Customer engagement and loyalty: the moderating role of involvement

Purpose – The purposes of the present study were to analyse: (1) if there is a hierarchical relationship between cognitive dimension (attention) and emotional dimension (enthusiasm); (2) to what extent the cognitive and emotionaldimensionsofthecustomerengagement(CE)affectloyaltytoconsumerbrandsintraditionalsettingsandinsocialmedia;and(3)ifinvolvementmoderatestherelationshipsbetweencognitiveandemotionaldimensionsof CEandbetweeneachCEdimensionandthetwokindsofloyalties(offlineandsocialmedia). Design/methodology/approach – The authors applied structural equation model on a sample of 272 passengers of main airlines operating the domestic Argentinian market in 2018. The authors also used multigroup analysis to combine involvement as a moderator variable. Findings – Cognitive dimensions of engagement (attention) had a direct and positive effect on the emotional engagement (measured by enthusiasm). Capturing the attention of passengers is key to maintaining their loyalty both in offline and online environments, especially if they are lowly involved with brands. Research limitations/implications – The present study suggests and tests a model for the consequences of CE as a multidimensional construct in a specific service context. Originality/value – Following the attitude formation approach and the hierarchy of effect of advertising theory, this study researched the dynamic of relationship between cognitive and emotional dimensions of CE. The results contribute on the line of considering CE as a process, including stages that consumers go through until they achieve the engagement with the brand. The results offer evidence of the specific impact of each CE dimension on loyalty at two environments (offline and social media).


Introduction
Air transport is central to world tourism and trade, moving beyond 4.5 billion passenger journeys (IATA, 2020).Tourists travelling internationally by air are estimated to have spent about $900 billion in 2019.In the last three decades, liberalisation and deregulation have played an important role driving to the actual airline competitive landscape, which is characterised by three driving trends: hybridisation of business models following low-cost carriers' entry, consolidation through the proliferation of alliances, and high exposure to financial distress and government intervention (OECD, 2014).As an indicator of this process,

Customer engagement and loyalty
International Civil Aviation Organization (ICAO, 2019) reports that low-cost carriers carried approximately 31% of the world's total scheduled passengers.
Airlines are highly affected by perishability, as their service capacity cannot be stored for sale in the future.Besides, the intense competition of this market has led to a small profit margin.So, investment in passengers' loyalty can benefit the long-term financial performance of the airlines.Even though the use of loyalty programmes is a common practice in most airlines around the world, their members are far from loyal, and they fall far short in achieving their objectives (Deloitte, 2013).In other words, it seems that airline loyalty programmes fail to engage passengers.
Customer engagement (CE) represents an important concept for research in marketing and service management.CE is a psychological state that occurs by virtue of a customer's interactive and co-creative experiences with an agent/object (e.g. a brand) in service relationships (Brodie et al., 2011).From a relationship marketing perspective, a CE strategy overcomes the analysis of linear relationships between companies with their customers focused on exchange and advance on the co-creation of value and the behavioural intention of brand loyalty.
Hospitality and tourism scholars have displayed divergent understandings of the CE construct as there are numerous operationalisation (Rather et al., 2019;So et al., 2020); however, the CE's cognitive and emotional dimensionally have found widespread acceptance in the literature (Harrigan et al., 2018;Rasoolimanesh et al., 2021).From the perspective of hierarchy of effects in advertising (Lavidge and Steiner, 1961;Wijaya, 2012) as well as the attitude formation process (Fishbein and Ajzen, 1975), CE can be considered not only a multidimensional but also a hierarchical construct.However, the relationship hierarchical effects between the cognitive and emotional CE have not been sufficiently examined.
By getting engaged, consumers exhibit dispositions that go beyond traditional consumer behaviours.CE generates behavioural outputs, as advocacy (Sashi et al., 2019), intention of loyalty (So et al., 2014(So et al., , 2016;;Harrigan et al., 2017), as well as the brand usage intent (Harrigan et al., 2018).Additionally, with the emergence of social media, companies have new opportunities to connect with their customers through interactions other than service and experience (So et al., 2014).
In this study we focus on behavioural intention of loyalty, and because of the relevance of social media as an environment for manifestation of CE, we propose two kinds of CE behavioural outputs: offline loyalty and social media loyalty.
Besides, the process of CE can be influenced by involvement with the brand (Harrigan et al., 2018).Although moderator research of CE in the tourism context is highly desirable from a practical and conceptual standpoint (So et al., 2020), the involvement moderating role in the relationship between each dimension level and in CE impact on behavioural outputs has not been studied.
Considering these gaps in knowledge, we suggest a model that analyses (1) if there is a hierarchical relationship between cognitive dimension (attention) and emotional dimension (enthusiasm); ( 2) to what extent the cognitive and emotional dimensions of the CE affect loyalty to consumer brands in traditional settings and in social media; and (3) if involvement moderates the relationships between cognitive and emotional dimensions of CE and between each CE dimension and the two kinds of loyalties (offline and social media).
This study is an interesting contribution for the integration of CE psychology theories, a necessary step for the generation of studies on this topic (Chen et al., 2021).Likewise, it is relevant to study how CE is effectively translated into real consumer loyalty actions, beyond the loyalty programmes developed by airline brands to achieve their objectives (Deloitte, 2013).
Besides its originality is based on the contribution to the study of hierarchical dependence between cognitive and emotional dimensions of CE, which is a gap in the tourism marketing literature.

