With the continuous expansion of higher education and the rapid transformation of labor market structures, the proportion of non-traditional doctoral students has been steadily increasing. PhD students following a non-linear pathway represent a typical subgroup. Unlike those on a linear pathway, non-linear pathway students are those who experience a gap between completing their previous level of higher education and enrolling in a doctoral program (Zhuchkova & Terentev, 2023). In this study, We define them as PhD students who had formal working experience prior to enrolling in a PhD program. It is worth noting that, although this group of students constitutes a considerable proportion of the doctoral population (Offerman, 2011), the existing doctoral training system has long been designed around students with continuous educational trajectories[ (Gardner, 2008). Institutional structures, training schedules, and evaluation standards generally assume that doctoral entrants have followed an uninterrupted academic path prior to enrollment (Marine, 2020). This raises a critical question: to what extent can a training paradigm based on continuity effectively meet the academic development needs of students with non-linear educational trajectories?

Unfortunately, despite growing scholarly interest in non-linear educational trajectories among non-traditional doctoral students, research on this group's doctoral learning experiences and academic development remains severely limited. Existing studies have largely relied on qualitative approaches, using illustrative cases to document the academic trajectories and growth stories of students with non-linear pathways (Burgess et al., 2025; Jiménez & Escalante, 2017). Zhuchkova and Terentev ( 2023) made an initial attempt to compare publication outcomes between non-linear and linear pathway students. However, it should be noted that this study relied solely on chi-square tests to compare proportion differences, without controlling for potential confounding factors. Consequently, it is difficult to determine whether observed differences are attributable to the non-linear pathway itself rather than to other factors. These limitations underscore the need for a systematic and rigorous analysis of the academic development of students with non-linear educational trajectories, including cross-disciplinary variations, to provide more robust theoretical and policy insights.

In order to fill this gap, we utilize a large-scale dataset of 12,140 Chinese doctoral students and introduces Entropy Balancing to mitigate potential selection bias. By achieving covariates balance across personal characteristics and prior educational experiences, we establish a rigorous counterfactual framework to estimate the net effect of non-linear PhD pathway on students’ academic development.

Specifically, this study aims to answer the following research questions:

RQ1: What are the typical educational backgrounds and individual characteristics of students who pursue a non-linear PhD pathway?

RQ2: What is the effect of a non-linear path on PhD students’ academic development?

RQ3: To what extent do these effects vary across disciplines?

The objectives are threefold: (1) To characterize the students who pursue non-linear PhD pathways by examining their educational backgrounds and individual characteristics, thereby identifying the key factors associated with non-linear doctoral trajectories. (2) To quantify the effect of non-linear PhD pathways on academic development using a rigorous counterfactual framework. (3)To explore disciplinary differences in these effects to reveal how the impacts of non-linear pathways may vary across diverse academic contexts.

The findings contribute to the international literature on doctoral education by extending the analysis of PhD trajectories beyond linear pathways. Using evidence from China, it demonstrates how non-linear doctoral pathways shape PhD students’ academic development in ways that are both contextually embedded and internationally relevant. By foregrounding disciplinary heterogeneity, the study offers comparative insights that speak to the diversity of doctoral training systems globally. The study thus provides evidence relevant not only to national policy contexts but also to broader international debates on flexible doctoral training and diversified academic pathways.

2.1 Data The data come from the National Graduate Survey, which employed a stratified random sampling approach and covered universities across 26 provinces, autonomous regions, and municipalities in China, ensuring strong national representativeness. A total of 22,911 doctoral student questionnaires were collected. For the purposes of this study, only full-time, research-oriented doctoral students were retained. The dataset was further cleaned to address missing values and outliers in relevant variables, resulting in a final analytical sample of 12,140 doctoral students. 2.2 variables The independent variable is the non-linear PhD path. Doctoral students with prior formal work experience were assigned to the treatment group (coded as 1), whereas those without such experience were assigned to the control group (coded as 0). The dependent variable, academic development, is measured from both objective output and subjective dimensions. In terms of objective output, we consider students’ publication records during their doctoral studies. Specifically, a binary variable indicates whether a student has published in such journals, while a continuous variable captures the total number of high-quality publications. For subjective perception, we use four items to assess self-perceived academic competence development with a 5-point Likert scale. Higher scores on this scale indicate a greater perceived enhancement in academic competence. we also include some control variables such as personal characteristics, prior educational background, and the doctoral training process. 2.3 Analytical Strategy After completing data cleaning, the analysis proceeded in several steps. First, descriptive statistics and difference tests were conducted to preliminarily examine the mean differences in key variables between the treatment group (doctoral students with a non-linear path) and the control group (doctoral students with a linear educational path). Second, regression models were specified according to the measurement characteristics of the variables to identify the preliminary associations between non-linear educational trajectories and doctoral students’ academic development. Third, to address potential endogeneity arising from sample self-selection, Entropy Balancing was employed. This method imposes moment constraints on covariates that may bias the estimation of non-linear educational trajectories, generating a set of weights for each observation to achieve covariate balance between the treatment and control groups. These weights were subsequently incorporated into the regression models to examine the robustness of the baseline results. Finally, interaction terms were included to test for heterogeneous effects of non-linear path on academic development across different disciplinary groups.

Difference tests indicate that, among demographic characteristics, female students, those with non-agricultural hukou, non-only children, and students from urban areas are more likely to follow a non-linear pathway. In terms of educational background, overseas master’s graduates exhibit the highest likelihood of working before doctoral enrollment. Within domestic institutions, the prevalence of non-linear pathways follows a clear hierarchy, with the highest proportion observed among graduates from non-elite universities, followed by First-Class Discipline universities and First-Class universities. From a disciplinary perspective, PhD students in the humanities and social sciences are significantly more likely to choose non-linear path than those in engineering and sciences. The results of regression indicate a differentiated impact of non-linear path on PhD students’ academic development. In terms of research output, prior work experience is associated with a significantly lower amount of high-quality publications, amounting to only 92.1% of that of linear-pathway students . Consistently, the likelihood of achieving at least one high-quality publication is 9.2% lower for non-linear pathway students. In contrast, non-linear path exert a significant positive effect (β=0.044) on self-perceived academic competence development. Entropy-balanced regression confirm the robustness of the baseline regression results, demonstrating the dual effects of non-linear path, characterized by a publication penalty alongside a competence premium in doctoral development. Disciplinary heterogeneity analyses indicate that a non-linear path is associated with reduced probability and quantity of high-quality publications across economics, management and law, the natural sciences, engineering, and medicine, with the strongest negative effects observed in economics, management and law. By contrast, non-linear paths are positively associated with self-perceived academic competence growth in most disciplines except economics, management and law, with particularly strong marginal gains in agriculture and engineering.

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