based on customers (Chung et al., 2013;Huang & Sarigöllü, 2012;Suki, 2013). Indeed, the presence of brand awareness suggests that consumers know the brand name and this increases the likelihood that the brand is included in the list of potential candidates, and ultimately, that brand is chosen highly (Keller, 1993). When the brand engagement of customers is high, they tend to care more about the brand, and often search, discuss, and share about the brand with other customers. From there, the impact on brand awareness is higher. A previous study found that in the context of online social media, brand engagement significantly effects brand awareness (Hutter et al., 2013). In other words, increasing levels of brand engagement will encourage the delivery and sharing of brand-related information amongst the consumers. It increases the interaction between consumers and brands (Brodie et al., 2013;Richard et al., 2011), by attracting the customer's attention. It strengthens customer's ability to recall the brands in their minds, thereby increasing the brand awareness (Keller, 2013;Langaro et al., 2018).
Brand awareness is essential to indicate and determine if the brand exists in the mind of the consumer, it will make the brand be included in any set of consumer considerations, helping consumer perceive brands in product categories and this strongly influences them when making purchases intentions (Percy & Rossiter, 1992). For products or services of a new brand, consumers are always hesitant to go to purchase, they will have to search for information, and research about that new product, service, or brand. Therefore, consumers have favoritism for products or services of familiar brands in their perception over those of new brands (Hutter et al., 2013), this helps them reduce their purchase intention effort by relying on the research clues they have. Brand awareness and consumers' purchase intention have a direct relationship, consumers intend to buy the brands they find more familiar, and hence the perception of the brand has a positive effect on consumers' brand choice leading to purchase intention. Radder and Huang (2008) emphasize the importance of brand awareness in influencing purchase intention in highly competitive markets. Thereby, it can be seen that brand awareness is the first step in developing brand preferences and moving consumers closer to purchase intention (Ross & Harradine, 2004). Keller (2013) reveals that brand association is the other informational nodes linked to the brand node in memory and contain the meaning of the brand for consumers. Association comes in all forms and may reflect characteristics of the product or aspects independent of the product. Brand association would help consumers search and deal with information (Xiao & Hawley, 2009), moreover, it would provide consumers with a purchasing reason, because most brand association is related to brand attributes, the target consumer market, and the benefits which consumers want, from that they can form the foundation of consumers' purchasing intention (Wright et al., 2007). The brand association has a strong impact on consumers because the brand association is associated with their experience (Aaker, 2014). According to (Hutter et al., 2013), brand engagement of the customers enhances their brand knowledge, which in turn builds strong, favorable, and unique brand associations. The brand engagement creates associated with a particular brand (Brodie et al., 2013;Dwivedi, 2015). There has been previous research by (Bonhomme et al., 2010) that asserts the positive relationship between brand engagement and brand associations. Besides, consumers are increasingly interacting and having real, meaningful interactions with the brand through their own experiences instead of random interactions (Hollebeek, 2011), thus it affects their purchase decisions, and develops a deep relationship with that brand (Dwivedi, 2015). The brand engagement on social media also reflects a consumer's need to interact with other consumers who have similar needs. This interaction often enhances a sense of belonging (Eisenbeiss et al., 2012), and brand association. Can be seen that brand engagement as an incentive for consumers' brand association. Therefore, in this study, we believe that brand engagement leads to more brand associations due to positive consumer perceptions, emotions, and actions.
Brand association has a significant impact on the purchase intention of the consumer (French & Smith, 2013). Through social media marketing, brand association increases the probability of the brand being included in the consumer's set of purchase considerations. Brand associations create value in different ways, such as helping to process and find information, helping consumers get information, seeing brand differentiation and brand positioning, and create positive brand impressions (Dew & Suk Kwon, 2010;Jyothsna et al., 2016). Through those positive impressions can lead consumers to have that brand as a reference and it can lead to higher purchase intention above all else. In addition, brand association builds a positive relationship that will leads to repeated consumer attitudes and behaviors in the future, according to Aaker, 2014), which is more effective than depending on product prominence. Paço et al. (2015) suggest that some specific positive aspects of brand association, such as utility and influence lead to an impact on consumer purchase intention. Many other studies have mentioned the positive impact of brand authenticity, brand trust, relationship quality, brand equity, etc., on purchase intention of customers (Morhart et al., 2015;Fritz et al., 2017;Lee & Chung, 2019;Cinelli & LeBoeuf, 2019;Stuppy et al., 2019;and Jing;Yang et al., 2021).