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The contribution to the tourism services sector is relevant because it is a topic rarely addressed in hotel and tourism magazines (So et al., 2020), and particularly, studying the commercial airline market in Argentina.
In the following sections, the paper presents the literature review and hypotheses development.Later, the research methodology and empirical results are presented.We close the paper by discussing the research conclusion, implications, limitations and further research directions.

Literature review and hypotheses development 2.1 Customer engagement: a hierarchical and multidimensional construct
The initial conceptualisations of CE came from other fields of social sciences, such as educational psychology and organisational behaviour.In the marketing literature, this construct has recently acquired importance.CE is an individual-level and motivational variable, it is a psychological state that emerges from two-way interactions between subject and the brand (Brodie et al., 2011).As an outcome may exist at different intensities and as a process develops over the time (Hollebeek, 2011a).
Because the concept of attitude has provided a significant contribution in explaining the consumer behaviour in service context, we use this theory for a better explanation of CE dimensionality.Attitude is defined as "learned predisposition to respond in a consistently favourable or unfavourable manner with respect to a given object" (Fishbein and Ajzen, 1975, p. 6).Attitude model consists of three components, namely cognitive, affective and conative.The cognitive component refers to knowledge or beliefs about the attitude object.The affect (or emotional) refers to a person's feelings towards and evaluation of some object.The conative component reflects the behavioural tendencies towards the attitude object.
The CE's cognitive-emotional dimensions have found widespread acceptance in the literature (Hollebeek, 2011a, b;Rasoolimanesh et al., 2021).In CE context, the cognitive dimension is related to the customer's attention and interest in a brand; and the emotional dimension is linked to the feelings of inspiration or pride caused by a brand.The CE's literature still lacks the theoretical foundation to specify the relevant variables that represent each dimension as well as their interrelationships.A contribution for the first of these problems in the tourism context, is the work of Harrigan et al. (2017).They merged previous conceptualisations of CE (So et al., 2014) for the study of tourism brands in social media context, proposing attention as a cognitive dimension of CE; and enthusiasm as an emotional dimension of CE.Attention is the customer's level of focus, consciously or subconsciously, on the brand (Harrigan et al., 2017) while enthusiasm is a strong excitement or zeal about the brand (Vivek, 2009).
Based on the Fishbein model and the theory of hierarchy of effects in advertising (Lavidge and Steiner, 1961;Wijaya, 2012), we propose that CE is not only a multidimensional, but also a hierarchical construct.This approach considers that customers do not change instantaneously from disinterested people to engaged customers.Instead, we propose a two-stage process: cognitive and emotional.
According to the hierarchy of effects model, the cognitive stage of customer engagement begins with the perception of the company (Lavidge and Steiner, 1961) and leads to the second emotional stage.This means that a direct and positive relationship is expected between attention and enthusiasm (Figure 1).
Attention is a customer's level of focus, consciously or subconsciously, on the brand (Harrigan et al., 2017).It is related to the amount of cognitive resources that the consumer spends thinking about the brand, and can be thought of as a finite cognitive resource that individuals can choose to allocate in different ways (Ho et al., 2011).Information appears in consciousness through the selective investment of attention, and one once attended to, Customer engagement and loyalty information enters awareness.The system encompasses all of the processes that take place in consciousness, such as thinking, willing and feeling about this information (i.e.cognition, motivation and emotion) (Nakamura and Csikszentmihalyi, 2014).
In line with the above, we propose that: H1. Attention directly and positively influences enthusiasm.

