Adjust resident and extension student credit hour ratios by residency and CIP level Adjust assigned housing meal plans and parking ratios Operational areas establish tentative goals for new students ID: 421015
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Slide1
Establish retention probabilities
Adjust resident and extension student credit hour ratios by residency and CIP level
Adjust assigned housing, meal plans, and parking ratios
Operational areas establish tentative goals for new students
Review revenues, student credit hours, and housing in light of tentatively established goals
Monitor progress toward goals, adjust model and report progress
Projections Flow Model
An Iterative Process
1
Operational areas establish goals
Establish new student goal forecasts/ ranges
Undertake new student goal setting and what if analyses with operational areas
2
3
4
5
6
7
8
9Slide2
Establish retention probabilities
1Slide3
Establish retention probabilities
Adjust resident and extension student credit hour ratios by residency and CIP level
Adjust assigned housing, meal plans, and parking ratios
Operational areas establish tentative goals for new students
Review revenues, student credit hours, and housing in light of tentatively established goals
Monitor progress toward goals, adjust model and report progress
Projections Flow Model
An Iterative Process
1
Operational areas establish goals
Establish new student goal forecasts/ ranges
Undertake new student goal setting and what if analyses with operational areas
2
3
4
5
6
7
8
9Slide4
Establish new student goal forecasts/ranges
2Slide5
Establish retention probabilities
Adjust resident and extension student credit hour ratios by residency and CIP level
Adjust assigned housing, meal plans, and parking ratios
Operational areas establish tentative goals for new students
Review revenues, student credit hours, and housing in light of tentatively established goals
Monitor progress toward goals, adjust model and report progress
Projections Flow Model
An Iterative Process
1
Operational areas establish goals
Establish new student goal forecasts/ ranges
Undertake new student goal setting and what if analyses with operational areas
2
3
4
5
6
7
8
9Slide6
Undertake new student goal setting and what if analyses with operational areas
3Slide7
Undertake new student goal setting and what if analyses with operational areas
Establish retention probabilities
Adjust resident and extension student credit hour ratios by residency and CIP level
Adjust assigned housing, meal plans, and parking ratios
Operational areas establish tentative goals for new students
Review revenues, student credit hours, and housing in light of tentatively established goals
Monitor progress toward goals, adjust model and report progress
Projections Flow Model
An Iterative Process
1
Operational areas establish goals
Establish new student goal forecasts/ ranges
2
3
4
5
6
7
8
9Slide8
Adjust resident and extension student credit hour ratios by residency and CIP level
4Slide9
Undertake new student goal setting and what if analyses with operational areas
Establish retention probabilities
Adjust resident and extension student credit hour ratios by residency and CIP level
Adjust assigned housing, meal plans, and parking ratios
Operational areas establish tentative goals for new students
Review revenues, student credit hours, and housing in light of tentatively established goals
Monitor progress toward goals, adjust model and report progress
Projections Flow Model
An Iterative Process
1
Operational areas establish goals
Establish new student goal forecasts/ ranges
2
3
4
5
6
7
8
9Slide10
Adjust assigned housing, meal plans, and parking ratios
5Slide11
Undertake new student goal setting and what if analyses with operational areas
Establish retention probabilities
Adjust resident and extension student credit hour ratios by residency and CIP level
Adjust assigned housing, meal plans, and parking ratios
Operational areas establish tentative goals for new students
Review revenues, student credit hours, and housing in light of tentatively established goals
Monitor progress toward goals, adjust model and report progress
Projections Flow Model
An Iterative Process
1
Operational areas establish goals
Establish new student goal forecasts/ ranges
2
3
4
5
6
7
8
9Slide12
Operational areas establish tentative goals for new students
6Slide13
Undertake new student goal setting and what if analyses with operational areas
Establish retention probabilities
Adjust resident and extension student credit hour ratios by residency and CIP level
Adjust assigned housing, meal plans, and parking ratios
Operational areas establish tentative goals for new students
Review revenues, student credit hours, and housing in light of tentatively established goals
Monitor progress toward goals, adjust model and report progress
Projections Flow Model
An Iterative Process
1
Operational areas establish goals
Establish new student goal forecasts/ ranges
2
3
4
5
6
7
8
9Slide14
Review revenues, student credit hours, and housing in light of tentatively established goals
7Slide15
Undertake new student goal setting and what if analyses with operational areas
Establish retention probabilities
Adjust resident and extension student credit hour ratios by residency and CIP level
Adjust assigned housing, meal plans, and parking ratios