Purchase intention
Purchase intention is the motivational factor that influences the behavior of customers (Ajzen, 1991). They are indication of how hard people are willing to try how much of an effort they are planning to exert and performing a behavior. In the context of this study, purchase intention can be defined as the probability of users and willingness to buy a suggested product after using social networking sites. In addition, purchase intention is the possibility that consumers will plan or be willing to purchase a certain products or services in the future (Wu et al., 2011). It is considered as a step which is related to actual purchasing behavior or as an intermediate antecedent of consumer behavior (Magistris et al., 2008). Past studies have shown that when purchase intention increases, the chances of a purchase will increase. Determining purchase intention through the future behavior of customers Based on their attitudes (Kim & Eunju, 2012), such as personal preferences towards others and compliance with expectations, and unpredictable situations that consumers may change their purchasing intentions due to situational factors (Zhung & Bong, 2017). If a consumer intends to purchase a product or service, then a positive interaction with the brand will promote that purchase (Martins et al., 2019). Purchase intention develops from consumers' perceptions of products/services from peers or social media signals (Wu et al., 2011).
When people buy a product, they look for relevant information based on their own experiences and the external environment. After collecting data, consumers start to evaluate, weigh and compare, ending with purchasing behavior (Chen and Lin, 2019). Beside that social media marketing is an important factor in arousing the purchase intention of consumers, it improves customers' trust in the brand so they are willing to buy the brand increase (Aji et al, 2020).
Consumers tend to shop online with an increasing commitment to a brand (Kim et al., 2008), they engage in interactions with the brand stemming from their experiences or from other consumers, these people will influence their consumption behavior. Surprisingly, consumer brand engagement not only increases overall brand engagement, but can also help increase brand sales. The likelihood that customers intend to purchase services and goods is better if their buying experience and brand engagement is positive. Consumer purchase intention is highly dependent on the value of the product and the recommendations that other consumers have shared on social media platforms (Dehghani & Tumer, 2015). Through social media, consumers can directly interact and share their buying experiences, and it can make them feel more confident when making purchasing decisions (Aji et al., 2020). Indeed, brand engagement facilitates customers to transition through a continuous trust-attitude-behavior cycle (Vivek et al., 2012), and that influences the purchase intention of customers towards the brand. Stronger brand engagement can lead to strong relationships in the form of memberships, allowances, discounts, and other incentives for consumers, which in turn lead to the intention to purchase a brand specifically in the future (Algesheimer et al., 2010).
Based on the reviewed theory, the research model in Figure 1 and hypothesis are proposed: The research hypotheses are put forward: H1: Brand engagement has a direct impact on brand awareness.

Measurement scales
The social brand engagement scale is based on the theory of Hammedi et al. (2015), and Laroche et al. (2012), this scale includes variables: following the brand, participate in interactive activities with the brand, share experience using the brand, and take the side of the brand. The scale of brand awareness is based on the Seo and Woo Park (2018), Aaker, 2014) through the following factors: brand awareness, aware and remember the characteristics of the brand (such as colors, logos, images, slogan, etc.,), and have special memories of the brand. The research scale on the brand association through Xiao and Hawley (2009) and Wright et al. (2007): the brand has a very unique brand image compared to competing brands, the brand has better product attributes than other brands, and the quality of the brand brings satisfaction to customers. Based on Sofia and Martins (2018), Zhung and Bong (2017), and Wu et al. (2011) purchase intention scale includes a consideration and comparison between brands, I will give preference to brand; I will buy the products of brand; and become a customer of the brand in the future. On the basis of the scales for the components in the proposed model, the 5-level Likert scales, from 1: very low to 5: very high, to measure the evaluation of the research sample for the components in the model. Research models. The questionnaire consists of 3 parts: (1) Respondent information; (2) Interactive behavior on social networks and online consumption and (3) Evaluation of all items in the model for all components. The language used in the questionnaire is Vietnamese, the data collected from the questionnaire is translated into English.

