tailieunhanh - Statistical Methods in Medical Research - part 7

Một điểm thêm rằng việc chuyển đổi probit không ổn định chênh lệch, thậm chí cho các quan sát liên tục n. Một số hình thức trọng do đó mong muốn trong bất kỳ phân tích. Một cách tiếp cận nghiêm ngặt được cung cấp bởi các phương pháp gọi là phân tích probit | 488 Modelling categorical data calculate p 1 2u when r 0 and p 2n l 2u when r n and obtain y from p . A further point is that the probit transformation does not stabilize variances even for observations with constant n. Some form of weighting is therefore desirable in any analysis. A rigorous approach is provided by the method called probit analysis Finney 1971 see also . The effect of the probit transformation in linearizing a relationship is shown in Fig. . In Figure b the vertical axis on the left is the NED ofp and the scale on the right is the probability scale in which the distances between points on the vertical scale are proportional to the corresponding distances on the probit or NED scale. Logit transformation The logit of p is defined as y ln- -. 1 - p Occasionally Fisher Yates 1963 Finney 1978 the definition incorporates a factor I so that y ln p l p this has the effect of making the values rather similar to those of the NED . probit 5 . The effect of the logit or logistic transformation is very similar indeed to that of the probit transformation. The probit transformation is reasonable on biological grounds in some circumstances for example in a quantal assay of insecticides applied under different controlled conditions a known number of flies might be exposed at a number of different doses and a count made of the number killed. In this type of study individual tolerances or their logs may be assumed to have a normal distribution and this leads directly to the probit model . The logit transformation is more arbitrary but has important advantages. First it is easier to calculate since it requires only the log function rather than the inverse normal distribution function. Secondly and more importantly the logit is the logarithm of the odds and logit differences are logarithms of odds ratios see . The odds ratio is important in the analysis of epidemiological studies and logistic regression can be used for a variety of .