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47

Traditional (linear) PCA and Factor analysis require scale-level (interval or ratio) data. Often likert-type rating data are assumed to be scale-level, because such data are easier to analyze. And the decision is sometimes warranted statistically, especially when the number of ordered categories is greater than 5 or 6. (Albeit purely logically the question ...


28

Why try to force a calibration on something which is not true? As Maarten said, this is not a loss of data but a gain of information. If the magical pill you are looking for exists, it would mean that there are some assumptions about your population that are made, for example, a bias in favor of one particular label even though users say "I don't know". I ...


14

Exploratory factor analysis (EFA) is appropriate (psychometrically and otherwise) for examining the extent to which one may explain correlations among multiple items by inferring the common influence of (an) unmeasured (i.e., latent) factor(s). If this is not your specific intent, consider alternative analyses, e.g.: General linear modeling (e.g., multiple ...


11

Pretty obviously not normal. A step function is not a straight line. However, you also seem to be checking (unconditional) normality of the response, which is not assumed to be normal in a mixed model (you'd have some mixture of normals, depending on the fixed effects) You clearly have discrete data. So your response's conditional distribution will be ...


11

If this was a standardized questionnaire that has been validated independently, then you cannot claim that the new questionnaire is equivalent, and the data is no longer comparable. You could try to validate and examine the questionnaire in separate experiments (very time- and effort-consuming, especially if you also want to show comparability to the old ...


9

It is generally fine to use predictor and outcome variables that use different metrics when performing multiple regression. To demonstrate the point, you can rescale predictor or dependent variables using a linear transformation (.e.g., z-scores, centering, and so on) and this will not influence your $R^2$ or your standardised regression coefficients (note ...


9

When you say things like 4+1 = 3+2 = 5, -- which you must do when you sum the components -- you (pretty much unavoidably) assumed they were interval at that time. [If the components weren't interval, in general 4+1 $\neq$ 3+2 ... so you'd certainly have no business calling both of them "5".] If the components were interval when you summed them, their sum ...


8

How to judge if 5 point likert scale data are normal distributed? Values on 5-point ordinal scales are never normally distributed. But that's probably not the question you really need answered. I have read that the t-test is used when the population is normally distributed. It's an assumption of the test, but it's often reasonably robust to mild ...


7

(What a fun question! My answer is a reflection, and others might have interesting opposing viewpoints.) No. The pairs of ordinal numbers 1 & 4 and 2 & 3 both sum to 5. But suppose such variables were coding, for example, functional mobility in an individual, where 1 indicated no impairment, 2 impairment not requiring assistance, 3 impairment ...


7

Normal distribution is a continuous distribution while 5-point Likert-type scale is an ordinal variable, so by definition it is not normally distributed.


7

A likert scale, as the term is typically used, is just an ordinal rating scale. The phrase is often used for a single rating, which might have been called a likert item. Traditionally, the idea was that you would have a set of likert items that all measure the same thing and have the same measurement properties. The result is that you could sum (or ...


6

In following up on @caracal's reference suggestions, I found an almost-direct answer (no, these two rating systems are not equivalent if presented as number options to respondents) from Schwarz, Knäuper, Hippler, Noelle-Neumann, and Clark (1991). They present data on responses to the question, "How successful have you been in life, so far?" One version gave ...


6

Likert ratings are ordinal data. If you want to predict your four Likert rating variables individually using your country and study-years data, you can fit four separate ordered logit or probit models. This will involve estimating separate regression coefficients for your two independent variables (IVs) in each of your four regression models. The typical ...


6

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 ...


6

I was wondering, is there any reason I should not use a scale like: 0, 1, 2, 4. From a modelling perspective, no, there is no reason why you shouldn't use such a scale, because, as mentioned in comments, the numbers themselves have no meaning, because a likert scale is ordinal. That is to say, a "value" of 4 does not mean that whatever is being measured is ...


5

Ordered categorical items and normality: First, ordered categorical items are discrete and lumpy. In particular, 3-point response scales lack the granularity required to even provide a rudimentary approximation of normality. When you have more response options in your ordered categorical variable, the item has more potential to approximate a normally ...


