The theory of dynamic capabilities has some aspects related to its conceptualization that seem not to be completely clear, especially in relation to the factors that compose them. Teece (2007) proposed a new model to explain the dynamic capabilities concept detailing some factors that influence their development. This model is formed by some elements that belong either to the absorptive capacity (e.g., learning activities and skill accumulation, processes to identify target market segments, and so on) or the innovative capacity concept (e.g., processes to direct internal R&D and select new technologies, delineating the customer solution and the business model, etc.).

In the literature, we can find up to four main components of the dynamic capacities that, together, explain the mechanisms by which the advantages of internal resources are linked to the competitive advantage based on the external market of the companies: the adaptative capacity or flexibility, the absorptive capacity and the innovative capacity, which could be correlated (Wang and Ahmed, 2007); also, authors as Zollo and Winter (2002) consider in addition the learning capacity. Therefore, within this framework of dynamic capacities are located the absorptive capacity and the innovative capacity, together with flexibility and learning. However, some authors argue that the first two appear to be true components of the dynamic capabilities given that taking into account the adaptative capacity would be a tautological error since the definition of adaptative capacity is implicitly given in the definition of absorptive capacity (Teece, 2007; de Castro et al., 2009). Similarly, differentiating learning capacity from dynamic capacities when the absorptive capacity is taken into account seems to be another tautological error (de Castro et al., 2009), since the absorptive capacity process carries implicit the learning capacity (Cohen and Levinthal, 1990; Lane et al., 2001) or, in any case, the learning capacity would emanate from the absorptive capacity, being two similar and interrelated processes and even “interchangeable” terms (Cohen and Levinthal, 1989). For these reasons, a large number of researches have focused their interest in the dynamic capabilities of absorptive capacity and innovation.

In previous studies, authors like Brettel et al. (2011); Todorova and Durisin (2007); and Van den Bosch et al. (1999) suggest the importance of absorptive capacity (hereafter ACAP) to improve performance and build competitive advantages.

Hernández-Perlines and Yáñez-Araque (2015) provide a theoretical overview of the interlinking relationships between complementary concepts of training, as a starting point for the Intellectual Capital and other multiple interactions among Knowledge Management, Organizational Learning, ACAP, training and performance. Thus, according to these authors, training has an impact on results through the ACAP process. They conclude that ACAP is the necessary mechanism to turn training into tangible benefits.

The literature recognizes that both ACAP and innovation are two key dynamic capabilities in obtaining competitive advantages. What is more, several authors have studied the interrelationships between these two dynamic capabilities, confirming that firms with a higher level of ACAP invest more in Research and Development (R&D) and can therefore perform more innovations (Tsai, 2001; Mei and Nie, 2007; Aljanabi et al., 2014). “The ability of a firm to recognize the value of new external know-how and assimilate it (ACAP) is critical to its innovative capabilities” (Montazemi et al., 2012, p. 36).

In other words, absorptive and innovative capabilities are so closely related that, should a firm not have the necessary absorptive capacity, it will not get any benefit from innovation (Kostopoulos et al., 2011). Therefore, if—as Hernández-Perlines and Yáñez-Araque (2015) suggest in their seminal work—training only translates into tangible results through ACAP, the question arises whether also innovation plays a mediating role in obtaining revenue from training activities.

In the following sections, interrelations among the main concepts of this study will be specified based on the literature review, which will help state the research hypotheses.

Most studies examining the relationship between training and performance (Wright et al., 1994; Kamoche, 1996; Mueller, 1996; Barney and Wright, 1998; Bassi et al., 1998; Lee and Yang, 2000; Hitt et al., 2001; Tung-Chun, 2001; Ordonez de Pablos, 2004; Tharenou et al., 2007; Saks and Burke-Smalley, 2014; Úbeda-García et al., 2014) focus on the role training plays in the development of human capital (Schultz, 1961; Becker, 1964; Fahy, 2000; Úbeda-García, 2005) and organizational knowledge (Alavi and Leidner, 2001; Bollinger and Smith, 2001).

