Introduction

Expectancy-value theory (EVT) is one of the most influential frameworks in the context of achievement motivation (Eccles & Wigfield, 2020; Gaspard et al. 2017; Guo et al. 2016; Meyer et al. 2019) and central to the understanding of higher education students’ motivation and its relation to study success (Breetzke et al. 2023; Schnettler et al. 2020). EVT posits that individuals’ expectancies for success and their subjective values are the most proximal determinants of achievement, engagement and choice (Eccles & Wigfield, 2020). Empirical studies in the higher education context support this notion and suggest that students’ expectancies and study values are related to dropout intention (Breetzke et al. 2023; Schnettler et al. 2020), major retention (Robinson et al. 2019), grade point average (Breetzke et al. 2023; Robinson et al. 2019), exam scores (Part et al. 2020) or effort (Wu et al. 2020).

Recent research in the secondary-school context has found that in addition to the above-described first-order effects, expectancy-value interactions predict different measures of academic achievement and behaviour (Guo et al. 2016; Meyer et al. 2019; Nagengast et al. 2011; Song & Chung, 2020; Trautwein et al. 2012). However, study motivation might undergo significant changes as students transition from secondary-school to higher education (Benden & Lauermann, 2022; Fredricks & Eccles, 2002; Keyserlingk et al. 2022; Kyndt et al. 2015). For instance, higher education students may see their studies as more proximal and connected to their future careers. Alternatively, students may lower their expectancy for success to match the elevated demands of higher education. The many differences between the two educational stages highlight the need to extend the scope of existing research and broaden the application of expectancy-value interactions to the higher education context. To address this, we investigate the interactions between higher education students’ expectancies and their subjective study values in predicting dropout intention. This can clarify whether current findings from the secondary-school context are replicable across different educational stages and therefore reflect a generalisable prediction of expectancy-value theory.

The relevance of students’ dropout intention

Approximately one-third of higher education students drop out of their study program without graduating (OECD, 2018). Given the high costs that dropout has for individuals, institutions, and society, it is vital to analyse and understand its formation and the determinants behind it (Bohndick et al. 2018; Messerer et al. 2023; Schneider & Preckel, 2017). In this study, we refer to dropout as a gradual and long-lasting decision process (Bäulke et al. 2021; Mashburn, 2000), that ultimately leads to a situation where students leave their study program before they have obtained a formal degree (Larsen et al. 2013) – which includes both the decision to change one’s major and the decision to drop out of university entirely (empirical examples are Bäulke et al. 2021; Dresel & Grassinger, 2013; Messerer et al. 2023; Schnettler et al. 2020).

Because the final dropout decision is preceded by a long psychological process that includes different withdrawl cognitions (Bäulke et al. 2021; Mashburn, 2000), empirical research often investigates students’ dropout intention as the more proximal indicator (e.g., Breetzke et al. 2023; Dresel & Grassinger, 2013; Messerer et al. 2023; Schnettler et al. 2020). Furthermore, dropout without prior intention (e.g., involuntary dropout due to a medical or family emergency) does not represent a lack of motivation or success from students (Bean, 1985). Because they emerge with very few prior indicators and can not be predicted, involuntary dropouts introduce unexplained variance into subsequent empirical analyses (Bean, 1985; Bohndick, 2020).

Study motivation through the lens of expectancy-value theory

Expectancy-value theory is a very well-established approach to investigate motivation and decision-making in the educational context (Eccles et al. 1983; Eccles & Wigfield, 2020). According to EVT, study motivation is dependent on two factors. Students’ expectancies for success regarding the completion of their major, and students’ subjective study values, describing the extent to which they value their study subject (Eccles & Wigfield, 2020). Subjective study values are seen as a multidimensional construct, including four theoretically distinct components (Barron & Hulleman, 2015; Eccles et al. 1983; Gaspard et al. 2017): intrinsic values, attainment values, utility values, and costs. First, intrinsic values address the subjective interest and enjoyment associated with studying. Second, utility values refer to the usefulness that studying has for students’ short-term and long-term goals. Third, attainment values describe the personal importance of being successful at studying. Fourth, costs gather the negative consequences that are associated with studying, namely the loss of valued alternatives (opportunity costs), the amount of effort (effort costs), and the negative feelings associated with studying (emotional costs).

Related empirical research supports the multidimensionality of study values and indicates that intrinsic values, utility values, and costs, but not attainment values were related to dropout intention (Wu et al. 2020). Similarly, a longitudinal study on undergraduate students of math and law indicates that, intrinsic values, attainment values, and costs, but not utility values, were associated to students’ dropout intention (Schnettler et al. 2020). All in all, both theoretical and empirical research highlights the importance of expectancies and the different components of subjective study values as important predictors of higher education students’ dropout intention.

