Research on Cross-lagged Model of Career Planning Course and Employment Situation in Colleges and Universities

Using whole cluster sampling, students employed in five universities were selected as subjects and administered three consecutive questionnaires, with the first administration in December 2022 (T1), followed by follow-up surveys at six-month intervals thereafter (denoted as T2/T3, respectively), with the first one administered on-site and the second and third ones answered on-line to avoid the practice effect and to disrupt the order of the previous questionnaire questions. The first measurement obtained 350 valid subjects. The first measurement obtained 350 valid subjects, the second measurement obtained 342 valid subjects, and the third measurement obtained 338 valid subjects. After integrating the three measurements and removing all kinds of invalid subjects, a total of 320 valid subjects were obtained, and the attrition rate of subjects was 8.6%, and an independent samples t-test was conducted to compare the attrition of subjects at the time of the first administration with that of the overall subjects in terms of the career planning courses and employment status, indicating that the difference was not statistically significant. The difference is not statistically significant, indicating that the subject’s attrition is normal systematic attrition.

Tracking data refers to the measurements of identified groups of subjects on one or more variables at multiple points in time.The main methods for analyzing tracking data include one-way ANOVA, multivariate ANOVA, time series analysis, latent variable growth curve modeling, and multilayer linear modeling. Time series analysis was used in this study. Time series analysis is the theory and method of building mathematical models through curve fitting and parameter estimation based on time series data obtained from multiple measurements of the same subjects at multiple consecutive time points. Time series analysis is a commonly used predictive tool in statistics, which can not only quantitatively reveal the development and change law of a phenomenon, but also dynamically reveal the inherent quantitative relationship between a phenomenon and other phenomena and their regularity of change.

In terms of data processing, this study used SPSS 21.0 statistical software to perform common method bias test, descriptive statistical analysis, independent samples t-test, correlation analysis on the data obtained from this study, and cross-lagged analysis of two individual variables using AMOS 22.0 statistical software.

In statistics, Pearson’s correlation coefficient is widely used to measure linear correlation between two variables. It assesses the strength of the relationship between two vectors based on the covariance matrix of the data. Typically, the Pearson correlation coefficient between two vectors α_i and α_j is: (1) P(αi,αj)=cov(αi,αj)var(αi)×var(αj)\[P\left( {{\alpha }_{i}},{{\alpha }_{j}} \right)=\frac{\operatorname{cov}\left( {{\alpha }_{i}},{{\alpha }_{j}} \right)}{\sqrt{\operatorname{var}\left( {{\alpha }_{i}} \right)\times \operatorname{var}\left( {{\alpha }_{j}} \right)}}\] where cov(α_i,α_j) is the covariance, var(α_i) is the variance of vector α_i and var(α_j) is the variance of vector α_j.

The Pearson correlation coefficient can be applied to either the sample or the population. The absolute value of the Pearson correlation coefficient for both the sample and the aggregate is less than or equal to 1. In the case of sample correlation, a correlation coefficient equal to 1 or 1 corresponds to data points that lie exactly on a line. In the case of overall correlation, this corresponds to a line that fully supports the bivariate distribution. The Pearson correlation coefficient is symmetric: P(α_i,α_j) = P(α_j,α_i).

In this paper, the analysis is performed using a cross-lagged path model, the structure of which is shown in Figure 1.

Figure 1.

Cross-lag path model structure

Its characteristic is that the estimated cross-lagged path coefficients have a clear time-order relationship, which provides the principle of causal inference in epidemiology, “the cause comes before the effect comes after”:

Measurement model: (2) xit=μt+pit;yit=πt+qit\[{{x}_{it}}={{\mu }_{t}}+{{p}_{it}};{{y}_{it}}={{\pi }_{t}}+{{q}_{it}}\]

Structural modeling: (3) pit=αtpi,t−1+βtqi,t−1+uit;qit=δtqi,t−1+γtpi,t−1+vit\[{{p}_{it}}={{\alpha }_{t}}{{p}_{i,t-1}}+{{\beta }_{t}}{{q}_{i,t-1}}+{{u}_{it}};{{q}_{it}}={{\delta }_{t}}{{q}_{i,t-1}}+{{\gamma }_{t}}{{p}_{i,t-1}}+{{v}_{it}}\]