The literature has extensively analyzed the positive impact of training on organizational results. There are studies linking training and benefits, training and productivity, training and competitive advantage; and studies linking training to other aspects of business results (Marin-Diaz et al., 2014).

According to the above ideas:

Based on the above, firms could believe that the simple introduction of training is enough to improve their performance. However, without absorptive capacity, firms would not obtain the expected benefits from training. Some early studies in literature already approached the idea that absorptive capacity helps to explain how the transformation process of training occurs in organizational performance (Spence, 1973; Taubman and Wales, 1973), thus being a mediating variable. In this sense, ACAP is revealed as one of the key elements that strengthens the relationship between training and business results. The meaningful learning theory helps to better understand how training and ACAP are closely linked. Meaningful learning is the type of learning by which a student relates the new information to the one he already has, adjusting and reconstructing both information in this process (Ausubel, 1968). Meaningful learning is what leads to transference. Similarly, the dynamics of ACAP have a cumulative development, in the same manner as in the process of meaningful learning. Experience or performance in a learning task can influence and improve performance in a subsequent learning task (Ellis, 1965). Van den Bosch et al. (1999) study the determinants of ACAP, being the level of prior related knowledge one of its determinants. Cohen and Levinthal (1990) propose that ACAP affects a firm's expectation formation, allowing the company to more fully predict the nature and commercial potential of technological advances (path dependency of ACAP). As a direct consequence, by similarity with cognitive structures literature, they conclude that the accumulation of ACAP in a given period allows a more efficient accumulation in the next one. These authors see ACAP as a self-reinforcing process, through which ACAP enriches the learning capacity of the firm, and vice versa. They define the absorptive capacity of a firm as “prior related knowledge confers an ability to recognize the value of new information, assimilate it, and apply it to commercial ends” (p. 128). Finally, they consider a capacity to absorb knowledge requires a pertinent formal training.

Zahra and George (2002) present a fresh conceptualization of ACAP as a multidimensional construct representing the firms dynamic capacity to create and use knowledge relating to the firms ability to compete. According to them, ACAP comprises four dimensions split into two capacities: potential ACAP (acquisition and assimilation) and realized ACAP (transformation and exploitation).

By definition moderator effect happens if the intensity or direction of the relationship between a dependent variable and an independent one is affected by another independent variable (Hair et al., 2000) which has the ability of distorting this relation. The moderator variables are always independent variables. Thus, whereas a priori, in order to have a moderator effect the moderator should not be related neither with the independent nor the dependent variable (it only affects their relationship), in the mediation, the mediator is explanatory (mechanism that shows how or why the outcome is generated from the input) and it is necessarily correlated with both the dependent and independent variables. The mediator is internalized as part of the process that takes place between the independent variable and the dependent variable. To demonstrate mediation, one must establish strong relations between the independent and the mediating variable and, in turn, between the mediating variable and some dependent variable (Baron and Kenny, 1986). In this way, from the theoretical point of view, we justify a mediating effect if there are some references in the literature that relate our mediating variable to the independent variable (causally antecedent of the mediator), on the one hand, and, on the other hand, with the output variable (the mediator as antecedent of the latter). This is what happens in our case: ACAP is related to both training (training is the causal antecedent of ACAP) and to organizational performance (ACAP is the causal antecedent of organizational performance). This is what this study does, which allows you to state the following hypothesis:

H2. ACAP positively mediates the relationship between human resources training and organizational performance.