Expectancy-value interactions

Why interaction effects matter

In the early (Eccles et al. 1983) and most recent (Eccles & Wigfield, 2020) graphic depictions of EVT, expectancies and values are connected by a two-sided arrow. While at first, Eccles and colleagues searched for evidence that this connection is multiplicative, they eventually stopped including interaction effects, because they were so rarely significant (Nagengast et al. 2011). As a result of this, most empirical studies have assumed that the connection between expectancies and values is additive and that each uniquely and independently predicts educational outcomes (Guo et al. 2016; Nagengast et al. 2011). However, recent research has argued that the decision to omit the interaction effect may have been the result of insufficient statistical models and not a deliberate theoretical consideration (Nagengast et al. 2011; Trautwein et al. 2012). Especially the inability to correct for measurement error might have been a problem: The multiplication of two predictor variables also leads to the multiplication of their error terms. This can result in a type 2 error, where significant interaction effects may go undetected despite their existence (Meyer et al. 2019; Trautwein et al. 2012). Instead, recent research highlights two multiplicative models that result from Eccles and colleagues’ EVT and might better conceptualise the relation between expectancies, values and achievement-related outcomes (Guo et al. 2016). To highlight the different conceptualisations, we provide an illustrative comparison of the three models in Fig. 1 (in which expectancies, values and their interaction have the same size and are related to a desirable outcome). As all three models lead to different predictions in regard to achievement-related outcomes, differentiation between them can have important implications for motivational research and practice.

Fig. 1
figure 1

The (a) additive, (b) compensatory, and (c) synergistic model displayed in a three dimensional plot

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Figure 1a provides a graphical depiction of an additive connection between expectancies and values. Low expectancies and high values balance each other out and result in a medium sized outcome (and vice versa), while high expectancies and high values combine to a high outcome (i.e. low dropout intention). Figure 1b shows a compensatory interaction between expectancies and values. The model indicates that high values can buffer the adverse effects of low expectancies (and vice versa). In contrast to the additive model, this would indicate that students have a high outcome (or low dropout intention), as long as either their expectancies or values are high. Each is sufficient to attain a high outcome (i.e. low dropout intentions), but neither is necessary. Additionally, students who see little value in their studies and do not expect to successfully finish them, would report an outcome that is far lower than (i.e. dropout intention that far exceeds) the additive effects of low expectancies and values. Figure 1c indicates a synergistic interaction. Here, outcomes are maximised (i.e. dropout intention is minimised), when students expect to finish their studies successfully and at the same time attribute a high value to it. In contrast to the compensatory model, high values or high expectancies alone are not sufficient to motivate achievement-related outcomes (i.e. low dropout intentions). A student who expects to successfully finish their degree but attributes very little value to it (and vice versa) would indicate low outcomes (i.e. high dropout intention). Interestingly, synergistic interaction models have often been slightly rotated in prior research and indicated that students with low expectancies and high values report the lowest outcomes (Trautwein et al. 2012). Students may be especially frustrated because they see the value in studying, but do not expect to be successful.

Each of the above-described models indicate different predictions in regard to achievement-related outcomes. While these differences are by no means extensive, they are still important for our understanding of dropout intentions: Are students most likely to dropout when they see the value in studying, but do not expect to be successful (similar to Trautwein et al. 2012 for achievement) or do high dropout intentions require both low expectancies and low values? Can high values buffer the adverse effects of low expectancies (and vice versa), or should we put equal efforts into increasing both expectancies and values? This last question, for instance, might be especially important for students with high costs. Those students already experience a lot of strains and time for additional counselling or intervention sessions might be limited.

Empirical results on secondary school students

In recent years, statistical models have become more advanced and easily accessible. Latent moderated structural equation modelling (LMS) has allowed researchers to correct for measurement errors in latent constructs and can provide unbiased interaction effects (see the large-scale simulation study of Su et al. 2019). As a result, empirical studies have started to reinvestigate the interactions between expectancies and values and how they simultaneously influence educational outcomes. The first study in this context was conducted by Nagengast et al. (2011) who found that expectancies, values, and the expectancy-value interactions had significant positive effects on both secondary school students’ engagement and career aspirations. Their results indicate a synergistic multiplicative relation where engagement and career aspiration are especially strong when both expectancies and values are high. This reintroduction of the expectancy-value interaction was followed by various additional studies in the secondary school context. One by one, they extended the understanding of expectancy-value interactions to additional samples, value dimensions, outcomes and subjects (Guo et al. 2015, 2016; Meyer et al. 2019; Song & Chung, 2020; Trautwein et al. 2012).

