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發(fā)表于 2007-5-7 23:23:43
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這是加拿大哥爾福大學(xué)Larry Schaeffer 教授在2003年-2006年為研究生講課的講稿.
原文是在講數(shù)學(xué)模型問(wèn)題,而我的問(wèn)題是在這個(gè)全段的第3,4,5標(biāo)題下面(我用紅字標(biāo)注了的部分)
全段如下
Fixed and Random Factors
In the traditional "frequentist" approach, fixed and random factors need to be distinguished. In a Bayesian approach there is no such distinction and all factors are random variables associated with some sort of distribution function.
Fixed factors are factors in which the classes comprise all of the possible classes of interest that could be observed. For example, the sex of an animal is either male, female, sterilized male, or sterilized female. If the number of classes in a factor is small and confined to this number even if conceptual resampling were performed an infinite number of times, then the factor is likely fixed. Other examples are age classes, lactation number, management system, cage number, and breed class. Usually if the sampling were to be repeated a second time, those factors which maintain the same classes between the two samplings would be fixed factors. For example, a growth trial on pigs using two diets would probably need to use the same housing facilities, the same age groups of pigs, and the same diets, but the individual pigs would necessarily have to be new animals because an animal could not go through the same growth phase a second time in its life. Pig effects would be considered a random factor while the other effects would be fixed.
Random factors are factors whose levels are considered to be drawn randomly from an infinitely large population of levels. As in the previous pig experiment, pigs were considered random because the pig population of the world is large enough to be considered infinitely large, and the group that were involved in that experiment were a random sample from that population. In actual fact, however, the pigs on that experiment were likely sampled from those relatively few pigs that were available at the time the trial started, but still they are considered to be a random factor because if the experiment were to be repeated again, there would likely be a completely different group of pigs involved.
Another way to determine if a factor is fixed or random is to know how the results will be used. In a nutrition trial the results infer something about the diets in the trial. The diets are specific and no inferences should be made about other diets not tested in the experiment. Hence diet effects would be a fixed factor. In contrast, if animal effects were in the model, inferences about how any animal might respond to a specific diet may need to be made. There should not be anything peculiar about the animal on the trial that would nullify that inference. Animal effects would be a random factor.
In general, a few questions need to be answered to make the correct choice of fixed or random factor designation. Some of the questions are
1.
How many levels of the factor are in the model? If small, then perhaps this is a fixed factor. If large, then perhaps this is a random factor.
2.
Is the number of levels in the population large enough to be considered infinite? If yes, then perhaps this factor is random.
3.
Would the same levels be used again if the experiment were to be repeated a second time? If yes, then perhaps this factor is fixed.
4.
Are inferences to be made about levels not included in the experiment? If yes, then perhaps this factor should be random.
(我的翻譯:是不是你要做出的關(guān)于各水平的推斷不包含在試驗(yàn)里啊?如果不包含,那么也許這個(gè)因子就是隨機(jī)的(因子).)
5.
Were the levels of a factor determined in a nonrandom manner? If yes, then perhaps this factor should be treated as fixed.
我的翻譯:(當(dāng)時(shí)你設(shè)計(jì)試驗(yàn)時(shí))一個(gè)因子的各水平是不是以非隨機(jī)方式?jīng)Q定的啊?如果是非隨機(jī)決定的,那么這個(gè)因子也許可按照固定因子對(duì)待.
By studying the scientific literature, a researcher should be able to get some help in this decision process. If in doubt, then the assistance of an experienced statistician should be sought.
In a Bayesian context, a prior distribution needs to be assumed about each of the factors. For random factors, typically these might be assumed to have a Normal distribution with a particular mean and variance. For fixed factors, an uniform distribution may be assumed or a prior distribution in which the factors are proportional to a constant. In a Bayesian context, even the variances need to have an assumed prior distribution. The prior distributions are combined to derive the distribution of the observations, and then are used with the distribution of the data to arrive at a posterior distribution from which inferences may be made.
上面加了漢字的是想請(qǐng)大家?guī)椭g的
我拿不準(zhǔn)啊
所以才拿來(lái)這里求教的
謝謝兩位了!
[ 本帖最后由 牧童 于 2007-5-7 23:54 編輯 ] |
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發(fā)表于 2007-5-7 18:03:15