Mathieu and Taylor (2006) define mediation in terms of understanding how some antecedent variable (X = training) affects a criterion variable (Y = organizational performance) as transmitted through a mediating variable (M = ACAP). Smith (1982) proposed an ingenious solution to the problem of feedback in mediational chains. His method involves the independent variable to cause the mediator, the mediator to cause the dependent variable and the dependent variable not to cause the mediator. Models of this type are estimated by two stages (Baron and Kenny, 1986). This logic is in line with the so-called causal steps strategy or approach (Preacher and Hayes, 2008; Taylor et al., 2008). Accordingly, mediation hypotheses must split into two sub-hypotheses of relations that are sequentially taken in pairs (X → M; M → Y).

Indeed, the origins of the ACAP concept had already reported the first connection between training and ACAP: Cohen and Levinthal (1990) argued that the concept of absorptive capacity can best be developed through an examination of the cognitive structures that underlie learning.

Acquiring new external knowledge is the antecedent of ACAP (Van den Bosch et al., 1999; Zahra and George, 2002), whereas training is the input of ACAP (Cohen and Levinthal, 1990; Yahya and Goh, 2002). In this sense, training generates a certain type of knowledge flow that should be absorbed and processed by the firm's ACAP in order to obtain results. In other words, training represents a particular source of “raw material” for knowledge; whereas ACAP is the way this raw material is managed, like a filter mechanism or sieve through which knowledge emanating from training is transformed into results for firms. Or put another way:

H2a. Training positively affects ACAP.

Several studies focus on how business performance results from ACAP. In fact, empirical findings reveal a significant positive relationship between ACAP and business performance (Mowery et al., 1996; Mukherjee et al., 2000; Lane et al., 2001, 2006; Tsai, 2001; Zahra and George, 2002; Jansen et al., 2003, 2005; Todorova and Durisin, 2007; Bergh and Lim, 2008; Yeoh, 2009). Therefore, this study suggests the following sub-hypothesis:

H2b. ACAP exerts a positive influence on organizational performance.

According to the above ideas, Figures 1A,B represents the direct or original model (Model A: model with total effect), i.e., the relationship between training and performance, which is mediated by absorptive capacity (Model B: model of simple mediation of absorptive capacity).

This study has used the definition of innovation provided by Carnegie et al. (1993: p. 3) “something that is new or improved and done by the enterprise to create significantly added value either directly for the company or indirectly for its customers.”

While this definition—which was also adopted by Prajogo and Sohal (2006)—represents a broad view of innovation which contrasts with the specific and traditional concept based on R&D, it suits the purpose of this study.

There are some studies that positively consider training as a determinant of innovative capacity (Greenhalgh and Mavrotas, 1994; Baldwin and Johnson, 1995; Frazis et al., 2000; Huergo, 2002; Beugelsdijk, 2008; Bauernschuster et al., 2009). However, these budding studies do not have enough empirical evidence to address this issue in depth. Thus, an interesting contribution would be to better clarify the relationship between the above two business strategies (García Espejo, 2008; Dostie, 2014).

Much more addressed and demonstrated is the relationship between innovation and performance, where high levels of innovation are generally associated with high levels of performance (Armour and Teece, 1978; Rosenberg, 1982, 1994; Damanpour et al., 1989; Subramanian and Nilakanta, 1996; Crépon et al., 1998; Klomp and Van Leeuwen, 2001; Lööf and Heshmati, 2006; Rosenbusch et al., 2011).

There are even authors who have suggested the link between training and performance to be partially established through innovation (Laplagne and Bensted, 1999; Dostie, 2014).

Hence the following set of hypotheses:

H3. The relationship between training and organizational performance is positively mediated by innovative capacity.

Hernández-Perlines et al. (2016) argue that ACAP is a mediator in the relationship between training and performance. In other words, ACAP completely absorbs the effect of training and transforms it into a better performance. However, taking into account earlier views and literature, besides the direct effect exerted by ACAP on performance, there could also be an indirect effect, generated by the inclusion of innovative capacity as a second variable mediator of training and by the inclusion of a part of the effect of ACAP on performance. In theory, the inclusion of this second dynamic capacity (innovation) in the model should explain the greater variability in performance (dependent variable) as compared to the simple mediation model of ACAP.

