The cultural and heritage tourist, SEM analysis: the case of The Citadel of the Catholic King

This study researches the loyalty of travelers to destinations which include material cultural heritage. It analyzes the loyalty of visitors to a destination with cultural heritage sites in order to provide results which can be used to improve the management of the destination. This research used Warp-PLS 7.0 software with a structural equations model to evaluate the 8 proposed and validated hypotheses. A questionnaire was given to a sample of 499 tourists who visited The Citadel of the Catholic King in Córdoba and the statistical study of the replies gave results about the loyalty of visitors to a destination which includes cultural heritage. This study adds an innovative component by analyzing the moderating effect of perceived heritage quality and perceived cultural quality on the relationship of perceived value and visitor satisfaction. This study shows that visitor loyalty to The Citadel of the Catholic King depends on the visitor satisfaction with the cultural heritage, it also analyses how the quality perceived by the tourist modulates to varying degrees the relationship between perceived value and tourist satisfaction. Areas which can be improved at cultural heritage sites have been identified and these include the professionalization of tour guides specialized in cultural heritage sites, improving and showing the cultural importance of the heritage, the information available about the heritage and the access to the heritage. These findings are important for city managers when preparing projects to increase the loyalty and competitiveness of the city compared to other similar destinations with cultural heritage.


Introduction
Cultural material heritage has become a factor which can make a city more attractive to visitors. Adequate management of the heritage is essential to achieve visitor satisfaction during and after the visit as well as improve the visitor expectations before and the perceived quality after the visit. Continuous improvement of these aspects can be the differentiating factor for the loyalty of the visitor to the city. The strong competition for visitors between destinations with heritage and culture sites, especially UNESCO listed sites, means that making continual improvements to the management of these sites is essential. The current situation will only become more difficult in the future [1]. In view of this, visitor loyalty to a destination is an important factor to take into account, especially for tourist destinations in areas with cultural heritage [2]. This research makes a valuable contribution to this subject [2].
The Citadel of the Catholic King is material heritage that has a lot of historical and cultural relevance. Firstly, due to the cultures that used the site. The first record of the existence of the enclave comes from Roman culture when it was used as a way to defend the city against incursions made on the Guadalquivir River. After that it became the center of Arabic culture in Spain, being used as the residence of the city rulers. After the reconquest of Cordoba by the Catholic kings, it was transformed into a building where the monarchs could rest and relax. The Citadel of the Catholic King is also a place where important historical changes for Spain and the world happened. It was the place where Cristopher Columbus met the Catholic Kings, who were the Monarchs that unified Spain into a Kingdom [3]. The building that can be visited today was built by Alfonso XI in 1328 on the site of the Omeya Citadel (Arabic origin) [4]. From 1492 to 1811, it was owned by the holy Catholic inquisition. From 1822 to 1931 it was a prison and later used as a military installation until its transfer in 1955 to the Córdoba City Council, which now owns it and manages it as a tourist site [5]. The Alcázar was classified as a Historical Monument in 1931 and is in the area in Córdoba that was declared a World Heritage Site by UNESCO in 1994. Currently, The Citadel of the Catholic King is the third most visited material heritage in Cordoba, the second being the synagogue of Cordoba and the first is the Mosque-Cathedral. In 2019 it had 615,737 tourist visits, and an average growth in visits of 10.69% in the last 10 years (Observatorio de turismo de Córdoba, 2019).
The model is based on the expectations that are created before visiting a heritage tourism destination (expected quality). Tourists once they arrive at their destination, live the experience at destination, perceive the quality of different factors that build the perceived quality. Both constructs, (expected quality and perceived quality) relate to the perceived value, which compares the balance or imbalance between perceived cost at its destination and the value received at it. Once the tourist has internalized the perceived value, he is able to assess the level of satisfaction at the destination. The satisfaction level allows you to decide to recommend and repeat the destination (Loyalty). " This study expands the existing literature about the satisfaction and loyalty of heritage and cultural tourists, since the expected quality of the heritage and cultural aspects are separated, as are the perceived cultural quality and the perceived heritage quality. The concept of moderating constructs is also added to the classic theory of the Structural Equation Model. Two hypotheses specifically analyze the modulating effect of the constructs perceived cultural quality and perceived heritage quality of the visiting tourist. This study is configured as follows: first the introduction, secondly there is the theoretical framework that explains the constructs of the theoretical model and structural equations, below explains the methodology used and the fourth section summarizes the results of the research. To finish the article we find the discussion and conclusions of the study, followed by a list of the references used in the article.
