[R-sig-ME] Is it ok to use lmer() for an ordered categorical (5 levels) response variable?

[Doran, Harold]

Steven

CFA *is* IRT. IRT parameters can also be estimated using generalized
linear models as we show in this paper. I also show in this paper how IRT
models are specifically derived from the classical test theory measurement
model (see section 1.1). Social scientists often think of these as models
that somehow do different things and have different reasons to exist.
Perhaps it¹s because I¹m older now, but I want to view the statistical
world as a unified model that, under constraints, can be used to estimate
different things. 

https://www.jstatsoft.org/article/view/v020i02

This thread has deviated a bit to a degree that is not helpful to the OP I
think. We started with the question on whether ordered, categorical data
can be (or should be) estimated using a linear mixed effects model. I
still can¹t see any reason to support that idea and recall that the OP
began with an ordered logit but got stuck on the hessian singularity
somewhere. My recommendation is to go back and figure out why that is
happening in the context of that model rather than ditching that model for
use of a different one.

In other words, don¹t let software determine what model is most
appropriate. 



On 3/7/19, 3:47 PM, "Pierce, Steven" <pierces1 using msu.edu> wrote:

>Landon,
>
>I'm familiar with IRT methods as well as CFA and agree IRT also provides
>a good measurement approach here. Raykov & Marcoulides (2016) point out
>that in some situations (possibly including this one), one can compute
>the relevant IRT parameters from the CFA results and the CFA parameters
>from the IRT results. My discussions with Raykov lead me to believe that
>CFA and IRT models are completely interchangeable in those scenarios.
>They accomplish the same thing. That relationship has not been proven to
>generalize to all situations (to my knowledge), but it is worth noting
>when it applies to a given problem.
>
>Raykov, T., & Marcoulides, G. A. (2016). On the relationship between
>classical test theory and item response theory: From one to the other and
>back. Educational and Psychological Measurement, 76(2), 325-338.
>doi:10.1177/0013164415576958
>
>Steve
>
>-----Original Message-----
>From: landon hurley <ljrhurley using gmail.com>
>Sent: Thursday, March 7, 2019 1:58 PM
>To: r-sig-mixed-models using r-project.org
>Subject: Re: [R-sig-ME] Is it ok to use lmer() for an ordered categorical
>(5 levels) response variable?
>
>Steven,
>
>Since you ask:
>
>On 3/7/19 8:55 AM, Pierce, Steven wrote:
>> Neither you nor Harold have (a) made a principled argument about how
>> using CFA and SEM would be flawed, or (b) suggested a better
>> approach. Instead you've criticized a minor point where I
>> acknowledged a similarity between how the scores Nicolas had
>> described were constructed and a commonly-used but flawed approach
>> to measurement in the social sciences. I only mentioned that
>> similarity as a bridge to suggesting the CFA approach that more
>> statistically rigorous social scientists have develoto tped for
>> translating binary item-level data into decent measures of
>> theoretical constructs.
>
>The problem with traditional factor analytic models with respect to the
>theta score estimation lies in that the amount of information changes
>relative to each persons' location on the theta scale. This has negative
>impacts as a consequence of the so-called "factor score indeterminacy."
> An item of average difficulty is most probable to be located near that
>location on the scale, which is a reflection of the theta score the item
>was calibrated upon (the item regularity parameters are trained).
>Further, let us assume that there is a more complicated relationship
>than merely a proportional equivalence between the sum score and the
>theta score. If this were false, than at best we would have ordination
>(i.e., theta rankings) which were equivalent to the ranks of the sum
>scores. This rank equivalence is lost once the model is expanded, but it
>allows for differing amounts of information contained in each item to be
>allocated across an entire ability level. The discrimination parameter
>of an item serves to reflect the slope of the change from one response
>to the next. A perfect step function (for example, a Heaviside function)
>has perfect discrimination: an ability below the threshold (the
>difficulty parameter, where there is a 50% probability of endorsement)
>will always respond 0, otherwise 1.
>
>Expansion of the factor model for handling discrete items under item
>response theory, would be the typical solution for determining a theta
>location for any given respondent. CFA does not represent a solution to
>this problem because it specifically avoids the question of the
>operation of the production of factor scores themselves (by
>integrating/averaging out the individual scores). Instead, it is looking
>for the structure of the model, but not how or where it is a useful tool
>in the sample data. IRT, on the other hand, enables us to assess how
>reliably (how accurately) an estimated location is upon the sample. More
>items, and higher discriminating items provide more information, and
>serve to change the test information.
>
>If scoring items were the desired approach, then IRT has been developed
>for much of the existing standardised testing (e.g., SAT, ACT, GRE,
>LSAT, MCAT). It would appear to be the ideal solution.
>
>-- 
>Violence is the last refuge of the incompetent.
>
>
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