Therefore, this study suggests a multiple mediation model to explain how training is transferred to performance through not only ACAP, but also innovative capacity, where ACAP would sequentially precede innovation (Cepeda-Carrion et al., 2012). In fact, some authors have already studied this sequence, demonstrating that ACAP and similar processes of absorption of knowledge positively influence innovation; and the latter, in turn, has a positive effect on performance (Tsai, 2001; Darroch, 2005; Wang and Wang, 2012).

In view of the theory and empirical evidence aforementioned, training is related to performance in the first place, through ACAP, and in the second, through innovative capacity. The integration of these two mediation models (ACAP and innovation) generates a model with a three-path mediated effect (Figure 1C, Model C) (Taylor et al., 2008; Hayes, 2009). Therefore:

H4. The dynamic capabilities of absorption and innovation sequentially mediate the relationship between training and organizational performance.

This mediation hypothesis supports the breakdown in H2a and H3b sub-hypotheses listed above and poses a new sub-relationship that has been widely advocated in the literature (Orlay, 1993; Tsai, 2001; Matthews, 2002; Mei and Nie, 2007; Kostopoulos et al., 2011; Cepeda-Carrion et al., 2012; Aljanabi et al., 2014) namely:

H4a. Absorptive capacity exerts a positive influence on innovative capacity.

This study analyzes a limited number of variables from a broader research project. All selected variables were measured based on scales validated in previous studies. In particular, the following variables have been considered according to the research objectives (the complete list of the measurement items can be found in the Appendix).

For both PLS-SEM analysis and fsQCA the sample comprises 112 valid cases. These cases contain no missing values for the variables under study. The primary database is based on a final questionnaire entitled Spain Survey of Training and Dynamic Capabilities of the Firm (STraDyCaF) (www.stradycaf.org), which was pre-tested and improved in an earlier phase of the study. Data collection took place between May and December 2014 via LimeSurvey Version 2.05+. This open-source web application that specializes in creating and distributing questionnaires and managing target populations was used to send participants (senior executives) a personalized email, together with a cover letter introducing the research project. To encourage responses and improve the response rate, an automatic and individualized follow-up of the respondent was scheduled so that 15 days after the initial survey has been sent, an automatic reminder email was sent to respondents who had not responded (Dillman, 2007); likewise, the questionnaire followed a responsive web design, whereby managers could respond using mobile devices, including a text-to-speech assistant similar to CATI (Computer-Assisted Telephone Interviewing) systems. The sample is representative and consists of Spanish firms from the entire country, having 50 or more workers, and operating in any sector except public administration, agriculture, fishing, activities of households and extraterritorial bodies. Therefore, the analysis is multisectorial in order to avoid the biases of sectorial studies for which other research has been criticized (Huselid, 1995). Sample selection used simple random sampling without replacement, extracted from Iberian Balance sheets Analysis System (SABI) database developed by INFORMA D&B in collaboration with Bureau Van Dijk, which allows the handling of general information and annual accounts of Spanish companies and Portuguese ones. The response rate was 7.18%, similar to the average of postal surveys in Spain where there is no strong tradition of collaboration with centers of research in Spain (Very et al., 1997; del Brío et al., 2002; Roca-Puig and Bou-Llusar, 2007). Another reason for the low response rate is the extension of the entire survey (230 variables) along with the difficulty of getting executive staff to spend their time responding it.

Table 1 summarizes the technical specifications of the study.

As mentioned earlier, this study employs two methods. Firstly, the PLS-SEM method (Partial Least Squares Structural Equation Modeling) is conducted.

Following Lowry and Gaskin (2014) p. 123, first-generation (1G) techniques are statistical methods, such as correlations, regressions, or difference of means tests (e.g., ANOVA or t-tests), that are well suited to simple modeling scenarios. However, 1G techniques offer limited modeling capabilities, particularly in terms of causal or complex modeling. The strength of SEM is in modeling. In particular, SEM allows for complex models that include latent (unobserved) variables, chains of effects (mediation), as is the case at hand.