Research sample and data collection method
The observed variables were developed based on the literature review and changed to suit the research context of the topic. Each observed variable is measured on a five-point Likert scale from 1 (strongly disagree") to 5 ("strongly agree"). In order to fully capture the data and information, the observed variables are tested and measured accurately by different data processing methods. The sample size was 637 respondents across Vietnam aged 18 to 50 years old. The sample was selected by nonprobability method, the research team through social networking platforms, sent the link of the questionnaire designed on Google form to invite Vietnamese people aged 18 and over, who have active brand engagement experience while buying products online to participate, provide data according based on structured questionnaires are designed. Response samples were checked for completeness and reliability in order to be selected for analysis.

Analytical methods
Statistical Package for the Social Sciences (SPSS) 26 and Analysis of Moment Structures (AMOS) were used to analyze the data. The methods used are descriptive statistics to describe the research sample, besides that, the research used Cronbach Alpha method to test the reliability of the scale in the theoretical model, including: Social brand engagement (four observed variables); Brand awareness (four observed variables); Brand association (three observed variables); and purchase intention (three observed variables). Structural equation model analysis to evaluate the brand engagement, brand awareness, and brand association impact to purchase intention. Analysis of variance (ANOVA) method to test the difference in mean of the variables in the model.

Result and discussion
The study was conducted in 637 Vietnamese people aged between 18-50 years old, in which the sample group aged 18-22 years old accounted for 43.49%, the sample group aged 23-30 years old was 26.53%. The sample group aged 31-40 years old was 23.23% and the rest was in the age group 41-50 years old (6.75%). The sample structure is by gender, in which, the participants also provide information as male: 42.70% and female is 57.30% (Table 1).
In the research sample structure of the occupation, the sample group is students, accounting for 44.74%, followed by private enterprise employees (28.73%), freelance (13.34%), and the occupational group is civil servants and public employees (9.73%) and other occupations (3.45%). The

The reliability of the scales
The scale sets of the components in the model include: Brand engagement (including 4 observed variables: SBE1 → SBE4), brand awareness (BAW1 → BAW4), brand association (BAS1 → BAS3), and purchase intention (PI1 → PI3) was tested for reliability using Cronbach's Alpha method. The results are summarized in Table 2, recording the Cronbach's Alpha coefficient of all components from 0.75 to 0.84, they are all greater than 0.7 and the corrected item-total correlation coefficient of all observed variables is greater than 0.50, showing that the scale of all components in the model is reliable, meeting the analysis requirements.

The impact of brand engagement on social networks on perception of brand equity and purchase intention
To analyze the correlation between the components in the model, the study uses the linear structural analysis method, the results are summarized in Table 3, the correlations are not statistically significant with a confidence level of 99% will in turn be corrected, and removed from the model.
After removing the relationship between SBE and PI (P = 0.98 > 0.01), the linear structural analysis model was improved and the correlations between the components in the model were statistically significant with a degree of accuracy of 99% confidence, the results are summarized in Table 4. Table 3-4, this study rejects the hypothesis H3 (P = 0.98 > 0.01), meaning that social brand engagement (SBE) has not a direct positive impact on purchase intention. Meanwhile, hypotheses H1, H2, H4, and H5 are accepted (Table 5).

