This work uses the dataset from Aminer 1. As the release dataset version continues to update, it has become more popular and used for analyzing the information spread [33], studying the scientific influence [34–36], building recommendations in academic networks [37, 38], researching citation and cooperation networks [39–42], and developing the prediction in academic networks [43, 44]. This work adopts the 12th version of the dataset, which includes 4.9 million papers from 113,887 disciplines. The majority of papers contain the paper number, title, scientists, publication, citation, and field information [45]. Specifically, the field information is extracted from Mircosoft Academic Graph (MAG) [46], which contains field names and the weight w for fields of study. We selected 3,054,175 papers from 2000 to 2019, including 3,052,873 papers containing field information and 3,051,022 papers containing more than two fields information. For papers without two fields’ information, we consider the field information according to the fields’ proportion of the reference list, e.g., for paper P, the field A, B and C is 50%, 40% and 10% in the reference list, we attribute field A and B to the paper P.

The influence meaning of citations in different fields is different. In order to avoid the bias, field-normalization is needed. In this work, we introduce the method in [47], and use a weight of the paper given by the dataset to eliminate the impact of the field. Specifically, we define the citation C _f of paper p by, C f = ∑ i = 1 k w i w 1 + w 2 + ⋯ + w k ∗ C p C i ̄ (1) Here, k is the total number of fields covered by paper p, i is one of the fields (i = 1, 2, 3, …, k), and w _i is the weight of the i-th field; the field of research with weight w are given by the dataset; C _p is the number of citations we counted in the dataset; C i ̄ is the total number of citations received in the i-th field.

Our work explores the influence of interdisciplinary behavior based on large and small disciplines on scientists. Specifically, we extract the major and minor disciplines for the paper according to the field weight w and define the top 5% as the large discipline and the bottom 50% as the small discipline. Then, we map the relationship between each paper and large or small disciplines according to citations. For example, paper A has received 10, 5, and two citations in F1, F2, and F3 disciplines, respectively. We can determine that the major discipline of paper A is F1, and the minor is F2. Finally, according to the major and minor disciplines, all papers in the data set can be classified as the large discipline set P _l−l , the large cross the small discipline set P _l−s , the small discipline set P _s−s , and the small cross the large discipline set P _s−l .

To quantify the discipline distance of inter-discipline, we utilize the method proposed by recent literature to measure the research interest evolution [48]. Specifically, all papers are attributed to the first scientist, and we have counted all authors in the data set who have continuously published papers for more than 6 years, and the maximum “tolerance year” is 2 years. For example, a scientist who has continuously published papers in 2000 and 2001, and then continued to publish papers in 2003, is also considered as consecutive publisher. Then we consider paper series for each consecutive publishing scientist as sorted by the publication period. We select three papers at the beginning and the end of the paper series for each scientist, regarded as the scientific outputs of the early and later careers, respectively. It should be noted that the early and late career we defined is not the scientists’ career period, but the period before and after in a long time series. The dataset provides the discipline information representation of each paper, and we calculate the early and later discipline vector according to the discipline weight w. Finally, we can quantify the distance between the early and later career disciplines by calculating the cosine similarity of early and later career discipline vectors J. Figure 1 demonstrates an example of the specific calculation.

Different from correlation analysis, causal inference is not only based on correlation but also requires the temporal order of causality. Thus, correlation is only a necessary and insufficient condition for causal inference. In recent decades, causal inference has been dramatically applied in various fields, especially in finance [49] and education [50]. With the development of artificial intelligence [51–53], causal inference has new developments and applications [54, 55]. Currently, the most basic causal inference is to estimate the treatment effect by comparing the differences between the observation results of the control and treatment groups. the expected value of the treatment effect of all individuals receiving treatment, i.e., Average Treatment Effect on the Treated (ATT), can be defined as, A T T = E Y i 1 − Y i 0 ∣ D i = 1 (2)

where D _i = 1 means individual i is disposed, Y i 1 represents the observed value of individual i after treatment, Y i 0 represents the observed value of individual i in the control group. However, randomized controlled trials will consume a lot of time and resources, individuals participating in the experiment can only be grouped into the control or treatment group. Therefore, the current causal inference tends to analyze causal relationships from statistical data [56], e.g., Differences in Differences (DID) [57], Granger Causality [58], Propensity Score Matching (PSM) [59], Generalized Propensity Score Matching (GPS) [60], Instrumental Variable [61], and Regression Discontinuity Design [62]. Compared with the above causal inference methods, DID is more suitable for panel data [63]. Specifically, we conduct the scientists into treatment and control groups according to whether they have interdisciplinary behavior, and the regression equation for DID can be written as, Y i t = β 0 + β 1 t r e a t i + β 2 p e r i o d t + β 3 t r e a t i × p e r i o d t + ε i t (3)

