 By Fearn T., Brown P.J., Besbeas P.

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Sample text

However, as we shall see, it is the likelihoodratio statistic that is reported in statistical modelling output (although it is often simply referred to as ‘chi-squared’) rather than the Pearson chi-squared. The reason for preferring the likelihood-ratio statistic is that it can be exactly partitioned whereas the Pearson chi-squared cannot. We explain what is meant by partitioning below. Properties of chi-squared One of the most important properties of chi-squared is that it is additive, by which we mean that the sum of two chi-squareds is also a chi-squared (with degrees of freedom the sum of the two degrees of freedom).

But at what point do problems arise? 8. 6. What is the nature of the problem? If variables are highly collinear the coeﬃcients are unaﬀected but their standard errors will be large. e. b)) and the smaller the value of t the greater the probability and the lesser chance of obtaining a statistical signiﬁcant result. Hence the eﬀect of multicollinearity is to reduce the chance of getting a signiﬁcant result and some relationships which exist will be missed. How can multicollinearity be detected? Inspection of the correlation matrix can identify high intercorrelations between continuous variables which help diagnose potential problems.

2. ) Conﬁdence intervals From the data the model estimates the coeﬃcients bp. But the estimates are based upon one sample of data that was obtained for the study. Had another sample been drawn, a slightly diﬀerent estimate would have been obtained. So what conﬁdence can be placed on the estimates we have from the study? The theory of the normal distribution outlined above can help. 96(standard error of b). This range is called the 95% conﬁdence interval. 58 and the range increases accordingly. Conﬁdence intervals are related to signiﬁcant tests.