In recent decades Cultural tourism occupies a niche market with exponential growth in international tourism [20]. Visiting tourists have motivations perceptions and build their idea of satisfactory destination based on various factors. Cultural and heritage, as an important part of the demand for knowledge of the place visited, create the experience of the tourist's visit that allows to have the ability to make the decision to return, recommend and promote the destination as a prominent part of his historical heritage experience [21]. World heritage cities compete to offer recreational and cultural experiences that attract the greatest number of tourists with the desire to learn more about the history of the destination, enriching their knowledge and their life experience [22]. Ramires, Brandao, and Sousa describes cultural historical tourism as a social phenomenon [23]. Cultural heritage cities have to differentiate the difference from the competition, either including in their cultural offer local customs, centuries of history, art and traditions transmitted from generation to generation. Consequently, heritage tourism is important for the cities that have heritage sites [24].
In this context, the components that are related to satisfaction in the visit to the material heritage can cite how visitors seek new experiences, authentic contexts and unique or exceptional activities. Actions such as participation, hedonism, knowledge, nostalgia, history, novelty and local culture are the basic ingredients of a memorable and satisfying tourist experience [25], in the same line the authors [26] highlight how the experiences provided in the heritage present the same degree of satisfaction for visitors that aims to visit the material heritage itself as those who visit the heritage for the tourist experiences around it (theatrical visits, historical explanations). This, coupled with the fact that these activities are usually carried out on holidays and that holiday contribute to the satisfaction of life and its quality of life [27][28][29] in addition to adding congratulations and pleasurable effects to the activities carried out in the holiday period [30].
Studies have shown that loyalty to a visited place is directly related to the satisfaction and opinion of the visitor [31,32]. Studies which analyze loyalty in tourism have mainly looked into the attitude and intention of the visitor [32]. Academic studies can be grouped into two categories due to how loyalty is examined. The first group investigates repeat purchases, that is to say, tourists returning to a destination. The second, and far more interesting, group takes loyalty to mean recommending the tourist destination to other future tourists [33][34][35]. This means that the tourist feels a connection with a destination and intends to visit it again in the future, while also recommending it to third parties [36][37][38][39]. It should be pointed out that there are authors who warn that a tourist's desire for new experiences may counteract the loyalty shown to the destination [40]. Studies which investigate loyalty to cultural heritage are mainly cognitive and use structural equations to predict intentions to return to or recommend a destination [41,42].
How comfortable the tourist felt at the destination and the monument visited is one of the most important factors when deciding to return to a destination, and therefore for visitor loyalty [35,38,43]. The perceived quality is usually considered one of the most important factors in research on tourist behavior [44]. Researchers define perceived quality as the overall accumulation of the tourist's feelings about the experience at a destination [45,46]. Tourists value their experience as positive or negative for different attributes of the monument or destination [80]. Following on from this idea, the perceived value of a destination by a visitor is considered to be the most important indicator of their intentions to return to the chosen destination. It is possible that a customer does not buy a product or service because it is not considered value for money as the perceived value is not adequate for the price asked [47]. Studies by different authors explain that perceived value measures a tourist's general assessment of their experience at a destination from the feelings they had there [48,49]. Cossío-Silva et al. obtain a realistic idea of tourist behavior by means of this variable and the results obtained can be useful for public institutions and organizations that offer tourism [50]. Customers who are aware of the value of a service or product sometimes expect particular benefits from it [51]. For this reason, perceived value is related to the usefulness of a purchase because the purchase has intrinsic benefits that satisfy the buyer's needs [52]. A tourist who is interested in value will look for information and contemplate the idea fully before making a decision [53]. This means that perceived value affects the decisions of customers [54]. Perceived value can positively affect the loyalty of a customer [47] because customers who are aware of the value of a service make positive judgements about it, relating value to price and critically assessing all options.