SEM assesses in a single, systematic and comprehensive way (Gefen et al., 2011) the measurement model (relationships between latent variables and their indicators) and the structural model (the part of the entire model that describes relationships between latent variables; these relationships reflect substantive hypotheses based on theoretical considerations).

The holistic analysis that SEM is capable of performing can be carried out via one of two distinct statistical techniques (Barroso et al., 2010):

Methods based on the analysis of covariance (factors), i.e., Covariance-Based SEM (CBSEM);

The two approaches were designed to achieve different goals. CBSEM focuses on estimating a set of model parameters so that the theoretical covariance matrix implied by the system of structural equations is as close as possible to the empirical covariance matrix observed within the estimation sample (Reinartz et al., 2009). PLS works with blocks of variables (components) and estimates the model parameters by maximizing the variance explained by all the dependent variables (both latent and observed) (Chin, 1998b).

Going back to Lowry and Gaskin (2014), in choosing whether to use PLS or CB-SEM (both are two specialized forms of SEM), one should initially consider whether the research is exploratory (building or testing a new theory) or confirmatory (testing a well-established theory). For exploratory work, PLS should be selected. For confirmatory work, either technique may be used. PLS can provide advantages over 1G techniques and CB-SEM techniques for preliminary theory building. PLS is also especially useful for models that have higher-order constructs (in this study, three of all latent variables are multidimensional second-order constructs). PLS does not need to assume that the dependent variables conform to any particular distributions. As a result, it is robust to violations of multivariate normal distributions, whereas CB-SEM assumes data normality.

With this in mind, PLS is particularly interesting when theory development is in its early stage (Ringle et al., 2005; Gefen et al., 2011), when researchers adopt scales that studies have already checked or validated, when the analysis uses a relatively small sample (Reinartz et al., 2009) and/or non-normal data distributions (Lowry and Gaskin, 2014), or, finally, when models are highly complex (Hair et al., 2014) and with multidimensional constructs.

Other references in this line of research that justify using PLS are very recent advances (e.g., Henseler et al., 2014; Nitzl et al., 2016; Rigdon, 2016; Sarstedt et al., 2016; Nitzl and Chin, 2017).

For all the above reasons, PLS-SEM is suitable in this study. However, PLS-SEM is not free from limitations: causal symmetric relationships, net effects, etc. These limitations are largely attributable to the problems inherent in multiple regression analysis (MRA) and structural equation modeling (SEM) (Woodside, 2013; Skarmeas et al., 2014).

Secondly, the fsQCA method (fuzzy-set Qualitative Comparative Analysis) overcomes the limitations of the first method. This is a useful qualitative method for analyzing social phenomena with small data sets, allowing for a good management of uncertainty (Ragin, 2000, 2008). fsQCA is used for configurational and causal analysis, where different constellations of variables cause different outcomes. For this reason, we utilize fsQCA to make a post-hoc analysis to compare the results obtained by PLS. Our approach has been developed in the same way that El Sawy et al. (2010) to show a fsQCA-based configurational analysis. They followed the recommendations of Ragin (Ragin, 2008, Chapter 11). We are trying to demonstrate the influence of each variable in the outcome variable. The complete dataset is used as input to fsQCA to obtain the results.

For the PLS-SEM analysis, the software tool used was SmartPLS 2.0.M3 (Ringle et al., 2005). For the fsQCA analysis, the data analysis tool was FsQCA 2.5 Software (Ragin and Sean, 2014).

According to this research model (Figures 1B,C), H2, H3 and H4 represent mediation hypotheses, suggesting how or by what means an independent variable (training) affects a dependent variable (organizational performance) through mediating variables or mediators (dynamic capabilities of absorptive and innovative capacities) (Preacher and Hayes, 2008).