Behavioural intention: offline and social media loyalty
Although CE literature is growing significantly, there is limited empirical research on the outcomes (Leckie et al., 2016), and this knowledge gap is more observable when it comes to services.Considered as the focal point of interest for marketing researchers and practitioners, brand loyalty has been widely studied.Customer loyalty is the result of psychological processes and has behavioural manifestations; therefore, it should incorporate both attitudinal and behavioural components.From the research stream of service marketing, brand intention of loyalty measures a customer's intention to say positive comments about a brand, to recommend a brand and to purchase this brand in the near future (Zeithaml et al., 1996).
Considering that the CE, by definition, encompasses a consumer-brand relationship that exceeds the time of purchase, the behavioural intention loyalty seems to be the most expected output when consumers are engaged.In fact, there is evidence that CE is a predictor of the behavioural intention of loyalty (Bowden, 2009;Hollebeek, 2011b), even in the specific context of airline services.
In addition, because of the importance of digital media for the interaction between customers and brands, much of the CE occurs on the internet (Li et al., 2020) and the social media facilitates the behavioural intention of customer loyalty (Harrigan et al., 2017).There is evidence that consumer loyalty can differ depending on the environments (online vs. offline) Research model EJMBE (Shankar et al., 2003), which led to proposing differentiated hypotheses for each type of environment in which loyalty develops.In this research, we focus on both kinds of loyalty (online and offline) as consequences of CE.
Social media loyalty extends traditional brand loyalty to online consumer experience to the social media environment.It comes from e-loyalty, a previous and broader concept (Gommans et al., 2001).In this study, social media loyalty is defined as perceived loyalty towards the airline networks, with intent to comment positively about them and to recommend following the brand.
2.2.1 Attention as antecedent of loyalty.Cognitive psychology proposes that attention is related to behaviour (Skavronskaya et al., 2017).The control of action demanded a mechanism which could allow relevant information to control behaviour and decouple irrelevant information from interfering (Styles, 2006).Doing this, attention guide behaviour.For example, if an airline promotes a new route or a sale promotion, passengers filter this information using attention and this cognitive process guides them in future behaviours such as intention to flight or to recommend or give advice to other passengers.
The attention dimension of engagement with an airline brand denotes a level focused attention on it.Therefore, when consumers allocate cognitive capacity by concentrating and/ or engrossing on the brand they are more likely to develop loyalty towards the focal brand (Leckie et al., 2016).
Previous studies of tourism context have proved the relationship between cognitive engagement as an antecedent of offline loyalty intention (Harrigan et al., 2017;Ahn and Back, 2018), and the specific relationship between attention and offline loyalty (Rasoolimanesh et al., 2021).Besides, the study of Kanje et al. (2019) revealed that the cognitive CE relates positively with electronic word-of-mouth (eWOM) passing intentions.
These antecedents lead as to propose that attention, as a cognitive variable of CE, will impact on loyalty at both environment: H2a. Attention directly and positively influences offline loyalty.
H2b. Attention directly and positively influences social media (SM) loyalty.

Enthusiasm as antecedent of loyalty.
As tourist experiences are increasingly affective, emotions play a central role in determining tourists' future intentions (Bign e et al., 2005).Prayag et al. (2013) proved that emotions such as love, positive surprise and unpleasantness had a direct relationship with behavioural intentions as willingness to recommend and wordof-mouth.Affective CE positively relates to vacationers' eWOM seeking, giving and passing behaviours in tourism-related sites (Kanje et al., 2019).
This study proposes that enthusiasm with the airline brand may have an impact on consumers' loyalty.If consumers perceive strong excitement or zeal about the brand (Vivek, 2009), they will seek to recommend it offline and at social media; thus, it will become an antecedent of offline loyalty and SM loyalty.Based on previous antecedents, we propose the following: H3a. Enthusiasm directly and positively influences offline loyalty.
H3b. Enthusiasm directly and positively influences SM loyalty.