This study analyses the relationship between the following variables, perceived heritage quality (PPQ) and the expected heritage quality (EPQ), perceived cultural heritage quality (PCHQ) and the expected cultural heritage quality (ECHQ), the perceived value of the visit as a whole (PV), satisfaction (SATISFAC) and loyalty (LOY-ALTY). In literature there are several studies including these variables, however few studies include modulating variables in the relationships between constructs [55,56]. The different authors who have used this type of theoretical model are shown in Table 1.
The questionnaire with which the data was obtained was designed following various authors who have used constructs similar to those used in the theoretical model. The ACSI model has been used in multiple studies of satisfaction and loyalty in tourism in general and in heritage tourism [11][12][13][14][15][16][17][18][19].
The model is based on the expectations that are created before visiting a heritage tourism destination (expected quality). Tourists once they arrive at their destination, live the experience at destination, perceive the quality of different factors that build the perceived quality. Both constructs, (expected quality and perceived quality) relate to the perceived value, which compares the balance or imbalance between perceived cost at its destination and the value received at it. Once the tourist has internalized the perceived value, he is able to assess the level of satisfaction at the destination. The satisfaction level allows you to decide to recommend and repeat the destination (loyalty).
The variables which were investigated in this study are satisfaction and loyalty. These have been studied on several occasions in different areas by several authors [57,58]. Both variables are positively related showing that the probability of a visitor at a heritage site revisiting or recommending the destination is high [59,60] if they are satisfied with the visit. These are judgments made by tourists because of their experience at the destination, and these affect the likelihood of the tourist revisiting the site or city and their willingness to recommend it to friends and family [2,61].
Managers of cultural material heritage should have previous information about the visitors who visit the site in order to plan actions which will improve the visitor expectations about the heritage and cultural experiences. These modify the behavior of the tourist because of the relationship between the perceived value and satisfaction. This study uses structural equations with all the above variables and, as it also includes a new approach using moderating relationships at heritage sites, it is of academic interest. This research increases the contribution to academic literature around heritage, loyalty and satisfaction by adding culture on the visit.
There are not many Royal and historical Citadels (with a past dated at least from the Muslim era) in Spain which are put in tourist value and are visitable. The uniqueness that were the quarters of the Catholic kings, with a historical character and that are touristic. In particular, there are four: Royal Citadel Sevilla, Royal Citadel Madrid, the Muslim Citadel of Valencia and the Royal Citadel Almunia (Palma de Mallorca). In academic matters, different studies have been carried out from the historical or archaeological perspective [62,63] but not from the tourist management. The Citadel of the Catholic King of Cordoba is the most culturally, and architecturally significant. It belongs to the historic center of Cordoba being an inscription by UNESCO and is dated from roman times, an optimal conservation and valued for the tourism, therefore it is the most historical and cultural.
The aim of this study is to add to the information available about cultural heritage tourism, contribute to the improvement of the management of visits to the unique heritage sites and provide useful knowledge for cultural heritage managers and tourism companies. The most concrete objective is to detect how tourist experiences in culture and heritage increase satisfaction and loyalty by increasing visits, repetition and their recommendation. This research studies the loyalty of visitors to the cultural heritage site and to the city, along with the Satisfaction and Expectations of the tourists who visit The Citadel of the Catholic King. Scientific literature which studies cultural heritage tourism by investigating heritage and culture, and the influence on Perceived Quality at different Citadel s, is scarce. While it is true that there are some studies in tourism with modeling variables, the study in particular cases of heritage tourism in Spain (as a second country in the ranking of international tourists) is novel. It contributes to academic knowledge about the cultural and heritage aspects of material heritage. This means that it makes a contribution to the current knowledge of cultural heritage and city management.
Therefore this article contributes in several ways: first it contributes to scientific literature in the analysis of the modulation of cultural and heritage quality  perceived in the relationship between perceived value in general and satisfaction, considering ranges of low values and high values, secondly, provides the study of the characteristics of the cultural and heritage tourism through the visit to a cultural heritage and third place, provides conclusions to achieve or loyalty improve to tourists cultural and heritage.

