14

This answer is deliberately non-mathematical and is oriented towards non-statistician psychologist (say) who inquires whether he may sum/average factor scores of different factors to obtain a "composite index" score for each respondent. Summing or averaging some variables' scores assumes that the variables belong to the same dimension and are fungible ...


5

There are two ways you can take: (1) just use the sums of scores, (2) use an Item Response Theory (IRT) based method. Using sums of raw scores is very common in social sciences but many psychometricians do not consider it being a sound approach. If you sum up the different questions from the questionnaire you assume that every answer provides you with the ...


4

General points on composites using t-scores By t-scores, I assume you are saying that you have four variables each of which have been standardised so that the mean is 50 and the standard deviation is 10. By using standardised scores (i.e., t-scores) as your component items, you are in some sense ensuring that the weighting of each variable in your composite ...


4

Yes, both your points make perfect sense, and are indeed a standard practice - at least in an area called psychometry. But I cannot agree with the title question: it is not always valid to ordinal variables. In general case one cannot add nor subtract values measured on ordinal scale and hope, that the result would be independent from arbitrariness that ...


4

When you create a composite, you lose information. Therefore, it seems likely that p values will go up and $R^2$ will go down, although I don't think this is necessarily always the case. You shouldn't rely on correlations to test collinearity; use condition indexes or VIFs (I prefer the former) and, if you do find collinearity, creating a composite is only ...


3

Question 1: You are incorrect that "we don't need any distributional assumption for the biomarkers in logistic regressions." A single-predictor logistic regression specifically assumes that the log-odds of the binary outcome are linearly related to the values of the predictor. So if you are using, say, RNAseq data as predictors you will get different results ...


3

You should not have a $\hat{\theta}$ in your hypothesis. A likelihood ratio test can do what you originally want. If $\mathbf{\theta}=(\theta_1,\theta_2,\ldots,\theta_p)^\top$, it is not required that you have a null hypothesis of the form $\mathbf{\theta}=\mathbf{\theta}_0$. You have a composite hypothesis of the form where the subset of the parameter ...


3

I assume here that your study's requirement is something along the lines of: Given the ordinal responses to n questions for each candidate (a policy research institute in your case), rank/sort order the candidates by functionally combining the n-dimensional response tuple's elements into a score/metric. Then perhaps you can look into the work of Wittkowski ...


2

I would not discretize / categorize your date into quartiles and sum them. This is too coarse-grained as it does not take into account how far a data point is from the boundary between the quartiles, for instance. (For more information on this topic, you might want to read my answer here: How to choose between ANOVA and ANCOVA in a designed experiment, ...


2

The average variance extracted (AVE) calculated as follows: total of the squared multiple correlations plus the total sum of each variable, then divides it by the number of factors in that variable. In order to get square multiple correlation of each item, you need to find square of each item Standardized Regression Weight / Estimate. AVE- average variance ...


2

You can do this, but taking the simple mean is not good anymore because of different scales. You can do factor analysis to get at the "latent construct" you are trying to evaluate, or principal components for pure data reduction. There's been work on doing these with a mix of variable types.


2

Yes, you can. Exploratory factor analysis aims to reducing data to a smaller set of summary variables... which are not the initial factors. But, depending on the EFA you used, you can use, for instance, a linear model based on the EFA score to reduce some factors in one. But, you should discrib a little bit more what analysis you think to use.


2

In general, a simple weighted linear composite can be formed as follows: newvar = w1 * x1 + w2 * x2 + ... + w5 *x5 where w1 to w5 are your five weights and x1 to x5 are your five variables. The question is what weights should you use? A common approach in my field (psychology) would be convert each variable to a z-score and then unit-weight the variables ...


2

A simple metric that could work for a problem like this is: Scaled = P/(P+N) Anything that is purely positive will get the score 1. Anything that is purely negative will get the score 0. Equal P & N gets 1/2. It ignores the length of the vector. Along the lines of what was suggested by @sean507, this is just the proportion of all answers that are ...


2

One of the problems here is that you are using notation that is far too complicated for the question under consideration. This makes a very simple inference problem look far more complex than it is, and it taxes the reader by making them try to interpret large amounts of unecessary notation. In particular, since there are only two underlying hypotheses ...


