Jeromy Anglim
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OrdinalOrdered categorical items and normality:

• First, ordinal 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 categorical variable, the item has more potential to approximate a normally distributed variable.
• Ordinal items have ceilings and floors. If the mean is close the the ceiling or floor, then they are almost always skewed with the tail pointing away from the floor or ceiling as the case may be.

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 distributed variable.

Ordered categorical items have ceilings and floors. If the mean is close the the ceiling or floor, then they are almost always skewed with the tail pointing away from the floor or ceiling as the case may be.

There is a model of responding to ordinalordered categorical items, which suggests that a latent continuous numeric variable underlies responses. But that is different to examining the raw variable.

Whether to look at normality of items when doing CFA: When looking at typical self-report scales on 3,4,5 point scales, I don't think it makes much sense to look at normality.

Generally, you find that the size of the skew is related the degree to which the item deviates from the scale mid-point, and moves towards either the minimum or maximum possible value. Thus, I imagine your most skewed items would be those on a 0-1-2 scales that have means either close to 0 or close to 12. That said, there are exceptions where people can focus their responses towards either extreme (e.g., see some contaminated Amazon 5-star ratings).

So in summary, I think it is useful to get a sense of how people have used the response scale. Is it consistent with the most common responses being around the mean for the item or are scores around the extremes, or is there something else guiding responses. The aim here is just to build an understanding of how people have used the scale.

In most psychological contexts, I find that the mean captures most of what is going on with the distribution. The main preliminary step I like to do is to see whether there areany items suffer from severe floor or ceiling effects. So for example, if you had an item with a mean below 0.4 or above 1.6 on a 0-1-2 scale, you might want to think about whether the item is adequately discriminating people. I wouldn't automatically drop such an item, but I would think about what it is contributing.

Should non-normal items be transformed before CFA? As already mentioned, the items are not normally distributed anyway. Furthermore, the natural scale of ordinalordered categorical items, prevents extreme outliers, and limits extreme skew. Furthermore, items will typically be scored using their original scaling, so it is best to leave them as is. For this reason, I tend not to transform individual items when performing CFA.

A second point relates generally to how to model ordinalordered categorical items. While you can do CFA on individual items, there are also a range of more advanced, and arguably better, alternative approaches that are designed to explicitly model ordinalordered categorical items:

• MPlus has various models for ordinal items with thresholds between items
• Amos has some models for modelling ordinal items
• Optimal scaling PCA
• Factor analysis on polychoric correlations

You might want to read this presentation by Bowen and Wegmann where they discuss solutions.

deleted 2 characters in body
Jeromy Anglim
• 41.9k
• 23
• 144
• 248

Ordinal categorical items and normality:

• First, ordinal 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 categorical variable, the item has more potential to approximate a normally distributed variable.
• Ordinal items have ceilings and floors. If the mean is close the the ceiling or floor, then they are almost always skewed with the tail pointing away from the floor or ceiling as the case may be.

There is a model of responding to ordinal items, which suggests that a latent continuous numeric variable underlies responses. But that is different to examining the raw variable.

Whether to look at normality of items when doing CFA: When looking at typical self-report scales on 3,4,5 point scales, I don't think it makes much sense to look at normality.

Generally, you find that the size of the skew is related the degree to which the item deviates from the scale mid-point, and moves towards either the minimum or maximum possible value. Thus, I imagine your most skewed items would be those on a 0-1-2 scales that have means either close to 0 or close to 1. That said, there are exceptions where people can focus their responses towards either extreme.

So in summary, I think it is useful to get a sense of how people have used the response scale. Is it consistent with the most common responses being around the mean for the item or are scores around the extremes, or is there something else guiding responses. The aim is here here is just to build an understanding of how people have used the scale.

In most psychological contexts, I find that the mean captures most of what is going on with the distribution. The main preliminary step I like to do is to see whether there are items suffer from severe floor or ceiling effects. So for example, if you had an item with a mean below 0.4 or above 1.6 on a 0-1-2 scale, you might want to think about whether the item is adequately discriminating people. I wouldn't automatically drop such an item, but I would think about what it is contributing.

Should non-normal items be transformed before CFA? As already mentioned, the items are not normally distributed anyway. Furthermore, the natural scale of ordinal items, prevents extreme outliers, and limits extreme skew. Furthermore, items will typically be scored using their original scaling, so it is best to leave them as is. For this reason, I tend not to transform individual items when performing CFA.

A second point relates generally to how to model ordinal items. While you can do CFA on individual items, there are also a range of more advanced, and arguably better, alternative approaches that are designed to explicitly model ordinal items:

• MPlus has various models for ordinal items with thresholds between items
• Amos has some models for modelling ordinal items
• Optimal scaling PCA
• Factor analysis on polychoric correlations

You might want to read this presentation by Bowen and Wegmann where they discuss solutions.

Jeromy Anglim
• 41.9k
• 23
• 144
• 248

Ordinal categorical items and normality:

• First, ordinal 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 categorical variable, the item has more potential to approximate a normally distributed variable.
• Ordinal items have ceilings and floors. If the mean is close the the ceiling or floor, then they are almost always skewed with the tail pointing away from the floor or ceiling as the case may be.

There is a model of responding to ordinal items, which suggests that a latent continuous numeric variable underlies responses. But that is different to examining the raw variable.

Whether to look at normality of items when doing CFA: When looking at typical self-report scales on 3,4,5 point scales, I don't think it makes much sense to look at normality.

Generally, you find that the size of the skew is related the degree to which the item deviates from the scale mid-point, and moves towards either the minimum or maximum possible value. Thus, I imagine your most skewed items would be those on a 0-1-2 scales that have means either close to 0 or close to 1. That said, there are exceptions where people can focus their responses towards either extreme.

So in summary, I think it is useful to get a sense of how people have used the response scale. Is it consistent with the most common responses being around the mean for the item or are scores around the extremes, or is there something else guiding responses. The aim is here is just to build an understanding of how people have used the scale.

In most psychological contexts, I find that the mean captures most of what is going on with the distribution. The main preliminary step I like to do is to see whether there are items suffer from severe floor or ceiling effects. So for example, if you had an item with a mean below 0.4 or above 1.6 on a 0-1-2 scale, you might want to think about whether the item is adequately discriminating people. I wouldn't automatically drop such an item, but I would think about what it is contributing.

Should non-normal items be transformed before CFA? As already mentioned, the items are not normally distributed anyway. Furthermore, the natural scale of ordinal items, prevents extreme outliers, and limits extreme skew. Furthermore, items will typically be scored using their original scaling, so it is best to leave them as is. For this reason, I tend not to transform individual items when performing CFA.

A second point relates generally to how to model ordinal items. While you can do CFA on individual items, there are also a range of more advanced, and arguably better, alternative approaches that are designed to explicitly model ordinal items:

• MPlus has various models for ordinal items with thresholds between items
• Amos has some models for modelling ordinal items
• Optimal scaling PCA
• Factor analysis on polychoric correlations

You might want to read this presentation by Bowen and Wegmann where they discuss solutions.