where Y _it is a measurement of the influence (citations) of scientist i. treat _i is a dummy variable for group membership and ɛ _it is the error term. If scientist i has interdisciplinary behavior, then scientist i belongs to the treated group, treat _i = 1; otherwise, treat _i = 0. period _t is a dummy variable for the period. Assume that the time for the interdisciplinary is t, and the observe time t _i < t (|t − t _i | < = 2), period _t = 0, otherwise period _t = 1. The composite variable treat _i × period _t is a dummy variable, indicating whether the individual of the treated group is in the treated period, and the coefficient β ₃ represents the treated effects for interdisciplinary behavior. It is worth noting that DID requires the treated and control group to be entirely in accord with the parallel trend assumption before the treatment, i.e., the influence of scientists should increase at the same rate, whatever in treated and control groups. In addition, even if the parallel trend assumption is satisfied, it is still necessary to control features that may affect scientists’ influence, e.g., the career years of the scientist, the number of cooperation scientists, and the total number of publications. Thus, this work investigates the relationship between interdisciplinary behavior and scientists’ influence by utilizing PSM-DID. PSM transforms multi-dimensional features into one-dimensional propensity scores through a functional relationship, and matches individuals in the treatment group with the control group according to the propensity score. Specifically, we select four observable features (covariates) for 2 years before and after scientists’ interdisciplinary behavior: 1) the total number of publications; 2) the total number of disciplines of the scientist; 3) the career ages of the scientist; 4) the number of collaborators in each paper. Then, we calculate the propensity score of each scientist and conduct the match. The result of PSM provides supporting evidence for the parallel trend assumption. Finally, we consider citations and whether the scientist has interdisciplinary behavior as dependent and independent variables, respectively, and evaluate the treated effects of the treated group by utilizing DID.

Another goal of this work is to quantify the causal relationship between interdisciplinary distance and scientists’ influence, i.e., the treated effect of continuous variables. However, the usual causal inference models allow only binary variables, i.e., the treated variable = 0 (1) in the control (treated). Thus, we consider utilizing the GPSM to evaluate the treated effect of interdisciplinary distance. GPSM is an extension of PSM and is widely used in many different fields, such as economics [64], education [65], and medicine [66]. Furthermore, compared with the PSM, GPSM inherits the core concept and has similar covariate balancing properties. The most significant advantage is that it breaks the PSM constraint that the treated variable only allows binary variables. We consider the relative citation growth rate in early and late careers as the quantification of scientists’ influence (dependent variable). The independent variable is the interdisciplinary distance, and covariates are consistent in PSM.

Papers play an essential role in academic society, it is interesting to investigate the influence caused by interdisciplinary behavior. To investigate this, our work considers 2 years as the observed time (t _i ) and 3 years as the citation period to explore the citations of different types of interdisciplinary papers. Figure 2 compares the evolution of citations for papers with different interdisciplinary types. Compared with papers published in the large discipline (P _l−l ), papers published in the large across small discipline (P _l−s ) receive lower average citations (pink dot) in each interval. However, the papers in the small across large discipline (P _s−l ) receive more average citations (pink dot) than that in the small discipline (P _s−s ). On the one hand, it may be caused by the different citation dynamics in the inter-discipline and a single discipline, i.e., interdisciplinary papers need more than 3 years to reach peak citations. On the other hand, the large discipline cross to the small discipline receives less recognition and attention, and peers agree more with papers of the small cross to the large discipline.

In order to explore the underlying reasons for the different trends in the dynamic of papers with different types of interdisciplinary behaviors. We first investigate whether the interdisciplinary papers presented different citation dynamics from others by changing the citation period for papers. Figure 3 compares the citation period in three and 8 years in different disciplinary types. Papers published before 2008 are selected to avoid partial papers without 8 years citation period. When the citation period extends from 3 years (Figure 3A) to 8 years (Figure 3B), the citation of papers in the large cross the small discipline is less than that in the large disciplines, whatever three and eight citation period. Furthermore, citations of papers in the small cross the large discipline exhibit similar trends. This result indicates that the short- and long-term influence of interdisciplinary papers is similar to that of other papers, i.e., the increasing or decreasing of citations for interdisciplinary papers is irrelevant to the citation period. In particular, we further investigate the citation dynamics of papers in different disciplinary types published before 2008 in each year after publication. The average number of citation distribution is almost the same in different disciplines in Figure 4. We adopt the Z-test and Kolmogorov-Smirnov (K-S) test to examine distributions’ differences. Our null hypothesis is that the distribution of average citations of interdisciplinary papers is different from that of single-discipline papers. The result in Table 1 shows that P - value > 0.05, whatever P _l−l Vs. P _l−s and P _s−l Vs. P _s−s , which refuses the null hypothesis, and indicates that the citation dynamics of interdisciplinary and single discipline are the same distribution. It further indicates that interdisciplinary behavior will increase or decrease the citations, but the citation dynamics for interdisciplinary papers are similar to others.

