APPENDIX 3 - TECHNICAL NOTE - METHODOLOGY
INTRODUCTION
The data used for this analysis were collected as part of the 2006-07 Natural Resource Management Survey. The main purpose of the Natural Resource Management Survey is to provide an overview of the Natural Resource Management (NRM) activities undertaken by agricultural businesses in relation to the management of weeds, pests, land and soil.
For the 2006-07 NRM survey, questions with a climate theme were asked including whether there was a perception, by the land manager, that the climate affecting the holding had changed, and the experience, and the impact, as well as the modification of the management practices in response to the perceived change in climate.
As the main objective of the survey was to collect data for measuring the NRM activities of farm businesses, not all major factors potentially influencing farmers' perception of changes to climate are available for inclusion in this analysis. This, to a certain extent, limits the analysis. For example, it is possible that farmers with a greater level of education attainment may be more likely to perceive and react to a change to climate yet data on the educational level of farmers was not collected in the survey.
The 2006-07 NRM survey is a subsample of the Agricultural Survey which uses a stratified sample survey design. To account for design features of the survey data, the design variables (State, Industry and Estimated Value of Agricultural Operations) were included in the logistic model.
The analysis included data from 14,800 respondents to the 2006-07 NRM survey, representing 71% of the sample.
Regression analysis was used to enable the relationship between factors that affect the land managers perception that climate on the holding has changed to be fully assessed. This technique is used to measure association between variables rather than determine causality. For example, if a relationship exists between the perception of changes to climate and farming experience and perception of changes to climate and the location of farm business, then use of this methodology allows consideration of the effect of one of these characteristics (e.g. changes to climate and farming experience) after adjusting for the effect of the other (e.g. changes to climate and location of farm business) which is not possible by using simple 2-way tables.
The specific type of regression analysis used was logistic regression. Logistic regression describes the relationship between an outcome variable which is binary (zero-one) and a set of explanatory variables (which may be categorical or continuous variables). To describe these statistical relationships, the odds ratio is used. The odds of an event occurring is the probability of the event occurring relative to the probability of it not occurring. The regression estimates the odds of an event occurring given a set of explanatory variables.
In this analysis, the "event occurring" relates to the affirmative response to the perception that climate affecting their holding has changed. Thus the outcome variable has two distinct categories: perceiving a change to the climate affecting their holding; and not perceiving a change to the climate affecting their holding.
THE LOGISTIC REGRESSION MODEL
In this analysis, the logistic regression model can be used to estimate the odds of having the perception of change to the climate given a set of factors. The model is expressed in the form:
where p is the probability of having the perception of a change in climate, and (1-p) is the probability of not having the perception of a change in climate. X1,X2,...,Xk are explanatory variables. The intercept is denoted by 
and the model coefficients are denoted are denoted by 
The SAS procedure, Proc Logistic, was used to produce estimates of the regression parameters and to obtain results required for model diagnostics. The survey weights are not included in the estimation procedure, due to the inclusion of the design variables.
Perception of a change in climate was determined from the response to the question: "Do you consider the climate affecting your holding (average temperature, rainfall patterns, evaporation, etc.) has changed". The response variable takes a value of one if the respondent considers that the climate affecting their holding has changed and takes a value of zero if they have not perceived a change.
The explanatory variables for the logistic regression were determined by applying the stepwise selection procedure. All the design variables were included into the model regardless of their significance to the model.
EXPLANATORY VARIABLES AND BASE CATEGORIES
The logistic model expresses results relative to a base category. The choice of base category took into account the feature of the category (e.g. being average or typical) and the likely significance of other categories relative to it. Using different base categories would not have changed any fundamental conclusions, only the relativities between explanatory variables.
In the model, the explanatory variables are a set of land manager and farm business characteristics. Variables were chosen for inclusion in the model based on their potential association with the perception of change to climate. For example, those respondents with more farming experience are perhaps more likely to perceive there has been a change in climate on their holding, thus the number of years managing the farm was identified as a variable for inclusion in the model.
For each explanatory variable the model expresses results relative to a base category. For example the land manager of an agricultural business with a farm area of 3,000 hectares is neither more nor less likely to perceive a change in climate than a land manager of an agricultural business of the base farm size of less than 50 hectares.
INTERPRETATION
The estimates from the logistic regression model are expressed as an "odds ratio" and describes the "odds" of an event occurring for a particular category relative to the "odds" of the same event occurring for the base category (after taking into account the effects of all the other explanatory variables included in the model). It should be noted that the ”odds ratio” is not equivalent to the probability of the event relative to that of the base category.
“Odds ratio” values that are significantly less than one implies that there is less likelihood of an event occurring (i.e. the land manager having a perception of a change in climate) for a land manager with this particular characteristic than for a land manager with the base characteristic. An "odds ratio" of greater than one implies that these respondents are more likely to have a perception of a change in climate than respondents in the base category. If the "odds ratio" of a characteristic (category) is not significantly different from one, then respondents in that category are not significantly more or less likely to have a perception of a change in climate than those in the base category.
“Odds ratio” values generated from the logistic regression model are shown in Appendix 4. As an example, for the explanatory variable "state", it can be seen from Appendix 4 that the odds ratio for Queensland compared with the base category of Victoria is 0.535. This means the odds are that farm managers in Queensland are approximately 46% [(1- 0.535)*100] less likely to perceive a change in climate than not perceive a change in climate than farm managers in Victoria. Alternatively, it can be interpreted that Victorian farm managers are 1.9 times (1/0.535), or 90% more likely to perceive a change in climate than not perceive a change in climate than farm managers in Queensland. Where the odds ratio for a category of a explanatory variable is shown as 'not significant', then farm land managers in that category are not statistically more or less likely to perceive a change to climate than those in the base category.
QUALITY ASSURANCE - MODEL DIAGNOSTICS
Multicollinearity occurs when there are perfect, near-perfect or strong correlations among a set of explanatory variables. The existence of multicollinearity inflates the variances of the parameter estimates. To test for multicollinearity, the variance inflation factor (VIF) and the tolerance (TOL) were examined. Test results indicated that the explanatory variables included in the model are not closely related to each other.
The significance of model parameters associated with each variable was tested using the Wald test.
The Hosmer-Lemeshow goodness-of-fit test was used to indicate the adequacy of the model. The Hosmer-Lemeshow p-value provided no evidence that the model suffers from lack of fit (p= 0.7673).
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