2

This mentions about composite variable. http://www.r-bloggers.com/ecological-sems-and-composite-variables-what-why-and-how/. In R package lavann, you can create composite variable based on manifest variables (indicators). Then this composite variable can be treated as a dependent variable or independent as per the question of interest.


2

The power of a test is $\mathbb{P}(reject \ H_0 | H_A \ is \ true) = \mathbb{P}(\vec{X} \in R | \theta \in \Theta_A) = \beta(\theta)$ for the same $\theta \in \Theta_A$. This means that the power of a test depends upon the specific $\theta$. It is not necessarily the case that the test has a single value for the power. You might be confusing the size or ...


1

Please find below the link to the Chapter on reliability that discusses many of your issues. For the specific issue of test-retest reliability see p.27-28, and reliability of a composite test is covered on page 32. This Chapter is written by William Revelle, a reputable psychometrician, hence the source is credible. https://www.personality-project.org/r/...


1

Welcome to CV! While you are of course free to come up with your own new index, combining the existing index and the number of incidents, I see two issues with this: Is the security index rating not at all based on number of incidents? Wouldn't you rather regress both separately to preserve the counts? As for (1): If the security index in any way ...


1

Your error is that you use precisely the same $42$ probabilities (coins) in each of the $2^{20}$ simulations, and so lose the element of sample variance which would come from these varying You would get the Beta-Binomial distribution if you chose new probabilities each time, for example putting coins = np.random.beta(alpha, beta, size=N) inside the for ...


1

You don't need to include that evaluation inside the GLM_boot function, you can do it with a post-bootstrap processing step. This post-processing step modifies the returned bootstrap parameter values according to your desired transform. I've constructed an example with a simple linear model but the same transform you wish to use: # Construct data frame df ...


1

There is absolutely no problem using composite variables, no matter if they are sums, products... or whatever you think of. However you must be aware of the fact that if your composite variable is just a sum (or difference, or linear combination) of raw variables then the model you get is not more powerful than the model with raw variables. In this case, ...


1

You might want a finite mixture model, which is essentially a latent variable model (like factor analysis) with categorical latent variables. Your items are the indicators of class membership. Given that you know how many classes there are, you can fix the number of classes in the model (which is usually itself estimated by the procedure). The output is, for ...


1

I'm not certain—so don't take me at 100% here—but it doesn't feel right to me. Predicting y/x by x itself is strange. Of course you are going to get a significant prediction, because x is used to calculate the DV. I generated some random data (assuming no relationship between any of the variables)... set.seed(1839) # setting seed for replicability ebit <-...


1

Don't use a composite variable in a structural equations model. Instead, add a latent variable that the manifest variables (i.e., the items) all measure. The composite variable isn't what the items measure, it is just (presumably) a better measure of the latent variable in question. If you were to add a composite variable, it would decrease the ability of ...


1

Items are redundant as a function of other items. If I ask your height in inches, and your height in cm, one of them is redundant. Which one? Both, or neither. It doesn't matter which one you use, just pick one. Are you trying to reduce the length of your scale? Typically shorter versions of scales are developed through validity methods, not reliability ...


1

Yes. Yes. But not always. You need at least two variables to be regressed on that formative latent. No. You cannot use the formative indicated latent as an endogenous variable. Think about in terms of path tracing. The arrows go from your measured variables to the latent. The arrows from the predictor go from another variable to the latent. The implied ...


1

If you are summing $z$-scores it seems highly likely that the result contains some negative values, so logarithmic transformation is likely to be out of the question for that reason alone. The usual definition of $z$-scores is (value $-$ mean)/SD, so values less than the mean necessarily map to negative $z$-scores. I am amazed that you don't report a ...


1

There are two ways to identify the variance of a latent variable. You can constrain the variance to one, or you can fix a loading to 1. Most programs use the second option as a default. If you've done much SEM, then you're used to that idea. If you use Mplus, then your code for the first option is: F by x1* x2 x3 x4; F@1; The asterisk explicitly frees the ...


1

Code the Likert scale from 0 to 4 with "Neither.." being the 2. Then count Likert scores for all 8 items. Sum the total score. Item scores divided by the total are the relative weights that range from 0 to 1 and sum up to 1.


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