Hypotheses development
The variables used to measure the loyalty of the visitors to the city of Cordoba were, (1) The expected cultural quality of The Citadel of the Catholic King, (2) The expected heritage quality of The Citadel of the Catholic King, (3) The perceived cultural quality of The Citadel of the Catholic King, (4) The perceived heritage quality of The Citadel of the Catholic King, (5) Comparing the expected quality and the perceived quality we can estimate the perceived value, (6) Satisfaction, as an emotional or cognitive response of the visiting tourist, and (7) The loyalty that tourists feel as a result of their attitude and contact with the experience in destiny.
The following (Fig. 1) hypotheses were formulated using the existing literature: The expected patrimonial quality (EPQ) positively and significantly influences the perceived patrimonial quality (PPQ). EPQ influences PPQ.

Hypothesis 3 (H3)
The perceived cultural heritage quality positively and significantly influences the perceived value as a whole. PCHQ influences PV.

Hypothesis 4 (H4)
The perceived patrimonial quality (PPQ) positively and significantly influences the perceived value (PV) as a whole. PPQ influences PV.
Hypothesis 6 (H6) The perceived cultural heritage quality (PCHQ) positively and significantly influences the relationship between perceived value (PV) and satisfaction (SATISFAC). PCHQ moderates PV which influences SATISFAC.

Hypothesis 8 (H8)
The satisfaction of the visitor to the cultural heritage positively influences their loyalty to it. SATISFAC influences LOYALTY.

Questionnaire and data collection
This study was conducted in Córdoba, Andalusia, Spain. Córdoba, as with its four UNESCO world heritage sites, has an extraordinary cultural and heritage offer, full of history, traditions and centuries of Arab, Jewish and Christian knowledge [64].  [65]. To ensure the validity of the questionnaire, the questions were based on previous similar studies [66]. The information was collected using a questionnaire together with a personal interview with each tourist after their visit to Citadel of the Catholic King. The questionnaire was prepared in November 2019. The validation of the survey and the construction of the questions is based on consolidated indicators from previous research [114,115]. Once the indicators had been obtained, a two-stage refining process was used. First, the indicators proposed by an investigator were analyzed, then the final survey was tested and verified by a manager at the Citadel of the Catholic King. This meant that the validity of the indicators in the constructs of the proposed research model were checked twice.
The questionnaire consisted of five sections, which were, (1) Questions about the expected heritage quality, perceived heritage quality and perceived value at The Citadel of the Catholic King, which includes the Arabic and Christian heritage of the Citadel, the conservation of the heritage site and the culture on display (2)  Tourists were informed of the academic purposes and the anonymity of the study before completing the questionnaire. Verbal consent was requested before the tourist completed the questionnaire. The anonymity of the respondent was guaranteed at all times. The questions in the first four parts of the questionnaire used a sevenpoint Likert scale, where one was the answer totally disagree and seven totally agree. Participation in the study was voluntary. The questionnaire contained 68 items, the sample data was collected through a personal questionnaire at different times of the day. The questionnaire was only given to tourists who had visited the Citadel of the Catholic King and its cultural heritage. The sociodemographic profile and the details of the trip were completed with closed questions. There were 499 valid questionnaires in the sample, which had a 95% confidence level and a sampling error of 3.25%.

Scales
Many authors have used in their studies the latent variables seen in Table 1.

Results
This section describes the results obtained after applying the structural equation models. First, a summary of the sociodemographic profile is shown, then the reliability and validity of the proposed model, and finally, the contrast of the eight hypotheses raised in the theoretical model. Table 2 shows the sociodemographic profile. 45.5% of those interviewed were women, compared to 53.3 men, and 1.2% did not indicate their sex. The questionnaires were answered mainly by young people between 30 and 39 years old (31.1%) who had studied at the university (39.7%).
The relationship between the observed and latent variables is shown in Table 3. The structural coefficients of the normalized model have also been calculated.

Analysis of the individual reliability of the items
In order to validate the proposed model, the validity and reliability of the reflective and formative constructs were analyzed.
The formative construct (loyalty) follows the recommendations according to Sarstedt et al. Regarding the convergent validity of the constructs, all the articles proposed in the model (Table 4) had a value > 0.707 [99].
With an analysis of the reflective constructs we can study the individual reliability of the elements with an analysis of the simple correlations of each observed variable with respect to the construct to which it belongs. Following Carmines and Zeller [100] maintaining the values of 0.707 are necessary for a variable to be accepted as part of a construct. Fifty-six of the sixty-six reflective elements have values > 0.707, therefore we can affirm that it has good reliability for the elements that make up each first-order construct. Once individual reliability had been studied, the validity and reliability of the constructs were analyzed [101]. The analysis consisted of evaluating collinearity and verifying that the value of the inflation factor variance (VIF) is > five. The results did not show collinearity in the variables used for the loyalty construct.
Likewise, Table 5 shows the analysis of the reflective constructs (expected heritage quality, expected cultural quality, perceived heritage quality, perceived cultural quality, perceived value and satisfaction) [102].
After this analysis, we can affirm that the results indicated a quasi-optimal individual reliability, since all the load values were above the minimum required threshold of 0.505 or 0.6 according to Fornell and Larcker [103] and Barclay, Higgins and Thompson [101].
In fact, the analysis revealed that the loads were statistically significant at 99.99%. Based on the results of these calculations, the measurement model was considered valid and reliable, which meant that the structural model could then be analyzed.