PLS path analysis allows to evaluate mediation models and tests mediation hypotheses, using the bootstrapping method (Hayes, 2009). As a result, the study uses the bootstrapping method to test mediation, i.e., the importance of indirect effects. Bootstrapping is a non-parametric re-sampling procedure for the analysis of both simple and multiple mediation. It imposes no assumptions about the distribution of variables or the distribution of the sample and can be applied to small sample sizes with more confidence. Therefore, this approach is perfectly suited for the PLS-SEM method (Hair et al., 2014). Authors like MacKinnon et al. (2004) have proven that this method leads to higher performance and higher levels of statistical power than traditional ways of testing mediation hypotheses, such as the Sobel test (Sobel, 1982, 1986), which requires a normal distribution of indirect effects in the sample along with other problems that prevent its application with PLS.

Therefore, mediation hypotheses (H2, H3, and H4) and sub-hypotheses deriving from bootstrapping are contrasted by PLS-SEM.

PLS-SEM is applied to each of the two mediation models suggested. Namely:

Model B: model of simple mediation of absorptive capacity. It tests whether training affects performance through absorptive capacity (mediation hypothesis H2).

Finally, with the purpose of ensuring that the introduction of a second mediating variable explains the relationship between training and performance better than the simple mediation model, both models (B and C) are compared to each other.

Figure 1A shows the total effect of training on organizational performance, where c is the path coefficient or beta weight of training on organizational performance. This total effect can be reached through a variety of direct and indirect forces (Hayes, 2009).

Specifically, Figure 1B (Model B) expresses the total effect of training on performance as the sum of direct and indirect effects. The estimation of the latter uses the product of path coefficients in the mediation chain. Thus: c=c′+a1b1; where the latter is the indirect effect and c′ is the direct effect of training on performance (H1) that controls the absorption capacity mediating variable.

Figure 1C (Model C) expresses the total effect of training on performance as the sum of direct and indirect effects. The estimation of the latter also uses the product of path coefficients, but this time for each of the paths in the mediation chain (Alwin and Hauser, 1975). Thus: c=c′+a1b1+a2b2+a1a3b2; where the last three are the specific indirect effects and the sum of all of them is the total indirect effect (Hayes, 2009), whereas c′ is the direct effect of training on performance (H1), which now controls both mediators (absorptive and innovative capacities) (Taylor et al., 2008). The advantage of this approach is that it is capable of isolating the indirect effect of both mediating variables, i.e., absorptive capacity (H2: a₁b₁) and innovative capacity (H3: a₂b₂). Moreover, this method allows to analyze the indirect effects that go through both mediators in a series (H4: a₁a₃b₂) (van Jaarsveld et al., 2010).

This section analyzes and compares research models based on Table 6 (results from PLS-SEM).

Table 6 summarizes relationships and direct effects on endogenous variables in each of the models and results from the evaluation of the three models through the PLS method.

Firstly, this table shows significant results of direct effects transferred from evidence shown in Table 5. Next, it shows explained variances of endogenous variables (R²), along with the contributions of the direct effects of each of their immediate antecedent variables or predictor variables to these explained variances. R² indicates the amount of variance of the construct that is explained by the model. Although Falk and Miller (1992) set at 0.1 the critical value of R², levels from 0.19, 0.33 and 0.67 are considered weak, moderate and substantial levels, respectively (Chin, 1998b). For comparison purposes, it is worth observing changes in the R² indicator, to determine whether the influence of a particular latent variable on a dependent construct has a substantial impact. These R² changes are calculated based on the relevance of the effect (f2) (Chin, 1998b). Likewise, Q2 indicators of endogenous constructs are reported. When these indicators are greater than zero, they indicate predictive relevance of the structural model for that particular construct. The GoF criterion represents a measure of overall fit of the PLS path model, which ranges between 0 and 1. Although there is no consensus on a cut-off value, (i.e., the greater than 0, the better fit), Wetzels et al. (2009) establish the following reference values for the fit size to comprehensively validate the model: GoFsmall = 0.1, GoFmedium = 0.25, GoFlarge = 0.36, in line with the effect sizes recommended for R² by Cohen (1988) (small: 0.02; medium: 0.13; large: 0.26). Similarly, 0.02, 0.15, and 0.35 f2 levels can be considered as indicating a small, medium or large effect (respectively) of a latent predictor variable at the structural level (Chin, 1998b).

