Nurses' retention and hospital characteristics in New South Wales, CHERE Discussion Paper No 52

NURSES’ RETENTION AND HOSPITAL CHARACTERISTICS IN NEW SOUTH WALES

3. ESTIMATION OF THE NURSING RETENTION MODEL

In this section of the paper we present results of probit regressions explaining the retention of public
sector RNs. As described above, the sample consists of 16,393 nurses working in the public sector in
NSW in 1996. The dependent variable is an indicator variable taking the value of one if the person is
observed working as a nurse (not necessarily in the public sector) in NSW in 1997. Regressors
include personal, job, and hospital characteristics as well as the unemployment rate in the region.
These explanatory variables are all given their 1996 values.

We begin by estimating specifications with many additional hospital characteristics and tested down.
The model presented below is parsimonious and performs as well as the larger models. Table 4
presents estimation results for two models: in one case hospital characteristics are included while in
the other, only the information from the NRB data is used.

One surprising finding is that the dummies for hospital type do not contribute significantly to the
explanatory power of the regression. This is true in models where these dummies are entered as
regressors as well as in heteroskedastic probit models, where the dummies for hospital type shift
the variance of the error. Specifically, let the probit model including the hospital characteristics
presented in Table 4 with a log likelihood value (LLV) of -7669.8, be the restricted model. The probit
regression including hospital type dummies as regressors generates a log likelihood value (LLV) of -
7664.2; hence a likelihood ratio test would suggest excluding the dummies from the conditional
mean of the retention probability ( _2 = 11.23, dof = 10, p-value = 0.340 ). Including the hospital types
as explanatory variables in the variance of the error¹³ generates a LLV of -7663.3; again the test
suggests excluding the dummies in the variance ( _2 = 13.05, dof = 10, p-value = 0.221 ). Including the
dummies in both the conditional mean and the variance is also rejected in favour of the model
presented in Table 4. Controlling for the observed hospital and nurses characteristics captures any
significant difference in retention across hospital types.

A comparison of the two models presented in Table 4 shows the contribution of the hospital
characteristics. A likelihood ratio test of the exclusion of the hospital characteristics suggests a
rejection of the restricted model ( _2 = 61.82, dof = 18, p-value = 0.000 ). The same is true when
hospital type dummies are added to both models ( _2 =6 0.00, dof = 18, p-value = 0.000 ). In what
follows we concentrate on the full model presented in Table 4, noting that the coefficients in the two
models are quite close suggesting little correlation between the included hospital variables and the
NRB variables.

Although the pseudo R2 values indicated in Table 4 are not very high, they are not unusual for this
type of data. A hit/miss table shows that the frequency of predicted probabilities above and below the
mean corresponds to around 65% of the observed retention values. The inclusion of the hospital
characteristics increases the proportion of correct predictions for the smallest and most difficult
group to model (i.e. the proportion correctly predicted for quitters increases from 54.5% to 56%).

The coefficients in Table 4 reveal that the probability of retention is reduced (the probability of quitting
is increased) significantly by a registered nurse being male and UK born. The retention probability is
significantly increased by being foreign born (other than UK or NZ), older, working longer hours,
having post basic qualifications, having been promoted beyond entry level (but not in a managerial
job), being registered longer and engaged in surgical activity.

13 The variance is specified as the squared exponential of a linear function of the dummies.

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