The movement of students through the higher education system is likely to vary by the characteristics of the students and by field and level of study. Aggregate models provide useful information towards the understanding of the dynamics of the system. However, they alone cannot provide the details necessary to understand the behaviour of particular groups of students. Thus, whenever possible a separate input-output model is estimated for each group of students defined by sex, field of study and level of course. The disaggregation is limited by the need to ensure that there are sufficient number of student movements from one state of the system to another from which transition proportions can be estimated.
The general model building procedure is described in Section 4.2. The results from fitting and estimating input-output models to various groups of students at the undergraduate and postgraduate level are given in Section 4.3 and Section 4.4. The groups at the undergraduate level are defined by field of study, and that at the postgraduate level by level of course. For each of these groups three models are estimated, one for all persons in the group and one each for males and females.
Two sets of results are reported. The first set contains the summary statistics that emanate from approximating the input-output model as a regular Markov chain. For example, estimates are derived of the probability of a student completing a course given the student's age at course commencement and the average time to completion. The second set of results are a summary of the projections of the number of students at various stages of the system until the year 2001. Only projections based on one set of assumptions are included. Future work will include sensitivity analysis and alternate models for projecting the number of commencing students.
The procedure described below is general in nature and applies to all the input-output models that are developed and estimated. As a first step to constructing an input-output model the transient states must be defined. We define these states by age and year of enrolment in course. To ensure that all transition proportions are defined there must be at least one student in each transient state in 1993.
Next, tables showing the age of students by the time, in years, that they have been enrolled are extracted from each of the DEET course enrolment files of 1993 and 1994 and the course completions file for 1993. Data in these three cross-tabulations provide the basis for constructing the input-output matrix.
Students in a given transient state in 1993 move to another transient state in 1994, complete the course or drop out. The only unknown quantity is the number who drop out. However, this can be calculated because the other two quantities are known. Careful attention has to be paid when considering movements to and from states defined by grouped ages and multiple year of enrolment, such as being between 25 and 29 years of age and in the sixth or higher year of enrolment.
In theory the above process should result in an input-output matrix with a non-negative quantity in each cell. In practice, it was found that some of the movements into the dropout absorbing state were negative. This means that the compilation of the enrolment and completions data files is not consistent. There are two possible causes for these negative values. First, it could be a data recording error, and resources are not available, at this stage, to confirm whether indeed this is the case. The second possibility, which is more likely, is that there is a variation across institutions in the way completions data are recorded. Anecdotal evidence suggests that some institutions record a student as having completed a course when that student has satisfied all the requirements for the course, while others only record a completion when the student applies for graduation. There may also be other reasons why there is a lack of consistency between the enrolment and completions data.
The negative dropout values are a nuisance because they prevent a complete analysis of the dynamics of the system. In general, the negative values were very small in absolute terms and were more often than not associated with movement from transient states defined by an older age group and year of enrolment which was usually more than 3. It was decided to perturb some of the completions figures in order to eliminate the negative dropout numbers. The procedure for perturbing, which is ad hoc in nature, is described in the appendix to this report. A consequence of the perturbation is that the time to completion statistics may be slightly deflated. Since the magnitude and the number of perturbation is small, we assume the bias will be negligible.
The next step in the model building involves the calculation of the matrix of transition proportions, Q, and the matrix R of proportions moving into the absorbing states. The model can now be estimated as outlined in Chapter 2.
Students were divided into eleven age groups. Associated with each age group are up to six year of enrolment categories. The resulting model consists of 51 transient states. These are marked by a cross in Table 4.1.
Although a typical state such as being a 20-year-old and in the second year of enrolment means precisely that, the last state in each row in Table 4.1 is to be interpreted differently. For example, being under 18 years of age and in the first year of enrolment means being under 18 years old and in the first or higher year of enrolment, and being a 22-year-old and in the sixth year of enrolment means being 22 years old and in the sixth or higher year of enrolment. This sort of aggregation is necessary to contain the size of the input-output model. It is unlikely that there will be many under 18-year-olds in their second year of enrolment, and even less likely that there will be many in the third or higher year of enrolment.
| Age | 1 | 2 | 3 | 4 | 5 | 6 |
| Under 18 | X | |||||
| 18 | X | X | ||||
| 19 | X | X | X | |||
| 20 | X | X | X | X | ||
| 21 | X | X | X | X | X | |
| 22 | X | X | X | X | X | X |
| 23 | X | X | X | X | X | X |
| 24 | X | X | X | X | X | X |
| 25-29 | X | X | X | X | X | X |
| 30-34 | X | X | X | X | X | X |
| Over 34 | X | X | X | X | X | X |
| Note: Across indicates that the transient state is included in the model | ||||||
Three models, one each for males, females and persons, were estimated for each of the following groups of undergraduates:
Models for students doing Agriculture, Education (O) and Medicine could not be estimated satisfactorily as there was too much inconsistency between the course enrolment and completions data. The consequence of the inconsistency was that the movement between 1993 and 1994 of a large number of students could not be reconciled. Australian students were considered on their own because they make up the bulk of the students and they are also the primary concern of this study. Models for all students were estimated for use as a benchmark for other models.
