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statistics 2 11
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- 1issue of multicollinearity> the relationship between predictors or effects.
> ANOVA and Linear regression both automatically remove any multicollinearity, or “overlap between predictors/effects”.
- The advantage of this is that any effect we find can be uniquely credited to a single predictor
- but when multicollinearity is large, the predictor is but a shadow of its former self. - 2When is the problem of multicollinearity increased?> This problem is enhanced through an increased standard error
> - 3How to check if multicollinearity is an issue> calculate the Variance Inflation Factor (VIF) and/or Tolerance
> Both of these are based on a single value:R^2j, which means explained variance in predictor j by other
predictors - 4Formula: toleranceTolerance = 1 minus R^2j
- 5To find R^2j from VIF, all we need to do is transform the formula:R^2j = 1- 1/VIF
- 6The rule of thumb for reading VIF or Tolerance> for
VIF, anything under 4 is fine.
>for Tolerance, anything over 0.25 is fine. - 7When it turns out there is a problem with multicollinearity...> it means that the predictors are too much alike.
>remving the predictor with the highest VIF is a great solution of reducing all other VIFs in general - 8The further a predicted value is from the mean of predicted values,...the higher its leverage is
- 9regression outlierpoint that does have an unusual residual (bad)
- 10Cook’s distance> statistic to help us determine whether a point is influential or not
> compares the slope of the regression model with and without this score
> any value below 1 is good, and a
value above 1 is considered an influential point (bad) - 11Why is multicollinearity not an assumption?The four assumptions we discussed in the previous lecture are all fundamental to getting appropriate p-values and confidence intervals. There is no theoretical reason to use ANOVA or linear regression while these assumptions are violated, as it will always lead to results that are biased in some unknown way. There are, however, certain models which expect multicollinearity. For instance, it
may be known that many predictors are highly related, but we simply want to know which one of
them is the best. Linear regression is still appropriate in that case if all other assumptions are met.
While multicollinearity is a potential problem in many cases when the predictors are not supposed to
be highly related, it is not absolutely essential in every case. That is what makes it different from an
assumption. - 12Could the ANOVA table in a linear regression have problems with multicollinearity?No, as there is only ever one model in linear regression. There are no multiple models being tested at
the same time, unlike the multiple predictors that are being tested at the same time. Therefore,
multicollinearity is never a problem for the ANOVA table, and by extension, the value of R². - 13Name four of the five causes in practice outside of cheating that may lead to a significant effect1) A causes B
2) B causes A
3) A and B have a common cause (moderator)
4) A causes B through C (mediator)
5) Coincidence
> One other explanation: Questionable research practice - 14Which two assumptions do outliers have the most influence on?Normality and Homoscedasticity
- 15Between a point that has high leverage, a point that has a high residual, and a point that is influential, which is most likely to be causing problems for assumptions?The point that is influential. High leverage may have some influence on normality. High residual may
have some influence on homoscedasticity. An influential point likely has influence on both of these
assumptions, and it is definitely the worst out of the three. - 16Explain why it is important to select the right model and check the relevant assumptionswithout doing this, we may unknowingly draw the wrong conclusion based
on our data. In theory, it is possible for any type of data to have a fitting model to analyse it. SPSS provides most of the common ones that can handle almost any data in practice, but it is not even
close to being an exhaustive list of possible analyses. Selecting the most appropriate model for your
data will generally lead to more power, as the model gets everything out of the data that it can, and
the most accurate results.
We prefer using tests with as many assumptions as possible, as long as our data fits these
assumptions. The reason for that is that more restrictive tests always have more useful statistical
properties. To see this, compare the Kruskal-Wallis test, which basically only provides a p-value, to
the wealth of options we have when computing a Oneway-ANOVA. The trade-off is that the oneway-
ANOVA has two extra assumptions, making it a more restrictive test. This principle can be applied in
general. - 17A model is tested with two independent variables: “Gender” and a binary variable representing whether someone is physically able of having a baby. Both have a strong relationship with the dependent variable, but when they are both in the same model, neither of them is a significant predictor. What is going on here, and what is the best course of action to take?It appears there is a high correlation between these predictors, leading to large amounts of
multicollinearity. Combining is hard to imagine for this variable, and using other variables is not
needed, so it would be appropriate to remove one of the two variables. - 18In a model with n = 10, we find that the minimum Cook’s distance is 0.1, and the maximum Cook’s distance is 1.5. After removing the case with the highest Cook’s distance. Can we be sure that the maximum Cook’s distance is now smaller than 1? And can we be sure that the minimum does not change?While we are sure the next largest Cook’s distance will be smaller than the 1.5 we removed, it could
be 1.4 or 1.3 as well, so there is no way we can assume that the maximum Cook’s distance will be
smaller than 1 after only removing the value with the largest Cook’s distance. Note that because the
“full model” now has one less score (n = 9), the model, and therefore the predicted values have
changed as well, leading to different values of Cook’s distance for every other case as well. This
means the minimum may not be exactly 0.1 either.
This was meant to be a trick question, so please don’t feel bad if you got it wrong. If you got it right,
that’s very clever! - 19Consequence of having outliers> Sometimes none!
> But often: Large SE, biased results - 20Influential points> points with great influence on the
estimated values of beta
> When an influential point is removed from the data, the regression line would be considerably different - 21Univariate outlier (Does it affect regression estimates?)> Outlier of x or y (unconditional on each other)
> Not necessarily - 22Regression outlier (Does it affect regression estimates?)> Unusual y value for a given x
> Not necessarily - 23Observation with leverage (Does it affect regression estimates?)> Unusual x value
> Not necessarily - 24Observation with influence (Does it affect regression estimates?)> Regression estimates change
greatly with/without them
> Yes - 25Classification of ‘unusual’ observations> Being x-discrepant (leverage) or y-discrepant (regression outlier)
is not sufficient to identify influential observations
> However, it is a combination of both x- and y- discrepancies
that determines the influence of an observation. - 26When is model validity violated?> When the assumptions are incorrect
> When the model is incorrect
> When there is a major issue with multicollinearity, outliers, etc. - 27HARKing> In a paper, selectively reporting studies that ‘worked
> Hypothesizing After the Results are Known - 28Sequential sampling> Regular p-value is constructed for a single test
> With sequential sampling: multiple testing --> chance
capitalisation --> adjustments required
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- Psychologie Karteikarten am statistics 2 11, erstellt von Adrian Mayer am 04/12/2018.
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- Adrian Mayer · Dez 2018
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