Operational areas establish tentative goals for new students
Review revenues, student credit hours, and housing in light of tentatively established goals
Monitor progress toward goals, adjust model and report progress
Projections Flow Model
An Iterative Process
1
Operational areas establish goals
Establish new student goal forecasts/ ranges
2
3
4
5
6
7
8
9Slide16
Operational areas establish goals
8Slide17
Establish retention probabilities
Adjust resident and extension student credit hour ratios by residency and CIP level
Adjust assigned housing, meal plans, and parking ratios
Operational areas establish tentative goals for new students
Review revenues, student credit hours, and housing in light of tentatively established goals
Monitor progress toward goals, adjust model and report progress
Projections Flow Model
An Iterative Process
1
Operational areas establish goals
Establish new student goal forecasts/ ranges
2
3
4
5
6
7
8
9
Undertake new student goal setting and what if analyses with operational areasSlide18
Monitor progress toward goals, adjust model and report progress
9Slide19
Establish retention probabilities
Adjust resident and extension student credit hour ratios by residency and CIP level
Adjust assigned housing, meal plans, and parking ratios
Operational areas establish tentative goals for new students
Review revenues, student credit hours, and housing in light of tentatively established goals
Monitor progress toward goals, adjust model and report progress
Projections Flow Model
An Iterative Process
1
Operational areas establish goals
Establish new student goal forecasts/ ranges
Undertake new student goal setting and what if analyses with operational areas
2
3
4
5
6
7
8
9Slide20
Time Series and Forecasting
Time-series data describes the movement of a variable over time.Forecasting – Making quantitative estimates about the likelihood of future events which is developed on the basis of past and current information.Slide21
Stochastic Time Series Models
Regular least squares regression models are deterministic and do not rely on the randomness of the errors.Stochastic models are random process models, where we are assuming that the dependent variables are drawn randomly from a probability distribution.These models capture the characteristics of the series’ randomness.Slide22
Time Series Components
Trend – The upward and downward movement that characterizes a time series of a period of time. Seasonal Variations – Periodic patterns in a time series that complete themselves within a calendar year and are then repeated on a yearly basis.Cycle – Recurring up and down movements around trend levels (ex. business cycles).Irregular Fluctuations
– Erratic movements in a time series that follow no recognizable or regular pattern (what is ‘left over’ after trend, cycle, and seasonal variations have been accounted for).Slide23
Typical Forecast ErrorsSlide24
Serial Correlation
Common in time series data.Occurs when the errors corresponding to different observations are correlated.Violates the assumption that the errors are independent over time.Ordinary least-squares estimators will have lower efficiency.Detection:Durbin-Watson Test – Tests the null hypothesis that no serial correlation is present.Correction:
Generalized differencing.Adding an autoregressive (ρ) processSlide25
Stationarity
Stationary Time Series – A time series where the underlying stochastic process that generated the series can be assumed to be invariant with respect to time.If the characteristics of the stochastic process change over time then the series is nonstationary and the coefficients will not be fixed. Nonstationary processes can often be converted into stationary processes (typically through differencing).The residuals for a stationary time series should resemble white noise, with a mean of zero.Slide26
Sample Autocorrelation Function (SAC)
Measures the linear relationship between time series observations separated by a lag of k time units.Values close to +1 indicate that observations separated by a lag of k time units have a strong tendency to move together in a linear fashion with a positive slope, and values close to -1 move together with a negative slope.Behavior of the SACCut-Off – A spike at lag
k exists in the SAC if the value is statistically large.Regular peaks in the SAC are indicative of seasonality.Dies Down – SAC does not cut-off, but rather decreases in a “steady fashion.”A damped exponential fashion (with or without oscillation)A damped sine-wave fashionA fashion dominated by either one of or a combination of the two above
If the SAC either cuts off fairly quickly or dies down fairly quickly then the time series should be considered stationary.If there are spikes then the series may not be stationary at the seasonal levelIf the SAC dies down extremely slowly then the time series should be considered nonstationary.Slide27
ARIMA(p,d,q) Models
Objective is to explain the movement of a time series by relating it to its own past values and to a weighted sum of current and lagged random disturbances.Assumes stationarity and normally distributed error terms.Has a moving average component and autoregressive component.Moving Average Models – Used to smooth out short-term fluctuations in order to highlight long-term variation due to trends, cycles, and seasonality.Generated by a weighted average of random disturbances going back q periods.