One possible reason for the different trends in the citation of different types of interdisciplinary papers is the different recognition of scientific outputs. We analyze the citation sources for the different types of interdisciplinary papers within 8 years after publication in Figure 5. The disciplines with the most cited papers published by the large discipline (Figure 5A) and the small discipline (Figure 5C) are the large discipline (44%–46%) and small disciplines (41%–51%), respectively. It indicates that papers without interdisciplinary behavior have been widely recognized in self-discipline. Papers published in P _l−s (Figure 5B) receive more citations in the same interdisciplinary type (32%–36%), while papers in P _s−l (Figure 5D) are cited most in the small discipline (28%–33%). Compered Figure 5C with Figure 5D, despite the proportion of citations in the small across large discipline having decreased in the small disciplines, the proportion is the highest in different disciplines, i.e., the initial disciplines (the small disciplines) tend to accept the scientific outputs in the small across large discipline.

We further explore the influence of interdisciplinary behavior on scientists. Specifically, according to the interdisciplinary types and attributing each paper to the first scientist, we can define an interdisciplinary type for the scientist, including the large discipline scientist (S _l−l ), the large cross small discipline scientist (S _l−s ), the small discipline scientists (S _s−s ), and the small cross large discipline scientists (S _s−l ).

Since the dynamic distribution of citations in interdisciplinary papers is similar to that in others (Figure 4), we consider citations received within 3 years after publication to measure the scientists’ influence. Figure 6 compares the citations of scientists in different interdisciplinary types. In total periods, the influence of scientists in the large across small discipline (S _l−s ) is lower than that of scientists in the large discipline (S _l−l ) except in 2000. A different phenomenon is that scientists in the small across large discipline (S _s−l ) receive more positive impacts from interdisciplinary behaviors. This finding indicates that the risk of interdisciplinary behavior of large disciplinary scientists is more significant than the rewards. In contrast, scientists in small disciplines can enhance their influence through interdisciplinary behavior, which benefits the sustainable development of their careers.

Table 2 demonstrates the result of DID in the different interdisciplinary types. As shown in Table 2, the interdisciplinary behavior of scientists in S _l−s significantly reduces their influence, especially in 2004, nearly reduced 2.6 citations. However, scientists in S _s−l increase their influence on interdisciplinary behavior, and the most significant increase occurred in 2016, with an increase of about 7.2 citations. In general, our results exhibit a causal perspective for developing scientists’ careers, especially for scientists in the small discipline.

Interdisciplinary research is a tough career challenge for scientists, i.e., the trade-off between the new research field and influence [67]. Thus, the scientist may balance the risks and benefits of interdisciplinary behavior. To find out the “Sweet Spot” in the transition, this work further explores the relationship between interdisciplinary distance and scientists’ influence. Specifically, We consider J as the interdisciplinary distance and use the growth of citations to evaluate the scientists’ influence. The growth of citations is defined as G _c = (C _after − C _before )/C _before , where C _after and C _after is the citations for scientists in early and later careers, respectively.

Figure 7 compares the relationship between inter-discipline distance J and the growth of citations. We find that both long and short inter-disciplinary distances limit scientists’ benefits and that only appropriate interdisciplinary distances could enhance the influence of scientists. Furthermore, the interdisciplinary also may introduce negative influence, which displays a uniform distribution (inserted figure in Figure 7), which indicates that inter-disciplinary behavior may reduce the influence of scientists, whatever the interdisciplinary distance. This phenomenon suggests that scientists need to bear the risks through interdisciplinary behavior and turn an appropriate interdisciplinary distance if they want to increase their influence.

We further investigate the underlying relationship between interdisciplinary distance and scientists’ influence by utilizing GPSM. As shown in Figure 8, scientists’ influence increases have a non-monotonic behavior: it increases for small inter-disciplinary distances and decreases (i.e., J > 0.16) for large inter-disciplinary distances (i.e., J < 0.152). The result implies that interdisciplinary behavior is an effective way to enhance scientists’ influence. Furthermore, there exists a “Sweet spot” for the influence introduced by interdisciplinary behavior, that is, the interdisciplinary distance is 0.16.