Analysis of the reliability of the first-order constructs
In order to confirm whether the observed variables rigorously and adequately measure the latent variable they represent, following Nunnally and Bernstein [104], the Cronbach's Alpha and composite reliability values are taken, checking if they are higher or equal to 0.7 ( Table 7). As all the values exceed this lower limit, the reliability of the first order constructs and their ability to measure Loyalty are confirmed. In our analysis, all the constructs exceeded a value of 0.9 (expected heritage quality, perceived heritage quality, expected cultural quality, perceived cultural quality, perceived value and satisfaction) which means that there can be no doubt about the constructs capacity for measuring Loyalty (Table 6).

Convergent validity
To evaluate the convergent validity of a set of variables, that is, if it explains one construct and not another, the mean variance extracted (AVE) is used, it is the acceptance criterion most commonly used in research to evaluate this concept (Table 7). Fornell and Larcker [103] determined that the minimum value of the AVE must be > 0.5, which means that the construct shares more than half of its variance with its indicators, the rest of the variance is explained by the error measurement [68]. The mean variance extracted is applicable to latent variables with reflective indicators. The nine Loyalty variables share more than 69% of their variance. Based on the results obtained, we can confirm that the measurements made are valid.

Discriminatory validity
To verify the discriminatory validity, in line with Barclay, Higgins and Thompson the cross-factor loads of indicators of a latent variable are checked against the indicator loads of the other latent variables (Table 8). Factorial loads must have greater value with their own variable than with the others evaluated in the model.
In addition, Henseler et al., in conducting simulation studies, demonstrated that the lack of validity is better detected by means of the HTMT ratio (Table 9). If the monotrait-heteromethod correlations (correlations between indicators that measure the same construct) are greater than heterotrait-heteromethod (correlations between indicators that measure different constructs) there will be discriminatory validity. Thus, the HTMT key figure must be below one (Gold et al. consider a value of 0.90).
In this sense, you can also use a resampling or bootstrapping to test whether the HTMT key figure is significantly different from one using the confidence interval. According to the criteria set, the confidence  intervals for the HTMT must be less than one, allowing this criterion to be validated (Table 10).

Hypothesis testing
To verify the goodness-of-fit of the proposed model, different parameters that address said goodness were calculated in Tables 11 and 12. Once all the constructs (reflective and formative) have been verified and validated as well as the goodness of the fit of the model, we can affirm that the results obtained are adequate and justify their validity and applicability.
Then the significance of the Path Coefficient of each hypothesis was calculated (Table 13). This showed that all the hypotheses are compatible (H1, H2, H3, H4, H5, H6, H7 and H8).
Hypotheses H1, H2, H3, H4, H5, H6, H7 and H8 were all supported. This means that there is a positive and significant relationship between the expected and perceived cultural quality, and the expected and perceived heritage quality. There is also a positive and significant relationship between perceived cultural and heritage quality and the overall perceived value. The perceived cultural quality has a positive and significant moderating influence on the relationship between perceived value and satisfaction of the visiting tourist. There is a positive and significant relationship between the satisfaction and loyalty of visitors at the heritage site. Figure 2 shows the values of the structural coefficients of the constructs. The limiting probability (p-value) of each one is used to validate the importance of the relationships between the constructs of the proposed model.