Moderating role of involvement
Involvement represents the level of interest or importance of a brand for an individual (Russell-Bennett et al., 2007), and it is also related to the amount and type of information that a consumer processes in making decisions regarding their choice to purchase a brand (Ram ırez-Angulo and Duque-Oliva, 2013).This information depends mainly on the perceived risk in the consequences of making a wrong purchase decision.As a multidimensional Customer engagement and loyalty construct, involvement includes aspects such as interest, perceived pleasure, symbolic value, product importance, risk importance and risk probability (Vera-Mart ınez, 2003).
There is evidence that involvement impacts on CE dimensions (Harrigan et al., 2018), but its influence over the hierarchical cognitive-affective relationship is not studied.
The elaboration likelihood model explains why different levels of involvement result in varying degrees of extensiveness in information processing (Petty and Cacioppo, 1986).As involvement with the brand increases, consumers are likely to search information about the products more intensively (Wang and Wu, 2011).This results in a greater willingness to apply more cognitive resources to processing information.Besides, the findings of Krishnamurthy and Kumar (2018) suggest that consumers with high versus low involvement go through more information and spend more time with brand's information to develop an expectation or idea of it.
The affective dimension is also related to involvement.Previous studies showed that the mood of consumer when interacting with the brand can affect the effectiveness of its communications (Wen, 2021) and that involvement has a direct impact on CE affective dimension (Harrigan et al., 2018).
Based on these antecedents, we propose that involvement can be a moderator of the relationship between CE cognitive and emotion variables.We expect that when costumers are highly involved with the brand, their attention will generate enthusiasm to the brand in comparison to those consumers whose are lowly involved, because they will find the brand services as personally relevant to their needs and values.On the other hand, when passengers are lowly involved with the airline, attention will generate less enthusiasm.This leads us to propose the following H4: H4.For highly involved consumers, the positive effect of attention to enthusiasm will be stronger.
The CE can be influenced by involvement with the brand and generates consequences in the consumer behaviour (Harrigan et al., 2018).Rasty et al. (2013) found that involvement as a moderator had the greatest effect on the relationship between travel advertising attitude and travel advertising effect in the internet environment.
In the airline context, involvement plays an important moderating role on the relationships within the airline loyalty programmes (Wang et al., 2015).However, the moderating role of involvement for the relationship between each cognitive or emotional dimension of CE and loyalty has not been studied.We want to know if the effects of the dimensions of CE on behavioural intention of loyalty (both, offline and in social media) are different for highly and lowly involved consumers.
According to our H4, we expect that when consumers are highly involved with the airline brand, the cognitive-affective relationship will be stronger.This means that, in that situations where the purchase decision is complex and passengers need to process more information (e.g. when buying tickets for the summer vacation for a family group or for a more expensive destination), they need to be enthusiastic with the brand to be engaged.So, we expect that only when they are more enthusiastic, they will generate behavioural intention loyalty.
On the other hand, when the consumers are lowly involved with the airline brand, the affective engagement (enthusiasm) will not be so affected by cognitive engagement (attention).In situations, where the purchase decision is more routine and less risky for passengers (e.g. when tickets are purchased for work trips or frequently visited routes) they do not need to be so enthusiasm with the airline to generate behavioural intention of loyalty.Attention can serve as "sufficient" engagement dimension to generates loyalty.Just being attentive to what the airline communicates generates engagement and will cause behavioural intention loyalty.
Based on these arguments, we propose the following: EJMBE H5.For highly involved consumers, the positive effect of attention on (a) offline loyalty and on (b) social media loyalty will be weaker than on lowly involved consumers.
H6.For highly involved consumers, the positive effect enthusiasm on (a) offline loyalty and on (b) social media loyalty will be stronger than on lowly involved consumers.

Selection of the airlines and study population
The study was applied to consumers of airlines in Argentina, specifically to the domestic market that is made up of 14.2 million passengers (ANAC, 2018).The global airline industry trends also affected the domestic airline market in Argentina.In 2018, the national government developed a commercial air policy that aimed to double the number of people flying, through the entry of low-cost airlines.
As when developing this study, Aerol ıneas Argentinas and LATAM were the carriers with the highest market share, the study population was defined as Argentinean residents who have recently (last 5 years) and domestically travelled using one of these airlines.