Based on the results of linear structural analysis summarized in
Accordingly, the statistically significant correlations with 99% confidence of the components in the model are present in Figure Figure 2, explained as follows:

Brand engagement and brand equity
Two components of brand equity, brand awareness and brand association, were included in the analysis of the correlation with brand engagement, respectively. The detailed results noted that the correlation between social brand engagement (SBE) and brand awareness (BAW) is statistically significant with 99% confidence (λ = 0.57***), so the H1 hypothesis is accepted, which means that brand engagement has a direct and positive impact on brand awareness. If brand engagement on social media increases by 1 unit, it will increase brand awareness by 0.57 units. This study is similar to previous studies such as Hutter et al. (2013), Brodie et al. (2013), Richard et al. (2011), Keller (2013, and Langaro et al. (2018). Brand engagement as much as possible will contribute positively, promote customer awareness of the brand as possible, thereby contributing to improving brand equity. Similarly, note the statistically significant correlation of social brand engagement (SBE) and brand association-BAS (λ = 0.92***), so hypothesis H2 is accepted, brand engagement via social sites has a direct positive impact on the brand association. If the social brand engagement increases by 1 unit, the consumer has an active association for the brand by 0.92 units. The results of this study show that brand engagement on a consumer's social media platform has a positive effect, contributing to increased brand association component of brand equity. The results of this study are similar to previous studies such as Hutter et al. (2013), Brodie et al. (2013), Dwivedi (2015), Bonhomme et al. (2010), and Hollebeek (2011), and Eisenbeiss et al. (2012. The research results have demonstrated the great usefulness of social media marketing, creating favorable conditions for customers to engage with brands, thereby directly contributing to brand equity. On the other hand, through social brand engagement, it also contributes to increase the brand experience for customers, thereby contributing to improving the information, brand value brought to customers through social media communication programs.

Social brand engagement and purchase intention
The results of the correlation analysis between social brand engagement and purchase intention in Table 4 recorded λ = −0.01, P = 0.98 > 0.05, rejecting the hypothesis H3, not enough statistical basis to record a positive direct correlation between social brand engagement and purchase intention. The results from this study reinforce previous studies by Sohaib et al. (2022), Jing Yang et al. (2021), andThanasi-Boçe et al. (2022). According to visual results from the SEM analysis in Figure Figure 2 showed that social brand engagement has a positive indirect effect on purchase intention through two components of brand equity, namely brand awareness (SBE-BAW-PI; SBE-BAW-BAS-PI) and brand association (SBE-BAS-PI). Thus, brand engagement also actively promotes an increase in purchase intention for the brand. This study is similar to studies such as Dehghani & Tumer (2015), Aji et al (2020), and Vivek et al. (2012), Algesheimer et al., 2010). Social brand engagement has a direct positive impact on brand equity, and indirect effect on purchase intention through the elements of brand equity that are brand awareness and brand association.

Social brand engagement moderates the brand equity and purchase intention relationship
Results of analyzing the impact of social brand engagement moderator variable on (1) brand awareness and purchase intention relationship; and (2) brand association and purchase intention relationship in Table 6 records the relationship between brand awareness and purchase intention was significant moderated by social brand engagement (λ = 0.08, P = 0.02 < 0.05), in which hypothesis H6 is accepted. That is, the more social brand engagement, the more direct positive impact on the relationship between brand awareness and purchase intention in the fashion field. The results of this study are similar to previous studies such as Thanasi-Boçe et al. (2022) and Sohaib et al. (2022). However, the results show that there were nonsignificant (95% confidence level) moderating impact of social brand engagement on the brand association and purchase intention relationship (λ = −0.03, P = 0.35 > 0.05), so hypothesis H7 is rejected. Accordingly, it shows that social brand engagement has not mediating effect on the brand association and purchase intention relationship.
From the research results, it shows the important role of social brand engagement, which has a direct positive impact on improving brand equity through communication programs on social sites, but has not yet recognized the role that has a direct impact on consumer behavior towards the brand. In addition, the results also show that social brand engagement has a moderating role that has a direct positive impact on the relationship of brand awareness and purchase intention.