Discussion and conclusion
The satisfaction of the tourists who visit cities with cultural heritage is the determining factor for loyalty to the city. The tourists and visitors who would repeat       their visit also recommend and share their cultural and heritage experience with family, friends and co-workers. The public administration aims to preserve culture and heritage and maintain the sustainable value of the cultural heritage sites it manages. For private travel companies that have been trying for years to increase the number of visitors and the number of overnight stays, the loyalty of visiting tourists is the key to achieving their goal, which will also increase employment and the economy at the destination.
The analysis of the loyalty of tourists in the destination is important for obtaining excellence in tourist destinations. In this study, a model of structural equations was generated in which latent modulating variables of the main components that are part of satisfaction were implemented. The loyalty of the visiting tourist especially interested in the heritage and culture of the selected destination is analyzed. The results obtained in the study confirmed the hypotheses proposed in the theoretical    The main variables that influenced the choice of the destination city were the cultural and heritage quality that I expected to find when choosing to visit a city declared a World Heritage Site and the recommendation and loyalty of other visitors to the destination [105][106][107].
At the end of the visit to a world heritage city, the tourist evaluates the gap between the cultural and heritage quality that he expects at the time he prepares the visit, collects information and creates a preconceived idea of the destination and the one he perceives once arrives at the destination, has an experience through the professionals, the accommodations, the monuments and the heritage city as a whole. All this set of sensations and perceptions converge in the satisfaction of the visiting tourist, it gave a feeling of satisfaction that made the visitors recommend it to others as a tourist destination.

Hypothesis 1
The expected cultural quality of the visitor positively and significantly influences the perceived cultural quality. In Fig. 3, the sinusoidal behavior of this variable can be observed, and shows that for very high values of expected cultural quality there is no direct influence on perceived cultural quality. This result coincides with studies by [69,108]. Heritage managers must organize cultural activities at and around the heritage site. These activities increase the expected quality and therefore also the perceived quality. Visitors commented that they would like to see theatrical activities together with specialist guides at the destination to increase their satisfaction with the visit.

Hypothesis 2
The expected heritage quality of the visitor positively and significantly influences the perceived heritage quality. In Fig. 4 the sinusoidal behavior means that for very high values of expected heritage quality there is no direct influence on the perceived heritage quality. This confirms studies by [71,92]. This result suggests that the digital information available online and the information on display at the destination must be increased. The tourists interviewed in the study claimed   that there were not many references to this heritage site in terms of videos, photography, etc. and therefore they did not have any references for the expected quality of the heritage, which means that the perceived heritage quality was diminished.

Hypothesis 3
The perceived heritage quality of the visitor positively and significantly influences the perceived value of the destination as a whole. Figure 5 shows how the perceived value changes as the perceived heritage quality increases. These results coincide with other studies about heritage [71]. This means that managers of heritage sites should think about improving the maintenance at the site.

Hypothesis 4
The perceived cultural quality of the visitor positively and significantly influences the perceived value of the destination as a whole. Figure 6 shows the linear influence of perceived cultural quality on the total perceived value. This result coincides with the research of [109]. Heritage managers should be aware of the cultural quality of the heritage. A pile of stones means nothing without the culture that is attached to it. Therefore, heritage managers must make sure that the culture that is associated with a site is explained in the tourists visits.
Hypothesis 5 (Fig. 7a) The perceived cultural quality (PCHQ) of the visitor positively and significantly modulates the relationship between perceived value and satisfaction. Figure 7b shows that for a range of low moderating variable values (perceived cultural quality-PCHQ), in the face of unit increases in perceived value (PV), satisfaction (SATISFAC) increases more than proportionately; for a range of perceived cultural quality high values (PCHQ), in the face of unit increases in perceived value (PV) visitor satisfaction increases less than proportionately. Therefore, for both low values and high values of perceived cultural quality (PCHQ) the satisfaction (SATISFAC) of the visiting tourist increases in the face of increases in perceived value (PV). This matches the results found by other authors [68,73]. This means that increasing the quality of the heritage helps to increase the overall satisfaction of the tourist with the experience lived.
Hypothesis 6 (Fig. 8a) The perceived heritage quality (PPQ) by the visitor positively and significantly moderates the relationship between perceived value (PV) and satisfaction (SATISFAC). Figure 8b shows that in a range of low values of the modulating variable (perceived quality of equity-PPQ), in the face of unit increases in perceived value (PV) satisfaction grows more than proportionally. In a range of high values of the moderating variable, the relationship between perceived value and satisfaction is linear. This coincides with the results of studies by other authors [110,111]. That is, for both low values and high values of the modulating variable, satisfaction (SATISFAC) increases as the perceived value (PV) increases. We can say that in view of increases in the quality of the heritage, increasing the perceived value of the site increases the satisfaction of the tourist. Increasing the quality of perceived heritage helps to increase overall satisfaction with the tourist experience.