The majority of studies in the secondary school context find results in line with Nagengast et al. (2011) and indicate small synergistic interaction effects that appear to be similar across the different value dimensions (Guo et al. 2016; Meyer et al. 2019; Trautwein et al. 2012). Very high academic achievement emerged only when both expectancies and values were high. Additionally, high values could not compensate for low expectancies (and vice versa). However, studies exhibit some inconsistencies across outcomes and subjects. Results on test anxiety and standardised test scores also showed compensatory interactions (Guo et al. 2015; Song & Chung, 2020), while interaction effects were significant for grades in English but not Mathematics (Meyer et al. 2019). Consequently, studies have called for additional research to investigate the generalisability of interaction effects across other outcomes, domains, age groups and educational levels (Guo et al. 2016; Meyer et al. 2019; Song & Chung, 2020). Research in the higher education context is especially scarce.

The higher education context

Recent longitudinal studies on self-determination theory indicate motivational changes as students transition from secondary school to higher education (Kyndt et al. 2015). Considering this, it seems reasonable to assume that expectancies, values and expectancy-value interactions might also vary between the two educational contexts. For instance, complexity, depth, and volume of coursework increases when entering higher education (Lowe & Cook, 2003; McGhie, 2017). As students adapt to these higher academic demands, they may adjust their expectancies for success and even lower the values they associate with studying (in order to help protect their self-esteem; Fredricks & Eccles, 2002). Additionally, students’ values are likely to change during their educational career and become more differentiated (Eccles & Wigfield, 2020), important (Lee et al. 2022), proximal, and firmly developed. For example, higher education students can freely choose and pursue the study discipline they value most, while secondary school students have almost no control over their study subjects. Being able to choose the most valuable discipline for oneself should lead to stronger and more differentiated values for higher education (as indicated by the strong disciplinary differences in Breetzke et al. 2023). Furthermore, secondary-school students may have a less concrete understanding of their future career paths and the job-related utility of their studies (Witko et al. 2005). Higher education students, on the other hand, often have clearer career goals and may perceive their coursework as important and proximal to their future careers (Breetzke et al. 2023; Kosovich et al. 2017; Witko et al. 2005). Lastly, students’ expectancies and values are often very highly correlated in the secondary-school context (e.g., 0.50 to 0.76 in Meyer et al. 2019; 0.58 in Nagengast et al. 2011; 0.48 to 0.75 in Trautwein et al. 2012). Here, values might be less firmly developed and more implicitly assumed when students expect to be successful in a subject (e.g., I enjoy math because I am good at it). In contrast, studies in the higher education context generally find much lower correlations between both constructs (0.03 to 0.16 in Breetzke et al. 2023; 0.27 to 0.32 in Kosovich et al. 2017; 0.06 to 0.16 in Schnettler et al. 2020). Values may be less associated with students’ expectancies, presumably because they are more proximal and firmly developed.

The many differences between the two educational stages have raised the question whether or not expectancy-value interactions in the higher education context exhibit different relations to achievement-related outcomes than expectancy-value interactions in secondary-school context (Guo et al. 2016; Meyer et al. 2019). While research on secondary-school students is plentiful, only very few studies have investigated latent expectancy-value interactions in the higher education context. Existing research has (a) been limited in its scope, investigating a single facet of study values at a timeFootnote 1 (Kim et al. 2022; Schnettler et al. 2023; Wu & Kang, 2021) and (b) set a different conceptual focus, both in terms of the methods used and contents investigated (e.g., B-ESEM, manifest interactions, interactions between the value components).

Two studies investigated the latent interactions between expectancies and different components of costs in the higher education context (Kim et al. 2022; Schnettler et al. 2023): Kim et al. (2022) found significant interaction effects between expectancies, emotional and opportunity costs which predicted students’ persistence. However, no interactions between self-efficacy, task-effort costs and outside effort costs were found. Schnettler et al. (2023) found (a) a small interaction effect between opportunity costs and expectancies which negatively predicted performance and (b) a small interaction effect for emotional costs and expectancies which negatively predicted dropout intention. Again, no interactions between expectancies and effort costs were found.

Interestingly, significant interaction effects differed across the investigated cost components, which highlights the need to address the full scope of value dimensions posited in EVT. In line with research on secondary-school students, Kim et al. (2022) found a synergistic interaction effect, indicating that high self-efficacy does not compensate for the negative effects of high costs. Schnettler et al. (2023) additionally found a compensatory interaction where high expectancies were able to buffer the negative effect of high costs in predicting dropout intention. A compensatory interaction can also be found in Y. Wu and Kang (2021), who investigated the interactive relation between expectancies for success and attainment values, and how they predict students’ foreign language performance via behavioural engagement using LMS. High attainment values were able to compensate for a certain extent of low expectancies in the context of language learning.