These f2 indices, along with Q2 test and GoF criterion, allow comparing the different alternative models A, B, and C.

In view of the above results, the first observation is as follows: in general, based on an initial model with acceptable values (Model A), all parameters progressively improve (i.e., increase) from Model A to B, from B to C and therefore, from A to C, which is the most important increase. In other words, Model B is better than Model A, and Model C is better than Model B and much better than Model A. Not only Model C is the best model, but it also presents excellent values of structural assessment, as discussed below.

All three models present high levels of R² for all endogenous variables, where performance reaches the highest value (substantial) in Model C. The same applies to Q2 values of the dependent variable (performance): all Q2 values are greater than 0, where Model C reaches the highest value, thus becoming the model with the greatest predictive relevance for performance. And the same applies to GoF values, which are higher than 0.36 (cut-off value for large R² effect sizes) in the three models, where Model C is the model that presents the best overall fit. When the model does not include mediators (Model A), R² (0.33), Q2 (0.18) and GoF (0.49) are acceptable. When the mediating variable ACAP (Model B) is included, the explained variance of performance increases from 33 to 53.9%, with a wide significance of the effect (f2 = 0.46), which involves a significant improvement. Q2 values of performance also improve, increasing from 0.18 to 0.44, as well as GoF values, increasing from 0.49 to 0.62. When including the two mediating variables (ACAP and innovative capacity) (Model C), Q2 values of performance increase from 0.44 to 0.65, as well as GoF: 0.62 to 0.67. When including the second mediating variable (innovative capacity), ACAP transfers a part of its direct effect to performance through innovative capacity. This explains the greater amount of performance variance than before including innovative capacity. Regarding the explained variance of ACAP on performance, it decreases from 58.3% in Model B to 24.5% in Model C, although innovative capacity emerges here as a new net contribution (52.6%), much higher than the explained variance of performance. Similarly, although the R² of the ACAP in Model C is slightly smaller than that in Model B, it does not yield a significant f2, implying that the importance of this decrease is small and insignificant. In contrast, the explained variance of performance increases from 53.9% to 77.8%, with a very wide significance of the effect (f2 = 1.08), which involves a substantial improvement.

Based on the above, the significant improvement of Model C on Model B is confirmed. Therefore, it dramatically improves Model A too, by substantially improving Q2 of performance, GoF and finally, the explained variance of performance in more than 45 percentage points, with a substantial impact (f2 = 2.03).

fsQCA was run in order to generate the combinations of conditions leading to dorgfs. fsQCA calculates three solutions: the complex, the intermediate, and the parsimonious solutions. Following the recommendations of Ragin (Ragin, 2008, Chapter 11), the parsimonious and intermediate solutions will be used in this test (Table 8). As it can be seen, both solutions obtain the same combinations of conditions. The obtained model is informative since its consistency is above 0.74 (Woodside, 2013).

Table 9 shows two obtained solutions using the notation introduced by Ragin (2008). We want to emphasize that the parsimonious and the intermediate solutions are identical. For this reason, there are no conditions of the contributing causal condition type, neither present nor absent, in that table. The combinations from A₁ to A₃ have been obtained. A₃ reaches the maximum raw coverage and a great unique coverage (0.30). The other two combinations (A₁ and A₂) attain 0.06 and 0.09 as unique coverage. A₁ corresponds with the hypothesis H1, and shows that there exists a relationship between the variable condffs and the outcome in absence of the mediators. This relationship gets a low value of unique coverage that indicates a weak influence of the training in the organizational performance. A₂ reaches a value of unique coverage greater than A₁, which shows that innovation by itself has a greater influence than training on the organizational performance. Finally, A₃ is the more prominent combination to achieve a strong performance. It gets a value more than three times greater than the other two combinations, showing a big influence in the organizational performance. This last combination indicates that the three conditions are needed to achieve good organizational performance.