Data collection and research sample
The data collection instrument was a structured online survey.It was applied in two versions, with identical questionnaires, but each referred to one of the airlines under study.The questionnaires were previously pre-tested with a sample of 50 students of tourism degree and by two senior researchers.
Due to the lack of a sampling frame to apply a random sampling of the study population, a quota sampling was used, seeking to complete similar representation for each airline.Each participant answered only one of the two versions of the questionnaire, and the respondent was reached by email and social networks.Through filter questions at the beginning of the questionnaires, we confirmed that the respondent corresponded to the population to be studied.
The data were collected between the months of April and July 2018, obtaining 272 completed and valid questionnaires, 133 (49%) about LATAM airlines and 139 (51%) about Aerol ıneas Argentinas.
The sample included 34.56% of males and 65.44% of females.About 34.56% of the passengers were 18-34 years old and 40% were 35-49 years old, mostly with high levels of formal education (54% had university studies and 38% had postgraduate studies).This profile was similar for each airline subsample as Chi-square showed that differences between them were no significant (gender Chi-square 1df 5 0.600, sig. 5 0.439; Age Chi-square 3df 5 4.439, sig. 5 0.219; Education Chi-square 2df 5 0.938, sig. 5 0.625).

Measurements
The measures of the relevant constructs primarily were based on scales taken from previous works.The scale of So et al. (2014) was used for measuring each dimension of CE, an adaptation of Vera-Mart ınez (2003), for customer involvement, and Harrigan et al. (2018) and Zeithaml et al., (1996), for social media loyalty and offline loyalty, respectively.

Descriptive, normality and multicollinearity analysis
An analysis of descriptive statistics and extreme scores was carried out, as well as an inspection of the correlation matrix in order to assess that the collinearity assumption is met and rule out the existence of multicollinearity (see

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Regarding the descriptive analysis of the items, it was found that they present adequate indicators of skewness and kurtosis, considering that they do not exceed the range ± 1.5.
However, the critical ratios analysis showed that in many variables univariate normality was not achieved.The critical ratios are formed by taking the ratio of the estimate (for skew or kurtosis) to its standard error.This ratio is distributed as a unit normal variate or z-score.Adopting a conventional alpha of 0.05, then a c.r. < À1.96 or >1.96 for a given test may be an indicator of departure from normality.Besides, the multivariate kurtosis, used to assess whether the data are departing from multivariate normality, resulted in higher than 5. So, we assume that the variables in this analysis reflect a departure from multivariate normality.
Table 1 also allows us to examine the degree of association between the items that make up the test and total scale score for latent variables.The items on the scales present item-total correlations ranging from 0.728 (Attention item "I like to learn more about X") up to 0.889 (offline loyalty item I would make positive comments about X face-to-face to other people), which accounts for an adequate homogeneity.
To have an overview of the state of multicollinearity, the Pearson correlation matrix was analysed.The bivariate correlations that are observed in the matrix range from 0.446 to 0.834.6% of them indicate low collinearity (correlation up to 0.5), 76% medium collinearity (correlation between 0.5 and 0.7) and 18% high collinearity (correlation between 0.7 and 0.9).The determinant of the matrix was 1.150E-5, typical of a matrix with medium collinearity, although it was not equal to zero (non-singular matrix).
In order to analyse the feasibility of the use of factor analysis for the determination of the construct validity were used the Kaiser-Meyer-Olkin (K-M-O) measurement and the Barlett's Sphericity test.The measure of K-M-O adequacy gets a score of 0.918 value considered adequate (Hair et al., 2010), while that the Barlett's Sphericity test presents a significant value of 3027.197(df 5 66, p 5 0.000).These determinations indicate that it is factor analysis possible exploratory.
The varimax rotation confirms the total independence (item discrimination) of the four latent variables.