Brand equity and purchase intention
If customers aware well about the brand will have a positive impact on a purchase intention (λ = 0.40***), hypothesis H4 is accepted, meaning that brand awareness has a direct positive impact on a purchase intention. According to the results from this study, when the customer's brand awareness increases by 1 unit, it will promote an increase in the purchase intention of the brand by 0.40 units. This study is similar to the research results of Percy and Rossiter (1992), Hutter et al. (2013), Radder and Huang (2008), and Ross and Harradine (2004). The research results have confirmed the position and importance of brand awareness to a purchase intention, especially in the fashion field, the competition among brands is great, brands have high awareness of customers, then the brand will have the opportunity to increase the purchase intention of the customer, contributing to better sales. The research results also noted a direct positive correlation of brand association and purchase intention (λ = 0.52***), hypothesis H5 is accepted, when consumers perceive brand association increased by 1 unit, it will have a positive impact of adding 0.52 units to a purchase intention. This positive correlation coincides with previous studies such as Dew and Suk Kwon (2010), Aaker, 2014), French and Smith (2013), Paço et al. (2015), and Jyothsna et al. (2016). Customers who have good awareness of the brand will have a great impact on a purchase intention and a repeat purchase intention. This study provides important information for fashion brands, is a product that customers have a very high frequency of acquisition, if great brand awareness increases, it will help the brand get a huge number of loyal customers, helping the brand development very well over time.
Three components in the model, including social brand engagement, brand awareness and brand association explain 69% of the variation of a purchase intention, thereby demonstrating the correlation of cohesion and mutual promotion between social brand engagement → brand equity (brand awareness and brand association) → purchase intention. From this result, it proves the importance of brand engagement via social sites, which has greatly contributed to building and developing brand equity and increasing purchase intention towards brands. This study continues to demonstrate the inevitable development trend to invest in digital media on social media platforms of brands, to build and develop brand equity, to increase customer purchase intention towards brands.
The aggregated results in Table 7 show that the average level of brand engagement on the social media platform of Vietnamese consumers is 3.93/5.0, at a relatively fair level, showing that Vietnamese consumers tend to engage with brands on social media are quite active. In particular, customer groups aged 18-30 years (mean: 4.06-4.17/5.0) has a higher brand engagement than groups aged 30 and over (mean: 3.33-3.87). The ANOVA test results in Table 6 show that the difference between the age group 31-40 years old has a statistically significant difference of 95% or more in the age groups (1) 18-30 years (Sig. = 0.00 < 0.01); (2) 23-30 years old (Sig. = 0.00 < 0.01) and (3) 41-50 years old (Sig = 0.02 < 0.05). The results from this research help fashion brands define a target audience of 18-30 years old, this is a group of customers with high brand engagement on social networks and also a group of potential customers who have high demand for fashion products. In addition, brands should also pay attention to customizing social media content to match age groups, to optimize social media results, should pay attention to the relevance of content for the group. Customers aged 31-40 years old, currently having less brand engagement on social media than other groups of customers. To stimulate and increase engagement on social networks, brands need to invest in content, methods and engagement management, to increase follow, interactive activities, share experience using brand and take the side of brand that is of the online community towards the brand, there will be great significance and benefits related to customer interaction and brand experience through social networks. Through brand engagement, there will be a positive impact on the perception of brand equity, the results recorded in Table 7 show that social media users rate brand equity at a fair level, of which, on average, brand awareness is 3.95/5.0 and brand association is 3.98/5.0. The group of customers from 31-40 years old who feel about BAW is 3.25/5.0, the difference is statistically significant with 99% confidence compared to the rest of the sample groups: (1) 18-22 years (mean = 4.21/5.0); (2) 23-30 years old (mean = 4.10/5.0) and (3) 41-50 years old (mean = 4.05/ 5.0). Similarly, with the BAS component, the group of customers aged 31-40 (mean = 3.32/5.0) recorded a difference in mean that was statistically significant with 99% confidence with the rest of the groups. Research sample, which are: (1) 18-22 years old (mean = 4.26/5.0); (2) 23-30 years old (mean = 4.12/5.0); and (3) 41-50 years old (mean = 3.91/5.0). Group of customers aged 18-22 years old, the average assessment for the BAS component was also significantly different with 95% confidence with customers aged 23-30 years old (Sig. = 0.04 < 0.05). Based on the results of this research, it shows that the group of young customers aged 30 years or younger, participating in social media a lot, interacting with brands on social media platforms is also very positive, thereby, evaluating brand equity is also more positive than 31-50 years old customer group. With the social media programs of fashion brands that need to focus on young people aged 18-30 years old customer group, this customer group will be an attractive, large-scale, high-demand customer segment, and it also has the large spread to other groups of customers. In addition, more research on media content is needed to be more relevant to the 31-40 years old customer group, who has a relatively low rate of brand equity (mean = 3.25-3.32).
For a purchase intention, the average estimated result was 3.98/5.0, of which the group of customers aged between 31-40 years old customer group (mean = 3.13/5.0) noted the difference in mean with statistical significance with 99% confidence with other customer groups, they are: (1) 18-22 years old (mean = 4.21/5.0); (2) 23-30 years old (mean = 4.01/5.0); and (3) 41-50 years old (mean = 4.0/5.0). Group of customers aged 18-22 years old, the average assessment for a purchase intention also significantly different with 99% confidence level compared to customers aged 23-30 years (Sig. = 0.04 < 0.05). Thus, there is a very high positive correlation between brand engagement-brand equity-purchase intention. If customers engage with the brand via social sites well, it will contribute to improving a more positive perception of the brand equity, thereby increasing a purchase intention for the brand. The results from this research have confirmed the importance of social media in brand communication. The important goal to achieve is to attract and increase brand engagement. If customer engagement with the brand is good, it will contribute positively to build and improve the brand equity, thereby, increase a purchase intention for fashion brands in the Vietnamese market.