Probability of Completing Course
Table 4.2 shows the estimates of the probability of a student completing a course given his/her age at course commencement. For example, an Australian male student who starts as an undergraduate at the age of 18 years has a 58 percent chance of eventually completing the course, while an Australian female student of the same age has a 66 percent chance of completing. There is considerable variation in these probabilities between males and females, across age groups and fields of study. However, there is hardly any difference in the estimated probabilities for all students and just Australian students. This may be due to the behaviour of the overseas fee-paying students not being significantly different to that of Australian students, and even if the behaviour was different the number of overseas fee-paying students is relatively small to have much impact on the estimated probabilities.
If we concentrate on the results for the Australian group, there is a clear indication that females have a higher chance of completing a course than males irrespective of what age the course is commenced at. However, the difference in the probabilities between male and female completion of a course varies with the age at which the course is commenced. This difference can be as high as 10 percentage points, for example, if the course is commenced at an age of 20 years. In general, as the age at which a course is commenced increases, the chances of completing the course diminish for both gender groups. For both males and females the highest chance of completing a course is if the commencement age is 20 years, at which age the probability for a female completing is 79 percent and that for a male 69 percent. Among the females, those aged between 25 and 29 years have the least chance of completing the course, while the corresponding age for males is 30 to 34 years.
Table 4.2 Probability of Completing an Undergraduate Course by Age at Course Commencement
The comparison of the probabilities across fields of study reveal that, in general, Engineering students have the least chance of completing and Law the highest. If it was possible to model the behaviour of students in Medicine, then we would expect them to also have a very high chance of completing a course. Some estimates of the probabilities, if calculated on the basis of movements of only a small number of students, may not be all that reliable. For example, there are not all that many older females doing Engineering or Architecture, and hence, the estimates relating to these groups may be unstable.
In general, females have a higher chance than males of completing a course in Architecture, Arts, Education (I), Health and Science. In the other fields of study this pattern is not nearly as uniform across different course commencement ages. In Business the differences between the male and female chances are relatively small, with the maximum of only 5 percentage points for students commencing the course at the age of 20 years.
A person commencing a course in Business or Engineering at an age of 24 years or more has a 50 percent or less chance of completing it, and a person commencing a course in Architecture or Science at an age over 29 years has a less than even chance of completing it. In all other fields of study a person has better than even chance of completing a course, irrespective of the age of the student when the course was commenced.
Time in the System
The estimates of the mean and the standard deviation of the time spent in the system (number of years of enrolment in a particular course) by a student is given in Tables 4.3 and 4.4, respectively. A number of factors affect these estimates, but at this stage it is not possible to isolate, or measure, the impact of any one of them because of lack of data. The factors which are likely to have an impact are:
Table 4.3 shows that the mean time in the system varies by the age of the student when he/she commenced a course, gender and field of study. The mean time is 3.2 years for persons starting a course when they are 18 years old. In general, there is a steady decline in the mean time as the age at which a course is commenced increases, until around a course commencement age of 21 to 22 years when the minimum mean time in the system of 2.6 years is reached. A steady increase in the mean time can be observed as course commencement age increases above 23 years. This pattern repeats, more or less, for each field of study.
Australian male students spend, on average, a longer time in the system than females. This pattern of variation is not uniform across all fields of study. For example, the mean time in the system for male students in Arts who commence a course at the age of 23 years or more is shorter than that for females who commence at the same age. Architecture, Engineering and Law courses are of longer duration and this is reflected in the higher mean time in the system for students doing these courses.
The standard deviation of the time in the system also varies with course commencement age and fields of study. In general, the standard deviation is higher for students who begin their courses at an older age. A possible reason for this is that there are likely to be a relatively higher number of part-time students in the older age groups.
Time to Completion
The factors which are likely to have an impact on the mean time to complete a course are:
The mean and the standard deviation of the time taken by a student to a complete a course is given in Table 4.5 and Table 4.6, respectively. For example, it takes, on average, 4.4 years for an Australian male, commencing studies at the age of 18 years, to finish a bachelor's course, while for a female of the same age this time is 3.9 years.
For both male and female Australian students the minimum average time to course completion is achieved if the course is commenced at the age of 21 years. Overall, females take less time on average to complete a course than males, with the difference for some age groups, such as those commencing a course at the age of 21 years, being as much as 0.7 years.
Females who commence a course in Health at an age between 21 and 23 years take, on average, the shortest time to complete an undergraduate degree, while females who commence an Engineering course at the age of over 34 years take the longest time. However, there may not be all that many females over 34 studying a course in Engineering.
The standard deviation of the time to complete a course follows a pattern similar to that for the standard deviation of the time in the system-that is, it is higher for students who begin their courses at an older age.
Table 4.3 Mean Number of Years in the System for Undergraduates by Age at Course Commencement
Table 4.5 Mean Number of Years to Complete an Undergraduate Course by Age at Course Commencement