5

Is it a problem from a methodological point of view? Sort of, since strictly speaking, SEM assumes that the observed variables are normally distributed, which a fortiori, your likert items are not. So what to do? You could hold your nose and pretend that everything is normal, trusting in the Central Limit Theorem. I would probably do that, at least as a ...


5

Thorndike's Table 22 displays the expected value of a doubly-truncated normal distribution, which can be seen as a conditional expectation given that the variate is in an interval specified by quantiles: $$\mathbb{E}(Z \mid z_p<Z<z_{p+q}) = \frac{\phi(z_p)-\phi(z_{p+q})}{q}$$ where $z_p$ is the lower $p$th quantile of $Z\sim N(0,1)$, $\phi$ is the ...


5

Is it a crucial problem if my data isn't normally distributed? Data are (almost) never normal. Whether that's an issue depends what forms of deviation from normality the procedure you want to use is sensitive to (and how much), how non-normal it is and in what way it's non-normal (strictly we're talking about the distribution the sample was drawn from ...


5

In my opinion, I think the data should be analyzed as is. To some extent, these patterns are a reflection of the survey as well as a reflection of the population. Basically: crap in, crap out. Long winded questionnaires are guaranteed to fatigue respondents, sensitive or invasive questions will likely induce selective non-response, and younger participants ...


5

Yes, it is perfectly valid to conduct a Pearson's correlation between variables with different scales. The correlation coefficient is a standardized measure, so it is not influenced by scale. Here is a small simulation I did. First, I generate data on 7, 9, and 5 point scales. Then, I calculate correlation coefficients between each pair of variables. Then ...


5

To perform the simulation, here is a one line solution using the sample function: sample(0:4, N, replace = TRUE, prob = c(0.1, 0.2, 0.4, 0.2, 0.1)) #where: # 0:4 is the sequence of values (0 to 4 in this case) # N is the number of samples (participants) # replace = TRUE for sampling with replacement # prob = c(0.1, 0.2, 0.4, 0.2, 0.1) is the probability ...


4

This isn't a question where there is universal agreement. Some people say you cannot add Likert items together, because adding them implies that the individual items are interval scaled rather than ordinal scaled. E.g., suppose you just had two questions, each with 5 points from "strongly disagree" to "strongly agree". Suppose one person answered "Agree" to ...


4

I agree with the others that the design may not be optimal. But if it happens that you have such kind of data, what about a Heckman selection model. This is a well known model in econometrics (Nobel Prize) to account for the fact that some kind of selection process leads to a non-random sample introducing bias. It is a two-stage method: First, it is modeled ...


4

If you can define a reasonable similarity measure on the values, you can use any distance based algorithm, such as: Hierarchical clustering DBSCAN OPTICS K-Medoids (k-means for arbitrary distances) Given that you only have 5 values, you could just manually define a similarity matrix for these 5 values; then decide on a combination rule to merge multiple ...


4

As gung said, recoding reverse-scored variables will only reverse the sign of their factor loadings, so the decision is only important because you will have to keep track of (and specify in anything you write about it) which variables are reverse-scored, or whether you recoded them. An unrelated concern arises with factor analysis of Likert scale ratings. ...


4

K-means is for interval data. So, using it means that you assume Likert rating scale is interval. OK, you have your right for this, albeit puristic people will frown and mutter "likerts are ordinal, likerts are ordinal...". Next, K-means is expected to be "better", more discriminating, for finely grained scale (a one closer to be continuous). This is as in ...


4

(1) Yes you can, but nothing in either test takes the ordering into account. The ordered scales are reduced to nominal. The tests are applicable, but ignore much of the information you have. (2) Many researchers would be happy to use rank correlation here. At least it respects the ordering of the categories. Many ties are likely, but that's par for the ...


4

If you are considering t-tests on Likert items, I would primarily be worried about how many 1's and 5's there are, since those values might represent censoring of responses that could exceed 1 or 5 if it permitted. This censoring is much problematic than the fact that you would be treating a discrete distribution as if it were continuous. See How to model ...


4

Likert data simply cannot be normal. Although in some cases it is safe enough to treat it as normal, it isn't actually ever normal and treating it as such is potentially dangerous. In addition to the points @Glen_b has made, your residual plot doesn't look good. The residuals should be symmetrical (vertically) around the 0 line. Either there is ...


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