Hypothesis 7
The perceived value of the visit influences visitor satisfaction with the heritage site. Figure 9 shows that for values of − 1.8 and more the expected cultural quality has a linear and direct influence on perceived cultural quality and for very low values this behavior is reversed. This result has also been observed by other authors [105,112,113]. This result means that for the case being studied, and for cultural heritage in general, the visitor satisfaction can be increased by providing information about the history and the culture of the site. This can be done by having rooms dedicating to the cultures that inhabited the heritage site and explaining the significant milestones that took place there. A high entrance price without offering much cultural and heritage information is counterproductive for the perceived value.
Hypothesis 8 was also confirmed, showing the direct influence that visitor satisfaction in a destination has on tourist loyalty. Figure 10 shows the sine behavior of this relationship. Only in very low extreme values and very high satisfaction, it has no effect on the loyalty of the visiting tourist. For non-extreme values of satisfaction, in the face of increased satisfaction, there are proportional increases in tourist loyalty. The results showed that satisfaction, quality and expectations are positive factors that influence the visitor's decision to return, and recommend a destination. This coincided with the results of other studies [108,114]. This study confirmed the relationship between the high satisfaction of the tourist with the heritage of Cordoba and the willingness of tourists to return and recommend the Citadel of the Catholic King. This means that tourists' loyalty from cultural heritage to heritage is high, even though deficiencies that affected heritage expectations were also identified. These deficiencies included the lack of a website dedicated to the site and the lack of advertising. Deficiencies affecting tourist satisfaction were also found. These include the lack of specialized guides, the lack of theatrical visits, the lack of signs and indications and the lack of information on the culture and history of heritage. The latter affects loyalty. Although tourist satisfaction was generally acceptable, there were too many irregularities to achieve tourist loyalty.
This study outlines a reachable goal for the managers of the heritage in Cordoba so that the experience of visitors to the city can be maximized. This means that having visitors who are satisfied with their visit becomes one of the main reasons to exhibit the heritage. The results of this study agree with those found in previous studies [59,115] which indicate that satisfaction has a positive influence on loyalty to the destination, and encourages the tourist to return to the destination in the future and to recommend it to family and friends. This study states the most important factors to achieve loyalty of heritage tourists in a city which has been home to various cultures, and where there are different heritage sites that show the cultures that have inhabited the city.
This study identifies various factors which visitors to the city consider important when visiting a heritage site. The conservation and cleanliness of the heritage site were valued highly, as was the fact that the heritage sites are inside, or close to, the historical city center. In this way, Cordoba unites and links the tourist to the destination, which positively influences loyalty to the city. The brand created by this set of heritage sites, together with the perceived quality of the visit are factors which can be used to attract tourists who want to experience local culture by visiting these sites [95].
As general conclusions regarding the theoretical implications this research demonstrates, supports and verifies how variables in tourism affect each other. Research, search and study of new relationships and new variables becomes essential. Therefore, we must continue to study the different variables and their relationships in favor of the loyalty of the tourist in the destination. The practical implications for managers of this type of heritage is the importance of focusing on those who visit the heritage: that is, you have to think about all the tourist flows, motivations, moods, but always with the aim of giving a complete tourist experience and the highest quality for those who visit the heritage.
The limitations of this study were due to the sample which was used. The data was obtained from heritage tourists at The Citadel of the Catholic King, which means that the collected data is only valid for one type of tourist at one destination. It would be desirable to study elsewhere where kings stayed overnight and placed their base outside the capital. Another limitation is to perform the study at a time, being convenient to do it temporarily to see the evolution. Similarly, measuring loyalty as the intention of future behavior is a limitation of this study. Finally, loyalty does not always mean accurate behavior, the tourist can have amazing behavior [116].
For future lines of research, this study could be carried out in other destinations in Spain such as Madrid or Ibiza which have Alcazares of Catholic kings placed in tourist value, and the results obtained in this work could be compared with those of other destinations. Another possible line of research could be to perform this same study, but aimed at international tourists, in order to examine their motivations and thus establish a segmentation of the touristic offerings of the community according to the type of tourist, national or international.
On the other hand, this study does not deepen and concrete in the tourist experiences around the culture and heritage of a historical heritage asset and how each one affects the value of loyalty and recommendation, therefore, is a future line of research.