Results from conducting both methodologies (PLS-SEM and fsQCA) in the study of the same phenomenon validate and corroborate the suggested conceptual model. Results are convergent and more refined thanks to the contribution of each of these methods. This methodological dualism is already in itself a significant contribution to this research study.

Another novelty of this study is its contribution to literature in the field of absorptive and innovative capacities, by identifying a new role of absorptive capacity, as well as understanding the antecedent variables of innovative capacity that are related to training and their effects on organizational performance. Absorptive capacity fulfils the essential input function of innovative capacity. Therefore, a formal training model is suggested, with explanatory and predictive capacity, thus solving the gap in literature, which has systematically defended the positive relationship between training and business performance, but has failed to agree on an explanatory and predictive model regarding how that relationship occurs.

The most important conclusion of this study is that training translates into results if the dynamic capabilities of absorption and innovation mediate this process. Therefore, when firms plan their design of training programs, they should mobilize these dynamic capabilities and assess their level of current development, in order to decide the appropriate setting allocated to each dimension.

PLS-SEM extends the model to include absorptive and innovative capacities, thus obtaining the “true” relationship between training and performance. This relationship is systematically affected by the afore mentioned capacities, which in turn are explained by training. The fsQCA supports that organizational performance outcomes are explained by the configurations in a holistic causality fashion, rather than through any single condition. For example, we can infer that a certain “recipe” (i.e., A₃) results in a good organizational performance, but we cannot infer that training (or absorptive capacity or innovation) independently exerts a positive influence on the organizational performance. As a consequence, we can conclude that the three conditions are important to reach a good organizational performance highlighting the innovation among them. This conclusion supports the conclusions achieved with PLS. Therefore, training based on dynamic capabilities will guide and ease the design of appropriate human resources strategies, which will transform training into results. From all the absorptive capacities, realized capacity are necessary for potential capacities to be realized.

These findings have the following important implications for human resources managers:

Firms should establish training plans that consider absorptive capacity needs, not just training needs.

Finally, some limitations of this study are related to common problems of the dominant logic in research (Rong and Wilkinson, 2011; Woodside, 2011, 2013), cross-sectional surveys, one-shot, self-reports, Likert-scales, multiple regression analysis (MRA) techniques and structural equation models (SEM). Although the application of the fsQCA methodology has helped to alleviate these problems (Woodside, 2013), the following considerations for future research may be done.

Training may have delayed effects over time (D'Arcimoles, 1997; Murray and Raffaele, 1997). The mediation effect would need time to develop (training would increase absorptive capacity over time, which would increase future performance, again over time). In the same way, innovation may have delayed effects over time (Laplagne and Bensted, 1999; Kor and Mahoney, 2005; Kostopoulos et al., 2011; Dostie, 2014). However, two aspects must be pointed out: the low influence of the training effort made in a period on the results in the next period (Aragón-Sánchez et al., 2003), and that most empirical studies of the relationship between innovation and results are cross-sectional in nature (Hall, 2011), as is the case with most studies on training and results.

To explore this issue and reduce the common method bias, it would be advisable to carry out a time-lagged (multi-wave) data collection. One way is to create a temporal separation by introducing a time lag between the measurement of the predictor (for example, from actual data) and criterion variables (from a new data set), without compromising anonymity. This is achieved by using a linking variable that is not related to the respondents identity. This would be possible thanks to the support of the LimeSurvey software.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer TS and handling Editor declared their shared affiliation