where x_it and y_it denote the two random variables for individual i at follow-up cross section t. μ_t and π_t denote the overall mean of variables x and y at follow-up section t. p_it and q_it denote the variation of variables x and y compared to the overall mean. α_t and δ_t denote the autocorrelation coefficients. β_t and y_t are the cross-lagged path coefficients, which indicate the magnitude of the interaction between the two variables. u_it and v_it represent the error terms. The cross-lagged path model assumes that the values of the variables taken by each individual fluctuate around an identical mean over time and that there are no non-time-varying individual differences. With the model transformation, the difference between the two cross-sections for variable y, for example, can be expressed as: (4) yit−yi,t−1=(πt+qit)−(πt−1+qi,t−1)=(πt−πt−1)+(δt−1)qit−1+γtpi,t−1+vit\[\begin{align} & {{y}_{it}}-{{y}_{i,t-1}}=\left( {{\pi }_{t}}+{{q}_{it}} \right)-\left( {{\pi }_{t-1}}+{{q}_{i,t-1}} \right) \\ & =\left( {{\pi }_{t}}-{{\pi }_{t-1}} \right)+\left( {{\delta }_{t}}-1 \right){{q}_{it-1}}+{{\gamma }_{t}}{{p}_{i,t-1}}+{{v}_{it}} \end{align}\] where (π_t–π_t−1) represents the change in the mean of variable y, and (δ_t−1)q_it−1+γ_tP_i,t−1 indicates how the variation in variable y is related to the values taken in the previous cross sections x and y. The cross-lagged path coefficient γ indicates the extent to which the variation in y can be predicted by x in the previous section. The model can be fitted based on repeated measurements at both cross sections.

The cross-lagged path coefficient, which is the basis for determining the time-series relationship between the two variables, consists of the following cases: if β_t = 0,γ_t = 0, there is no time-series relationship between x and y. If β_t ≠0,γ_t = 0, and the difference between the two coefficients is significant, then the two variables are in a unidirectional time-series relationship of y→x. If β_t = 0,γ_t ≠ 0, and the difference between the two coefficients is significant, then the two variables are in a unidirectional time-series relationship of x → y. If β_t ≠ 0,γ_t ≠ 0, then the two variables are in a bi-directional time-ordered relationship with each other.

SPSS 21.0 and Mplus 7.0 were used for data processing. There were three main steps: in the first step, descriptive statistics with correlation coefficients and partial correlation coefficients were analyzed for the measurement data. In the second step, cross-lag analysis was performed on the eligible measurement data. SPSS 21.0 was used for entry, descriptive statistics analysis, confidence analysis, missing data pattern analysis, correlation, and partial correlation analysis. Mplus 7.0 software was used to build a structural equation model with longitudinal data from three measurements for cross-lag analysis.

Three conditions need to be met to establish the cross-lag model.

In this study, career planning courses emphasize the importance of both self-perception and career perception.The descriptive statistics results for the three grades are shown in Table 4.

The scores of career planning courses and employment situation in the lower and upper grades increased gradually, in which the scores of career planning courses in the lower grades increased from 85.56% in the T1 period to 90.13% in the T3 period, and the scores of career planning courses in the upper grades increased by 1.8% from the T1 to the T3 period. The scores of the employment situation in the lower and upper grades were 95.36% and 97.12% in the T3 period, respectively, which were both significantly higher than in the T1 period. As a whole, it can be observed that the scores of career planning courses as well as employment situation improved from T1 (71.12±2.79 and 70.05±2.91) to T3 (72.92±2.59 and 72.61±2.71) for the lower and higher grades, respectively, in each period.

In order to further examine the development of college students’ career planning courses and employment, a repeated measures ANOVA was conducted with the students’ career planning courses and employment as the dependent variables in the three quizzes, and the results of the repeated ANOVA measures are shown in Table 5. Significant differences were found in the scores between the three measures of the career planning course for lower, upper, and overall students (F=47.525, p<0.001, F=12.556, p<0.001, and F=85.592, p<0.001). Post hoc comparisons revealed that scores on the career planning course increased significantly over time for all groups of college students, except for college students who did not significantly improve between T2 and T3. There was a significant difference in scores between the three measures of employment among lower, upper and overall students (F=30.448, p<0.001, F=222.158, p<0.001, F=122.378, p<0.001). Post-hoc comparisons revealed a gradual increase in the employment of college students over time. Overall, career planning courses for college students grew rapidly and essentially peaked in the second semester of the senior year, and similarly, career planning courses for college students grew slowly in the lower grades and accelerated in the upper grades in order to cope with post-graduation employment.

A simple correlation analysis was performed between college career planning courses and employment at time band points T1 and T3. Figure 2 shows the correlation coefficients between the two at both stages.

Figure 2.

The correlation coefficients of the two phases

As can be seen from the figure, the correlation coefficients of college career planning and employment situation at time point T1 and time point T3 are 0.575 (P<0.01) and 0.668 (P<0.01), respectively, which indicates that the two variables of college career planning and employment situation are significantly correlated, and the first condition of the cross-lagged analysis is satisfied. The stability correlation coefficient of 0.538 is basically the same as 0.479, and the synchronization correlation coefficient of 0.575 is basically the same as 0.668, and the second and third conditions of the cross-lagged analysis are satisfied. Meanwhile, it can be seen from the figure that the cross-lagged correlation r_cpt3ept1 (0.343) > r_ept3cpt1 (0.322), which preliminarily verifies the hypotheses H1 and H2, i.e., career planning is the antecedent variable of the employment situation. Using structural equation modeling techniques, restricting the loadings of the items on the factors at the point in time to be equal to the loadings of the items on the factors at the point in time, each of the fitted indexes is within acceptable limits for cross-lagging tests.