In conclusion, only a few studies find initial support for the significance of expectancy-value interactions. Building on their results, we see arguments for both the synergistic and the compensatory interaction in regard to dropout intention in the higher education context. On the one hand, results from the secondary-school context have indicated that situations associated with high values but low expectancies for success results in the lowest achievement-related outcomes (slightly rotated synergistic effect; Trautwein et al. 2012). The same might be true for higher education students’ dropout intentions: for instance, medical students who really want to become doctors, but during their studies realise that they are unlikely to succeed, might be particularly frustrated with their situation and be the most likely to drop out. On the other hand, if students enrol in university, they are not doing so with the intention to drop out. Developing that intention is a big change in attitude and might require both low expectancies and values (i.e. compensatory interaction). Therefore, additional research investigating expectancy-value interactions in the higher education context is needed.

Contributions of this study

While various studies have indicated that expectancy-value interactions are important predictors for academic achievement and behaviour, many of these studies acknowledge that their results are limited to a specific context and have called for additional research to investigate interaction effects across other outcomes, domains, age groups and educational levels (Guo et al. 2016; Meyer et al. 2019; Song & Chung, 2020). By investigating expectancy-value interactions in the higher education domain, we could clarify whether the current findings are replicable across different educational stages and therefore reflect a generalisable EVT prediction. Furthermore, our results can help to build a more comprehensive understanding of students at the verge of dropping out. With expectancy-value interactions as potential important predictors, results of additive models might misrepresent the relation between expectancies, values and dropout intention. For instance, results following Trautwein et al. (2012) would indicate that the students most at risk would be those with low expectancies and high values (they are frustrated because they see the value in studying, but do not expect to be successful). Providing a clearer picture on this matter could help to identify at risk students and might open additional avenues for the development of targeted interventions and educational practices.

Additionally, we tackle limitations that are highlighted in earlier studies on expectancy-value interactions and incorporate recent developments in EVT research. First, a number of prior studies on expectancy-value interactions have used measures of self-concept instead of measures of expectancies for success (Guo et al. 2016; Meyer et al. 2019; Nagengast et al. 2011). While both constructs are difficult to distinguish empirically (Eccles, 2009), they show some theoretical differences (Meyer et al. 2019). Second, recent research has shown that study values differ markedly across higher education disciplines (Breetzke et al. 2023). To account for disciplinary differences in students’ value profiles, we focus our investigation on humanities and social science students (who have shown comparable value profiles). Third, prior research on expectancy-value interactions has often noted that their results have been limited by the use of short (and sometimes relatively unreliable) instruments for subjective values (Guo et al. 2016; Meyer et al. 2019; Trautwein et al. 2012). We follow calls for further studies with “a larger set of items” (Trautwein et al. 2012) and “different value facets” (Guo et al. 2016) by using a measure (Schnettler et al. 2023) with eighteen items and six different dimensions of study values. This includes measures for opportunity, emotional, and effort costs, which additionally addresses the idea that costs have often been ignored in empirical research on EVT (Flake et al. 2015; Kim et al. 2022). Lastly, we use three-dimensional response surface plots to provide a graphical depiction of the estimated interaction models. Response surface plots are often used in research on interaction and quadratic effects with manifest variables (Bohndick et al. 2022; Humberg et al. 2019). Even though they are much less prominent for latent interactions in expectancy-value theory (two exceptions are Guo et al. 2016 and Schnettler et al. 2023), they can enhance the presentation and guide the interpretation of our results.

The present study

With reference to the above, the present study aims to investigate the interactions between students’ expectancies and their subjective study values in predicting students’ dropout intention. We build on expectancy-value theory and capture the multidimensional nature of study values, following the theoretical framework displayed in Fig. 2 (Eccles & Wigfield, 2020; Schnettler et al. 2020; Wu et al. 2020).

Fig. 2
figure 2

Expectancy-value theory (Eccles & Wigfield, 2020) as the theoretical framework employed in this study

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For our analyses, we use latent moderated structural equation modelling to investigate N = 1140 higher education students in Germany. Our research is guided by the following question: How do expectancies, values, and specifically the expectancy-value interactions predict higher education students’ dropout intention? Our main hypotheses of the study are:

Hypothesis 1

Following EVT, we expect the main effect of expectancies, intrinsic values, utility values, and attainment values to be negatively related to dropout intention and the main effects of opportunity costs, emotional costs, and effort costs to be positively related to dropout intention.