Has a limited memory of past periods, which suggests that moving average models by themselves are poor forecasting models.Autoregressive Models - Tells us how much correlation there is (and how much interdependency there is) between neighboring data points in the series.Generated by a weighted average of past observations going back p periods, together with a random disturbance in the current period.If stationary then its mean must be finite and invariant with respect to time.Has an infinite memory, which means that the current value of the process depends on all past values, although the magnitude of this dependence declines with time.Slide28
ARIMA(p,d,q) Model Identification
Consists of a four-step iterative process:Tentative Identification – Historical data are used to tentatively identify an appropriate model.Estimation – Historical data are used to estimate the parameters of the tentatively identified model.Diagnostic Checking – Various diagnostics are used to check the adequacy of the tentatively identified model and, if need be, to suggest an improved model, which is then regarded as a new tentatively identified model.Forecasting
– Once a final model is obtained, it is used to forecast future time series values.Slide29
ARIMA(p,d,q) Model Identification (Continued)
Model
SAC
SPAC
Moving average of order q
Cuts off after lag q
Dies down
Autoregressive of order p
Dies down
Cuts off after lag p
Mixed autoregressive-moving average of order (p,q)
Dies down
Dies down
The first problem is to determine the degree of homogeneity
d
, that is, the number of times the series must be differenced to produce a stationary series. To do this we difference until the SAC shows stationarity.
To determine the orders of the autoregressive and moving average components we use both the SAC and SPAC (sample partial autocorrelation function). The SPAC operates in a similar manner to the SAC.
Spikes in the SAC are indicative of moving average terms.
The SPAC can be used for guidance in determining the order of the autoregressive portion of the process.Slide30
Seasonal ARIMA Modeling
We define lags L, 2L, 3L, etc. as exact seasonal lags.We define lags L-2,L-1,L+1,L+2,2L-2,2L-1,2L+1,2L+2, etc as near seasonal lags.Seasonal Moving Average Model of Order Q:SAC has nonzero autocorrelations at lags L,2L,3L,…,QL and zero autocorrelations elsewhere.SPAC dies does at seasonal lags L,2L,3L,…Seasonal Autoregressive Model of Order
P:SAC dies down at seasonal lags L,2L,3L,…SPAC has nonzero partial autocorrelations at lags L,2L,…,PL and zero partial autocorrelations elsewhere.To correctly identify a model we would use the SAC and SPAC at the nonseasonal level to tentatively identify a nonseasonal model, use the SAC and SPAC at the seasonal level to tentatively identify a seasonal model, and then combine the nonseasonal and seasonal models to arrive at an overall tentatively identified model.Slide31
Diagnostic Checking
The first step in diagnostic checking of the model would be to calculate the SAC for the residuals of the estimated ARIMA(p,d,q) model and determine if those residuals appear to be white noise. If they do not, then a new model specification can be tried.The Box and Pierce Q statistic and Ljung-Box statistic can both be used to test model adequacy.Can also pick the best model based on the basis of forecasting performance.We can do this by looking for the model with the lowest mean-square-error forecasts.
If the model has an autoregressive component stationarity can be checked by looking at the autoregressive parameters:First-order: -1<Ф1<1Second-order: Ф1 +
Ф2<1 and Ф2-Ф1<1 and -1<Ф2<1Slide32
Other Considerations
Time series data is usually nonstationary and therefore should be transformed.Even when the data appears stationary and the trend is not statistically significant it still might be worthwhile to difference the data in order to produce more accurate forecasts.Forecasting is an art as much as it is a science. Even though the SAC and SPAC may lead to a clearly defined model there may be other models that are more practical.The more data the better.Slide33
SAS vs. SPSS
SASMore fine grained control over modelingMore control over data manipulationBetter integration with other software
SPSSEasier to useEasier to read outputSlide34
Using Delaware Cost of Instruction (UNC Funding Model Example)
Student Credit Hours (SCH) per Instructional Position
Funding Category (CIP Codes)
Undergraduate
Masters
Doctoral
Category 1
708.64
169.52
115.56
Category 2
535.74
303.93
110.16
Category 3
406.24
186.23
109.86
Category 4
232.25
90.17
80.91
12-Cell Matrix of Instructional Level and Disciplinary Instructional Areas
CIP
Program Title
Funding Category
09
Communications
1
23
English Language and Literature/Letters
1
27
Mathematics
1
38
Philosophy and Religion
1
42
Psychology
1
43
Protective Services
1
45
Social Sciences and History
1
54
History
1
13
Education
2
16
Foreign Languages and Literatures
2
19
Home Economics
2
30
Mulit/Interdisciplinary Studies
2
31
Parks, Recreation, Leisure and Fitness Studies
2
52
Business Management and Administrative Services
2
03
Conservation and Renewable Natural Resources
3
11
Computer and Information Sciences
3
15
Engineering-Related Technologies
3
26
Biological Sciences/Life Sciences
3
40
Physical Sciences
3
44
Public Administration and Services
3
50
Visual and Performing Arts
3
51
Health Professions and Related Sciences
3
14
Engineering
4
51
Nursing
4Slide35
Student Credit Hour Projections
Applied averages of SCH to headcount by credit type and residence to projected headcounts to project future SCHs.Applied averages of SCH by funding category to overall SCHs to projected SCHs to determine projections by funding category.