Theoretical contributions
The results of this research study provide some theoretical contributions. First, to expand the research area for social brand engagement, that is to study the impact of social brand engagement on consumer intention, which not many studies have done recently (Sohaib et al., 2022;Yang et al., 2021;Thanasi-Boçe et al., 2022), especially in the Vietnamese market, there have not been any direct studies conducted in the fashion industry, most of the previous studies focused on evaluating the correlation between brand engagement and brand equity or brand authenticity (Hoyer et al., 2010;Dwivedi, 2015). Second, this study confirmed that the link of the relationship chain is social brand engagement-brand equity-purchase intention. In which, social brand engagement (brand communication results on social networks) effects brand equity (including brand awareness and brand association) and purchase intention in the fashion industry in Vietnam, which has not been seen through a literature review. Previous studies mostly focused on how social media marketing activities or social media marketing content effects brand equity, brand authenticity and, or purchase intention (Dehghani & Tumer, 2015;Kim et al., 2008); and Aji et al., 2020). Third, this study confirms social brand engagement is a mediator variable positively affects brand awareness and purchase intention relationship. But there is no mediator variable of social brand engagement influences on brand association and purchase intention relationship (Sohaib et al., 2022;Thanasi-Boçe et al., 2022;Yang et al., 2021). Thereby, affirming the role of social brand engagement is a positive contribution to the enhancement of brand awareness and brand association, but there is not enough evidence for the direct positive impact of social brand engagement on purchase intention in the fashion industry in Vietnam. Whereby showing that the factors affecting consumption intention must be value factors of the brand such as brand equity, brand authenticity (Faircloth et al., 2001;Majid et al., 2016;Sasmita & Mohd Suki, 2015;Singh & Pattanayak, 2016;Tolba, 2011) and the role of social brand engagement is not strong enough to promote consumer intention. From there, it shows that the level of consumer understanding of customers has increased significantly over time, regardless of whether the brand has received high praise from the community, as shown in the assessment of brand engagement (follow the brand, participate in interactive activities with the brand, share brand experience, take the side of the brand) but have not had a direct impact on purchase intention.