Hypothesis 2

Following prior research (Meyer et al. 2019; Nagengast et al. 2011; Trautwein et al. 2012; Wu & Kang, 2021), we expect the expectancy-value interactions to significantly predict dropout intention. Both a compensatory and a synergistic relationship (where main effects are comparable or stronger than the interactions) would be in line with modern EVT. In the secondary-school context, these interactions most often exhibit synergistic relations. Whether or not these results are similar in the higher education context remains to be seen and is analysed in an exploratory fashion. We expect interaction effects that are small to moderate in size, as cases in extreme conditions (e.g., high self-concept coupled with extremely low task values) are rather rare in empirical settings (Guo et al. 2016).

Method

Participants

The data used in this study is part of a larger research project that evaluates how different characteristics of university lectures, seminars, or workshops influence students’ perception of the vocational and civic relevancy of their studies. Between April 2022 and May 2023, participants were approached in lectures, seminars, career-service activities, and newsletters. Interested students could voluntarily participate in the study. Afterwards, they had the opportunity to enter a raffle with the chance to receive a small monetary compensation. To investigate our research question, we use data of N = 1140 higher education students from 12 German universities. The faculty with the most participants was sociology (12.3%) followed by political science (11.4%), history (7.6%) and philosophy (7.4%). Participants of our study had a mean age of 23.50 (SD = 5.05) years and n = 785 (68.86%) identified as female. The ethics committee of the faculty of education at the University of Hamburg approved the study prior to data collection. The corresponding code is: JB_22_024. The datasets used in the current study is available at: https://osf.io/zm2su/.

Research setting

This study is set in the German higher education context. As we focus on students of the humanities and social sciences, additional contextual information on these disciplines is required to make judgements about which findings may be context-bound and which may have general implications. Approximately 57% of subjects within the humanities and social sciences have no admission restrictions. Those who do are predominantly based on a-level grade in combination with external criteria such as foreign language skills, professional experience or voluntary work (Haase et al. 2022). In comparison to other disciplines, the humanities exhibit above-average drop-out rates of 41% (Heublein et al. 2020). Financial problems and a lack of study motivation are seen as the two big reasons for dropout from these disciplines (Heublein & Schmelzer, 2018). Even though public universities in Germany are almost completely free of charge (around 36€ a month; Kroher et al. 2023), students often rely on part-time jobs or support from their family or the social system (i.e., BAföG; Heublein & Schmelzer, 2018). Studies show that graduates have very diverse fields of employment (Zechner, 2020): Approximately half of the graduates follow typical careers and work in media, education or translation. The other half follows atypical careers such as business or information technology (Zechner, 2020). Even though the career entry often takes a bit longer, humanities and social science students are seen as generalists and all-rounders (Berg, 2009; Breetzke & Bohndick, 2024).

Measures

Validated and established scales from the literature were used to measure our variables of interest. Sample item, mean, standard deviation and Cronbach’s alpha of the measurement instruments can be found in Table 1.

Table 1 Sample item, mean, standard deviation and cronbach’s alpha of the measurement instruments
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Study motivation

We measured expectancies for success and subjective study values using the MoVE scale (Motivation: Values and Expectancies for Success) by Schnettler et al. (2023). Students’ subjective study values were measured using six subscales comprising three items each: intrinsic values, utility values, attainment values, opportunity costs, emotional costs, and effort costs. All items were measured on a 6-point Likert scale, ranging from 1 = strongly disagree to 6 = strongly agree.

Dropout intention

Students’ dropout intention was captured using four items on a 6-point Likert scale (1 = not true at all to 6 = completely true). While the original scale of Dresel and Grassinger (2013) contains five items, we dropped a single item (“I am sure that my current course of studies is the right one for me”) to increase model fit (after investigating item loadings and modification indices).Footnote 2

Control variables

We controlled for age, gender, first-generation status and grades. The status of first-generation student was assessed using their self-reported parental-education status. All students whose parents had not studied in a higher education institution were included as first-generation students. Students with at least one parent who had studied at a higher education institution were included as continuing-generation students. Grades were assessed as the current, self-reported grade point average in the respective study discipline. In most cases (93.72%) grades raged from 1.0 (highest) to 5.0 (lowest). Some disciplines use a 15-point system, which we recoded to match the grade system using university guidelines.