Reliability and discriminant validity
Confirmatory factor analysis was performed to test the psychometric properties of the scales using AMOS 23.0.This software provides bootstrap analysis for situations where the assumptions underlying the standard errors and maximum likelihood Chi-square may be violated.As our data departure from multivariate normality, we applied bootstrapping.
As observed in Table 2, the standardised loadings were all higher than 0.70.The bootstrapping analysis also resulted in satisfactory results.The standard error bias, which is the difference between the average of loading estimates obtained from 500 bootstrap samples, and the single estimate obtained from the original sample, resulted in low values.Besides, the bounders of the bias-corrected of 95% confidence interval do not include 0 value, and estimated probability was below 0.05.
To assess the reliability, Cronbach's alpha coefficients (α), composite reliability (CR) and average variance extracted (AVE) were estimated.Most of the factors exceeded the threshold of 0.7 suggested by Nunnally and Bernstein (1994), indicating that the scales used to measure each of the latent variables were reliable.The interpretation of the CR is carried out in the same way, so that the results obtained are satisfactory for all the factors.In relation to the extracted variance, Fornell and Larcker (1981) suggest that it is desirable for each factor to obtain an extracted variance equal to or greater than 0.5.This value was surpassed by all factors, as they presented an average explained variance between 0.728 and 0.883.
In order to assess discriminant validity, four statistical tests were performed: Chi-square differences (Bagozzi and Phillips, 1982;Anderson and Gerbing, 1988), Satorra-Bentler scaled Customer engagement and loyalty Chi-square (Satorra and Bentler, 2001), confidence interval (Anderson and Gerbing, 1988) and extracted variance (Fornell and Larcker, 1981).The Chi-square difference test starts from analysing the covariances between the factors, and detecting which are the most correlated with each other.In this case, the relationship between the attention and enthusiasm factor is the highest (correlation 5 0.777).This situation could ask whether the attention items would serve to measure enthusiasm or vice versa, so the discriminant validity of the two scales could be questioned.
The Chi-square difference test was then performed between the original model and a more constrained model in which the covariance between attention and enthusiasm was set to 1.The difference obtained is 177.600(df 5 1), therefore the difference between the two models is clearly significant.However, as our data depart from multivariate normality, the Satorra-Bentler scaled Chi-square statistic was used to provide an improved estimate of the fit of a model.Using Crawford and Henry (2003) computer program, we compared the more constrained model (correlation between attention and enthusiasm 5 1) with our model.Satorra-Bentler scaled difference resulted in 19.4232 (df 5 1) and significant (p 5 0.000).In other words, the standard measurement model in which the factors attention and enthusiasm are correlated, but are treated as two different latent variables, is significantly better than the model that considers both in a single factor.

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The Anderson and Gerbing test consists of calculating a confidence interval of ±2 standard errors of the correlation between the factors and determining whether this interval includes 1.This situation was not detected, thus confirming discriminant validity.
Finally, the third analysis to test discriminant validity consisted of comparing the variance extracted for each pair of factors versus the square of the correlation between them.If the variances extracted from the factors are greater than the square of the correlation between them, there is discriminant validity.As can be seen in Table 3, for all the factors, its AVE is greater than the squared correlations with other factors.

Relationships between CE's cognitive-emotional dimensions and impact on loyalty
To contrast H1-H3, an analysis of the structural equation model (SEM) was carried out with the total sample (N 5 272).Bootstrapping analysis was also performed.
The resulting path diagram and the causal relationships are presented in Figure 2. As attention has direct and positive effects on enthusiasm (β 5 0.780; p < 0.001; bias-corrected p < 0.01) H1 was supported.Our results provide support to the hierarchical relationship between cognitive and emotional CE's dimensions.The more attention to the airline brand, the greater enthusiasm with it.
These results support the hypotheses H2a, H2b and H3b.In other words, the more attentive consumers are with the airline brand, the more loyal they are in offline and social media environments.In addition, the more enthusiastic the brand consumers are, the more loyal they are to social media.