Managerial contributions
First, the research results show that the social brand engagement results of fashion brands in Vietnam during the period are quite good, the brands are interacting with and engaging with the brand quite high by the online community on the Internet. Social networking platform, thereby, promoting brand awareness and equity is also at a good level, thereby having a positive impact on consumption intention. This result contributes to providing information, helping fashion brands in Vietnam have a basis to evaluate the quality of brand communication on social networks in the past time and have an orientation to continue investing in the future. Second, the results confirm three target market segments in the fashion industry in Vietnam by age: (1) 18-22 years old; (2) 23-30 years old; (3) 31-40 years old; and (4) 41-50 years old. These four market segments have different levels of social brand engagement, perceived brand equity and purchase intention. Accordingly, fashion brands can orient their target market segments and have strategies and brand communication programs suitable for each target customer segment. Third, research confirms the role of social brand engagement has a great contribution to brand awareness and brand association, but there is not enough evidence to prove the direct impact of social brand engagement on promoting consumer intention. Hereby affirming the role of factors affecting consumer intention is brand equity, brand authenticity. The results from this study contribute to providing a basis for fashion brands to strategically invest in building and developing brand equity, brand authenticity, to promote consumer purchase intention for brands in the field of fashion in the Vietnamese market.

Conclusion
The results from this study contribute to affirming the role and importance of brand engagement via social networks, which has contributed to a very positive impact on brand equity and indirect increased purchase intention towards the brand. In which, brand engagement on social networking platforms has a direct positive impact on two components of brand equity: brand awareness and brand association. In addition, brand engagement also contributes to an indirect positive impact on purchase intention through brand awareness. Research results recognize the regulatory role of social brand engagement on brand awareness and purchase intention relationship. The findings also record the evaluation of the results of the implementation of social media programs on the social networks of fashion brands in the Vietnamese market in recent years positively, thereby positively influencing the positive perception of brand equity and positively promoting purchase intention. To increase social brand engagement, brand communication needs to focus on the interaction between customers and brands, encouraging customers to share, comment, and follow the brand. In social media content, it is necessary to customize to suit customer groups, which the customer group is 30 years old or younger, participates in social networks, and engages with the brand very actively, and this is also a group of potential customers with high demand for the fashion industry that many brands in the fashion industry focus on pursuing.
Brand equity is an important value for businesses, especially in the field of fashion, brand engagement on digital platform, and social networks have a direct positive impact on brand equity and this has the effect of increasing consumer purchase intention towards the brand. Research results show that customers aged 18-30 years old highly appreciate brand equity in the fashion sector compared to customer groups ranging from aged 30-50 years old. The group of customers aged 30 and under also have a higher intention to purchase in the fashion sector than the group of customers aged 30 and over. The research results have identified four potential customer segments in the fashion industry with statistically significant differences in brand engagement, brand equity perception, and purchase intention: (1) customer group is 18-22 years old; (2) customer group is 23-30 years old; (3) customer group is 31-40 years old; and (4) the customer group is 41-50 years old. This research result provides a basis for identifying and selecting target customer segments for the fashion industry in Vietnam. In addition, social media programs also need to be designed to match the characteristics and requirements of these four segments in terms of content and implementation in each communication programs.

Limitations and future research
Besides the results obtained from this study, there are also limitations that need attention. First, the sample size is small (637 Vietnamese people), so the representative area of the population is still limited. Further studies can increase the sample size, expand the study area, so that the results are representative of the population. Second, the research is carried out on each fashion industry, so the generalizability for the whole is still low. Accordingly, industries such as processed foods, pharmaceuticals and cosmetics can be considered to expand research. Final, there are many factors that may be related to, affecting brand equity and consumer intention that this study has not included in the analysis, such as: the authenticity of media content on social networks, the effect of consumption crowd, perceived quality, brand authenticity, etc., effect consumption intention. Therefore, in future studies, it is possible to add these components to the research model.