Statistical analyses

To investigate our research questions, we used a two-step estimation procedure for latent moderated structural equations following general guidelines (Maslowsky et al. 2015) and prior research on expectancy-value interactions in the secondary-school context (Meyer et al. 2019; Trautwein et al. 2012). As a first step, we estimated a structural model without the latent interaction term. In this model, expectancies and values were used to jointly predict dropout intention (Model 1). As a second step, we estimated a structural model with the latent interaction terms using the LMS approach to correct for measurement error in the predictor variables. In this model, expectancies, values and the expectancy-value interactions predicted dropout intention (Model 2). Both models were separately computed for each of the six dimensions of subjective study values (following Meyer et al. 2019; Trautwein et al. 2012). We employ the MLR estimator in Mplus (Version 8.5; Muthén & Muthén, 1998–2017), which uses standard errors and test statistics that are robust to non-normality. In all models, age, gender, first-generation status, and grade were included as control variables and were free to correlate with latent predictors and with each other. To present standardised beta coefficients, we standardised our data prior to analysis using the “standardize” command. A full information maximum likelihood (FIML) estimation was used to deal with missing values, while “type = complex” was used to account for the clustering of our data (students nested in courses). After calculating our models, three-dimensional response surface plots were estimated using the software R (R Core Team, 2023) and the package RSA (Schönbrodt & Humberg, 2021). They provide a graphical depiction of the estimated interaction models and were used to guide the interpretation of their results.

Results

First, we present the intercorrelation of all variables of interest in Table 2. Expectancy-value interactions are calculated using latent moderated structural equation modelling and were therefore not included in the correlation matrix. The correlations of dropout intention to expectancies and intrinsic, attainment, and utility values were negative, while the correlations between dropout intention and opportunity, emotional, and effort costs were positive. Correlations were particularly strong between dropout intention and expectancies (− 0.424), intrinsic values (− 0.527) and emotional costs (0.560). Correlations between the motivational variables itself were most often medium in size. However, both emotional costs and effort costs showed strong correlations to expectancies, intrinsic values, opportunity costs, and between each other (between 0.388 and 0.686).

Table 2 Intercorrelation of all variables of interest
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To investigate the interactions between expectancies and values in predicting students’ dropout intention, we then employed latent moderated structural equation modelling. In a two-step estimation procedure, a model with (Model 2) and without (Model 1) a latent interaction term was computed for each dimension of study values. Standardised beta coefficients and model fit indices are presented in Tables 3 and 4.

Table 3 Standardised beta coefficients and model characteristics of the latent (moderated) structural equation models predicting dropout intention
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Table 4 Standardised beta coefficients and model characteristics of the latent (moderated) structural equation models predicting dropout intention
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Model fit

In all cases, Model 1 showed a decent (CFI > 0.90 and RMSEA < 0.08 following Bentler, 1992; Byrne 2001) to good (CFI > 0.95 and RMSEA < 0.06, Hu & Bentler, 1999) fit with the data. However, we cannot compute common fit indices for Model 2, as they have not been developed for LMS models. To evaluate the fit of Model 2, we instead compare the relative fit of Model 1 and Model 2 using a loglikelihood ratio test (following suggestions of Maslowsky et al. 2015). The loglikelihood tests for intrinsic values, utility values, opportunity costs, emotional costs and effort costs indicate that Model 1 has a significantly lower model fit than Model 2 (see supplementary information). As Model 1 shows a decent to good fit with the data and has a significantly lower model fit than Model 2, Model 2 must be well-fitted and can be interpreted in the next section.

Main effects of expectancies and values

Results regarding the main effects of expectancies and subjective study values were in line with our first hypothesis: Expectancies (ranging from \(\:\beta\:=\:\) − 0.139 to \(\:\beta\:=\:\) 0.479), intrinsic values (\(\:\beta\:=\:\) − 0.452), and utility values (\(\:\beta\:=\:\) − 0.281) were negatively related to dropout intention, opportunity costs (\(\:\beta\:=\:\) 0.147), emotional costs (\(\:\beta\:=\:\) 0.568), and effort costs (\(\:\beta\:=\:\) 0.274) were positively related to dropout intention. While expectancies were the stronger predictor for dropout intention in the model for utility values, attainment values, opportunity costs, and effort costs - intrinsic values and emotional costs were the stronger predictor in their respective models. Against our initial hypothesis, attainment values showed no association with dropout intention.

Expectancy-value interactions

Results regarding the interactions between expectancies and values were in line with our second hypothesis: The interactions between expectancies and intrinsic (\(\:\beta\:=\) 0.135) as well as utility values (\(\:\beta\:=\:\) 0.168) positively predicted dropout intention, while the interactions between expectancies and opportunity costs (\(\:\beta\:=\:\) − 0.151), emotional costs (\(\:\beta\:=\:\) − 0.201), and effort costs (\(\:\beta\:=\:\) − 0.251) were negatively related to dropout intention. To further guide the interpretation of our results, the response surface plots presented in Fig. 3 were used as the graphical depiction of the estimated interaction models.