Consumer involvement as moderator
We ran a confirmatory factor analysis (CFA) for the involvement items ("I am interested in brand X", "I give a lot of importance to the purchases I make of brand X because of the security it generates for me", "When I shop at X, I know if I'm making the right purchase", "Using the X services is very valuable to me", "Using the service of brand X says what I am"), and we found that they reached reliability requirements (α 5 0.899, CR 5 0.904, AVE 5 0.653).The involvement factor scores for each respondent were saved and, through a k-media cluster analysis, the sample was divided into two significantly different groups (F (1/270) 5 479.877, p 5 0.000): lowly involved consumers (N 5 110, Mean 5 À0.969) and highly involved consumers (N 5 162, Mean 5 0.658).The pertinence of individuals to each cluster was saved in a new categorical variable and was included in the model as a moderator variable to test H4 to H6.
We performed a new discriminant validity analysis, this time for each segment (see Table 4).Results were mostly satisfactory.Only the correlation between offline loyalty and social media loyalty factors in the lowly involved segment resulted higher (0.714) than the AVE of social medial (0.699).
Then, we assessed the measurement invariance.The testing strategy began by running a CFA within each group separately for evidence of fit (Byrne, 2010;Ald as Manzano, 2013).The fit of the model in the lowly involved group is rather low (comparative fit index [CFI] 5 0.925, root mean square error of approximation [RMSEA] 5 0.123) while the model fits better in the highly involved group (CFI 5 0.969, RMSEA 5 0.084).
Assuming a reasonably good fitting model, we proceeded to test for evidence of configural invariance (M1), metric invariance or equal factor loading (M2), scalar invariance or equal intercept (M3) and invariance of residuals/measurement errors, also referred to as strict invariance (M4).When checking the moderation effects on the structural coefficients, it is essential to corroborate at least M2 (Ald as Manzano, 2013).
Results are presented in Table 5, and they suggest that M1 to M3 did not make significantly worse adjustment.However, the residual invariance was not reached (M4).According to Hair et al. (2010), the equality of covariances, variances of factors and variances of errors do not only rarely exist, but their effect is minimal for most research problems we face.

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Then, for the multigroup path analysis, we proceeded to test a fully unconstrained modelwhere there are no equality constraints imposedand several constrained models with those coefficients we wish to test according to our hypotheses (one at a time).In Table 5, the Chisquare difference test associated with each parameter is an examination of whether the model fit improves significantly because of relaxing the constraint.The assumption behind these tests is that if the fit of the model improves significantly with the relaxation of a constraint, then the parameter is non-invariant across groups.If significance is found, we assume the parameter is non-invariant (i.e.unequal) across groups, so the constrained model is worse than the unconstrained one.
Considering the size of the samples in both groups (110 and 162) we consider statistically significant p < 0.10 in the comparison of the relationships between groups.Table 6 shows that if we assume that highly and lowly involved groups have equal relationships between attention and enthusiasm, attention and offline loyalty, attention and social medial loyalty, and enthusiasm and social medial loyalty, it significantly worsens the model.As these relationships differ between the groups (lowly and highly involved), H4, H5a, H5b and H6b were supported at a p ≤ 0.10 significance level, while hypothesis (H6a) was rejected.
Figure 3 shows that the hierarchical relationship between attention and enthusiasm grater when consumers are highly involved with the brand.Besides, in lowly involved consumers, the effect of attention on offline loyalty and on social media loyalty is considerably higher than the effect of enthusiasm (on offline loyalty: 0.721 vs. 0.088; on social media loyalty: 0.712 vs. 0.207).However, in highly involved consumers, the effects of attention and enthusiasm on offline loyalty seem similar (0.331 vs. 0.400), and on social media loyalty, the effect of enthusiasm is considerably higher (0.621 vs. 0.169).

Conclusion and implications
Following the attitude formation approach (Fishbein and Ajzen, 1975) and the hierarchy of effect of advertising theory (Lavidge and Steiner, 1961), this study researched the dynamic of the relationship between cognitive and emotional dimensions of CE.Our results contribute on the line of considering CE as a process, including stages that consumers go through until they achieve the engagement with the brand.Besides, to the authors' knowledge, no study has investigated the hierarchical dependence between cognitive and emotional dimensions of CE.Rothbard (2001) and Dessart et al. (2016), the results showed that attention, as cognitive dimension of CE, generates emotional consequences that, in our model, was measured through enthusiasm.Our results are in line with the dynamic of attention-flowfeelings proposed by Nakamura and Csikszentmihalyi (2014) about cognitive process as an antecedent of emotion with the airline.If airlines want their passengers to be enthusiastic about the brand, they need to optimise the cognitive process.Their communication channels and messages must be focused on capturing consumers attention and achieving immersion states with the brand.
Prior studies have examined the CE influences on brand loyalty in the tourism services context (Harrigan et al., 2017(Harrigan et al., , 2018;;Li et al., 2020).However, these studies do not offer results of the specific impact of each CE dimension on behavioural intentions, an issue that we consider essential for a better understanding and prediction of consumers future behaviour.
Our results show that attention is a predictor of loyalty in offline and social media environments.When customers have high levels of focus on the brand, they tend to make positive comments of the brand and recommend it to other people in traditional ways (face-toface) or even on social media networks.
We also conclude that behavioural intention is achieved by the influence of the cognitive and emotional dimensions of the CE.Similarly to previous investigations (Bign e et al., 2005;Kanje et al., 2019) that found positive relationships between emotions and behavioural intentions in consumers, our results offer evidence that enthusiasm impacts on loyalty in social media context.
So, as suggested by Shankar et al. (2003), the impact of CE dimensions on loyalty is differentiated according to the environment.The offline loyalty is generated by attentive passengers, while social media loyalty is generated for attentive and enthusiastic passengers.
Following suggestions of new lines of research about CE made by So et al. (2020), the inclusion of involvement as a moderator variable is a novelty that this study offers to previous evidence.Involvement as moderator was introduced to explain how relationships between cognitive and emotional dimensions of CE, and between each dimension of CE and loyalty, change under certain conditions (lowly and highly involved passengers).
Once empirically supported, moderations tend to define the boundaries of a proposed model (So et al., 2020).In our study this was particularly evident in the cognitive-emotion CE's hierarchy.We conclude that when passengers are highly involved, their attention to the