Fig. 3
figure 3

Response surface plot for the significant expectancy-value interactions. The plots depict the interaction between expectancies and (a) intrinsic values, (b) utility values, (c) opportunity costs, (d) effort costs, and (e) emotional costs

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The response surface models indicated a compensatory interaction effect that is in line with modern EVT (main effects were comparable or stronger than the interactions). In models (a) and (b) students’ dropout intention was highest, when both expectancies and values were low (the center of the plots). When looking at the corners on both sides of the plots, we see that high study values could, to a certain degree, compensate for low expectancies, while high expectancies were able to buffer the adverse effects of low values. In model a), the main effect of intrinsic values was substantially stronger than the main effect of expectancies (shifted to the left side), therefore high intrinsic values could compensate low expectancies better than the other way around. A similar picture could be found for the three cost models (Model c, d and e). When expectancies were low and costs were high, students showed the highest dropout intention (left side of the plots). Again, low costs could, to a certain degree, compensate low expectancies and vice versa. Standardised regression coefficients of the (significant) interaction terms were small to medium (between \(\:\beta\:=\) 0.135 and \(\:\beta\:=\) 0.252) in size. Furthermore, interaction terms explained between 0% (attainment values) and 3.5% (effort costs) of the variance, while the full models explained between 21.4% and 39.9% of variance in dropout intention. When assessing these results, researchers should keep in mind that the mean and standard deviation of dropout intention in this (and many other studies on dropout intention) is relatively low (M = 1.86, SD = 0.99).

Discussion

Recent studies on secondary school-students have investigated expectancy-value interactions and found that they predict different measures of academic achievement (Meyer et al. 2019; Nagengast et al. 2011; Trautwein et al. 2012). In this study, we broaden the scope of expectancy-value interactions to the higher education context, which has barely been investigated. For this, we used data of N = 1140 humanities and social science students and investigated the relationship between expectancies, subjective study values and the expectancy-value interactions in predicting dropout intention using a latent moderated structural equation approach and three-dimensional response surface plots.

In line with the first hypothesis of our study, we find that the main effects of expectancies, intrinsic values, and utility values were negatively related to dropout intention and the main effects of opportunity costs, emotional costs, and effort costs were positively related to dropout intention. Regarding hypothesis two, our results indicate significant interaction effects between students’ expectancies and intrinsic values, utility values, opportunity costs, emotional costs, and effort costs (controlling for age, gender, first-generation status and grade-point average). The associated response surface models suggest a compensatory interaction between expectancies and values. More specifically, high study values and low costs could, to a certain degree, compensate for low expectancies. Likewise, high expectancies were able to buffer the adverse effects of low values and high costs. However, when both expectancies and values were low (or costs were high), students showed dropout intentions that far exceeds the individual effects of both. Similarly, Y. Wu and Kang (2021) found that high attainment values could, to a certain extent, compensate for low expectancies in predicting behavioural engagement (which in turn was related to academic achievement). In addition, Schnettler et al. (2023), found a compensatory interaction between expectancies and emotional costs in predicting dropout intention. Against our initial expectation, we find no significant relationship between attainment values, the associated expectancy-value interaction and dropout intention. As there are some empirical studies that find similar results regarding the main effects (Breetzke et al. 2023; Wu et al. 2020), it seems possible that (achievement related) attainment values might be a less important facet for students’ dropout intention.

Taken together, our findings extend the influence of expectancy-value interactions into the higher education context, which has important implications for research and practice. Our results emphasise the detrimental effect that the combination of low expectancies and low values (or high costs) can have for students’ dropout intention. Higher education institutions may want to pay special attention to students who see little value in their studies and do not expect to successfully finish them, because they report dropout intentions that far exceed the individual effects of low expectancies and values (and is much higher than previous studies that do not consider their interactions would indicate). Furthermore, high values and low costs can act as a buffer against the adverse effect of low expectations of success on dropout intention (and vice versa). Interventions that enhance study values might therefore be an effective way to reduce the dropout intention of students with low expectancies for success that are unable to change. Research on utility-value interventions (often a writing task in which participants explain how the material they were learning is relevant to their lives) reports findings following a similar pattern (Durik et al. 2015; Hulleman et al. 2010): Students who had low performance or performance expectancies benefitted the most from the intervention, reporting a stronger increase in utility values, interest or performance. As such, these types of interventions may be particularly effective for student groups who need them the most.