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airline brand generates more enthusiasm to it, in comparison to those passengers who are lowly involved.
Lowly involved passengers are consumers that have a low level of interest in the brand or that process a low level of information when making decisions with respect to the brand.They can be frequent travellers, business travellers or even passengers that usually fly routes operated by a single airline (i.e. they only have one alternative of purchase).
For this group, the hierarchical relationship between attention and enthusiasm is direct but weaker than for the group of high involvement.As regards the consequences of CE on behavioural intention and the moderating role of involvement, we found that attention is particularly important and sufficient for generating loyalty within these individuals.As this type of consumer is less interested in being involved with the brand, only capturing their attention is enough to obtain their loyalty.So, the more the airline brand can get their attention, the more it will obtain their loyalty in both environments (offline and social media).
On the other hand, highly involved passengers are consumers that go through more information and spend more time with airline's information to develop an expectation or idea of it (Krishnamurthy and Kumar, 2018), so cognitive dimension (e.g.attention) generates enthusiasm with the airline.In this case, attention is more influential on enthusiasm, showing a more intense cognitive process, which is expected from passengers that need more information.However, attention alone is not enough to build loyalty, they need to get excited about the brand.For highly involved consumers, they need to be enthusiastic with the brand to generate offline and, especially, social media loyalty.If airlines can enthusiasm those passengers making complex purchase decisions, they will probably obtain more recommendations specially at the social media environment.
So, involvement is a crucial variable for segmenting consumers and, in turn, the communication process provided to them.For those frequent or routine travellers, the communication strategy must emphasis on capturing their attention and they will be loyal to the airline (recommending face-to-face, or even on social media).While for those infrequent travellers, or travellers passing for a riskier circumstances of consumption (as travelling in big groups, to new or distant destinations), the airline communication must enthusiasm due to obtaining loyalty, which will be reflected specially at social media.

Limitations and future studies
This study collected data on both the independent and dependent variables from the same respondents at one point in time, thus raising potential common method variance as false internal consistency might be present in the data.Although the measurements showed satisfactory reliability and discriminant validity, and the model showed a good fit allowing us to test our hypothesis, an experimental design study is suggested for the future to corroborate our results through a different research method.
Our study was conducted in Argentina and for domestic airline services.Thus, future research should test the suggested model in other countries and contexts to support the development of a more generalised theory.Further work should be performed to validate the model across other tourism services to assess its general stability, especially for going deep around relationships between emotional dimensions of CE and intention of behaviour.
We also recommend replication studies which focus exclusively on the influence of the moderating variables and might include other influencing variables such as the generation of the consumers.By understanding how customer generations use social media and how this moderates the effects of CE on offline and social media loyalty, Customer engagement and loyalty airlines may be able to better target their passengers' needs, which may give them a competitive edge in a turbulent business environment.
The diagonals are AVE: average variance extracted; above the diagonal are the squared correlations between factors; below the diagonal, the 95% confidence intervals for the correlation between the factors are presented Source(s): Table by the authors

Table 5 .
The diagonals are AVE: average variance extracted; above the diagonal are the squared correlations between factors; below the diagonal, the 95% confidence intervals for the correlation between the factors are presented Source(s): Table by the authors Invariance of the measurement Table by the authors Table 6.