Furthermore, the compensatory interaction indicates that in order to reduce students’ dropout intention, it may be sufficient to enhance either students’ expectancies or their values. This can be especially helpful and important for students with high costs. These students are already highly strained and may find additional counselling or intervention sessions burdensome, worsening their already problematic circumstances. In such cases, prioritising one (short) intervention over simultaneous addressing both expectancies and values might be more effective. This would not only acknowledge time constraints faced by students and institutions but also optimizes the effectiveness of interventions. Our results are particularly important, when we consider that the most prominent studies in the secondary school context find interaction effects of opposite direction (Guo et al. 2016; Meyer et al. 2019; Nagengast et al. 2011; Trautwein et al. 2012). These studies have found a synergistic interaction effect, indicating that high values alone were not sufficient to compensate for low expectancies and result in low achievement-related outcomes (and vice versa). Achievement-related outcomes were optimised when both expectancies and values are high. If we were to generalise these results to dropout intention in the higher education context, the students most at-risk would be those with low expectancies and high values (they may be frustrated because they see the value in studying, but do not expect to be successful; Trautwein et al. 2012). In contrast, our study highlights students with both low expectancies and low values as the most at-risk for dropout.

While we can only speculate, we want to give two potential explanations as to why these studies might find synergistic interactions, while we (and similar studies in the higher education context) find compensatory interactions. First, students’ expectancies and values are often very highly correlated in the secondary-school context (Meyer et al. 2019; Trautwein et al. 2012), while they were only moderately correlated in our sample and in studies from the higher education context in general (Breetzke et al. 2023; Kosovich et al. 2017; Schnettler et al. 2020). In secondary-school, values might be less firmly developed and rather implicitly assumed when students expect to be successful in a subject (e.g., I enjoy math because I am good at it). While in higher education values should be more proximal, firmly developed and therefore less associated with students’ success expectation (e.g., because the first career-related decisions have already been made). If values are more detached, students might be more likely to accept lower expectancies in favour of higher values – which would make compensatory interaction effects in the higher education context more prevalent than they are in the secondary school context. Studies on behavioural engagement speak for this notion, as they showed a compensatory effect in the higher education (Y. Wu & Kang, 2021), but a synergistic effect in the secondary-school context (Nagengast et al. 2011).

Second, the two result patterns might arise due to differences in outcome measures instead of differences in educational level. Dropout is often the final resort of students who are unhappy with their studies and as such, is an inherently extreme decision to make. It seems possible, that such extreme decisions (and outcome variables) are only considered when both expectancies and values are low – and can otherwise be compensated for. Outcomes less detrimental for the academic career (standardised test scores and examination results), might be more likely to exhibit synergistic or even insignificant relationships. A similar idea has been voiced by Meyer et al. (2019) who theorised that stakes associated with an achievement test might affect the interaction effects.

Limitations

We believe that our two explanations for the result patterns do not have to be mutually exclusive, but consider this inconclusiveness one of the greatest limitations of our study. Further studies replicating our results with additional outcome variables (e.g., standardised achievement tests, actual dropout) might help to better disentangle why differences between our results and those of other studies in the secondary-school context arise. However, single studies will almost always be fragmented, because of the many different value dimensions, outcomes and samples investigated. To obtain a more precise estimate of expectancy-value interactions, a meta-analysis with value dimension, outcome, and educational level as moderator would be a worthwhile project for future research.

The time of the semester in which students were surveyed varied depending on the cluster under consideration. Participants in lectures were surveyed at the beginning of the semester (April 2022, October 2022, and April 2023), while surveys in seminars and workshops were spread out through the whole academic year. As a result, our sample has no common starting point, but rather includes students’ assessment of expectancies and values across different situations and points during the semester. On the one hand, this should make our results less susceptible towards the impact of motivational declines commonly found in empirical studies (Benden & Lauermann, 2022; Robinson et al. 2019). On the other hand, it prevents us from interpreting out results in light of the specific situation they occur in.

As our study is the first to comprehensively investigate expectancy-value interactions in the higher education context, we made no prior hypotheses on whether interactions were synergistic or compensatory. Instead, this question was exploratorily investigated. Future research might want to replicate our results and test concrete hypotheses regarding the type of interaction effect. We would hypothesise that questions regarding dropout and retention exhibit compensatory interactions, while less detrimental outcomes like standardised test-scores, effort, or exam scores might instead exhibit synergistic interactions.

Conclusion

In summary, we find that expectancies, values, and the expectancy-value interactions significantly predict students’ dropout intention (controlling for age, gender, first-generation status and grade-point average). Rather than the synergistic interaction of prior studies in the secondary-school context, we find a compensatory interaction effect between higher education students’ expectancies and values: High study values and low costs could, to a certain degree, compensate for low expectancies. Likewise, high expectancies were able to buffer the adverse effects of low values and high costs. However, students who see little value in their studies and do not expect to be successful in them, report dropout intentions that far exceed the individual effects of low expectancies and values. These findings extend our understanding of expectancy-value interactions in predicting academic achievement and expands their importance into the higher education context.