SPSSINC RASCH - DOCUMENTATION?
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Dear SPSS-L, With help from Jon Peck (Thanks Jon!), I have been able to install the SPSSINC RASCH extension command and dialog box. Question: Does anybody know where I can find documentation/manual that discusses the underlying algorithms, estimation method, etc. online? A link or path to where I can find it would be most appreciated. Perhaps it was automatically downloaded onto my machine and I didn't realize it? Whatever the case may be, I can't find it. Any help locating it would be appreciated.
Thanks, Ryan
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Re: SPSSINC RASCH - DOCUMENTATION?
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This is extracted from the help for the
ltm model. To read it directly, you would start R and do these
commands
library(ltm) help(ltm) The latent trait model is the analogue of the factor analysis model for binary observed data. The model assumes that the dependencies between the observed response variables (known as items) can be interpreted by a small number of latent variables. The model formulation is under the IRT approach; in particular, logit(pi_i)=beta_{0i} + beta_{1i}z_1
+ beta_{2i}z_2,
where π_i is the the probability of a positive response in the ith item, β_{i0} is the easiness parameter, β_{ij} (j=1,2) are the discrimination parameters and z_1, z_2 denote the two latent variables. The usual form of the latent trait model assumes linear latent variable effects (Bartholomew and Knott, 1999; Moustaki and Knott, 2000). ltm() fits the linear one- and two-factor models but also provides extensions described by Rizopoulos and Moustaki (2006) to include nonlinear latent variable effects. These are incorporated in the linear predictor of the model, i.e., logit(pi_i)=beta_{0i} + beta_{1i}z_1
+ beta_{2i}z_2 + beta_{nl}^tf(z_1, z_2),
where f(z_1, z_2) is a function of z_1 and z_2 (e.g., f(z_1, z_2) = z_1z_2, f(z_1, z_2) = z_1^2, etc.) and β_{nl} is a matrix of nonlinear terms parameters (look also at the Examples). If IRT.param = TRUE, then the parameters estimates for the two-parameter logistic model (i.e., the model with one factor) are reported under the usual IRT parameterization, i.e., logit(π_i) = beta_{1i}(z - beta_{0i}^*).
The linear two-factor model is unidentified under orthogonal rotations on the factors' space. To achieve identifiability you can fix the value of one loading using the constraint argument. The parameters are estimated by maximizing the approximate marginal log-likelihood under the conditional independence assumption, i.e., conditionally on the latent structure the items are independent Bernoulli variates under the logit link. The required integrals are approximated using the Gauss-Hermite rule. The optimization procedure used is a hybrid algorithm. The procedure initially uses a moderate number of EM iterations (see control argument iter.em) and then switches to quasi-Newton (see control arguments method and iter.qN) iterations until convergence. ...
Baker, F. and Kim, S-H. (2004) Item Response Theory, 2nd ed. New York: Marcel Dekker. Bartholomew, D. and Knott, M. (1999) Latent Variable Models and Factor Analysis, 2nd ed. London: Arnold. Bartholomew, D., Steel, F., Moustaki, I. and Galbraith, J. (2002) The Analysis and Interpretation of Multivariate Data for Social Scientists. London: Chapman and Hall. Moustaki, I. and Knott, M. (2000) Generalized latent trait models. Psychometrika, 65, 391–411. Rizopoulos, D. (2006) ltm: An R package for latent variable modelling and item response theory analyses. Journal of Statistical Software, 17(5), 1–25. URL http://www.jstatsoft.org/v17/i05/ Rizopoulos, D. and Moustaki, I. (2008) Generalized latent variable models with nonlinear effects. British Journal of Mathematical and Statistical Psychology, 61, 415–438.
Dear SPSS-L, With help from Jon Peck (Thanks Jon!), I have been able to install the SPSSINC RASCH extension command and dialog box. Question: Does anybody know where I can find documentation/manual that discusses the underlying algorithms, estimation method, etc. online? A link or path to where I can find it would be most appreciated. Perhaps it was automatically downloaded onto my machine and I didn't realize it? Whatever the case may be, I can't find it. Any help locating it would be appreciated. Thanks, Ryan |
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In reply to this post by Ryan
Thanks, Alex. I'm reading through the documentation now. Also, thanks
to Jon for sending that information and pointing me in the right direction. Dear SPSS-L, If you recall, GENLIN and WINSTEPS produced nearly identical results (even when I didn't take into consideration rounding issues). Llittle doubt, those two are fitting the same model. OTOH, I'm finding some meaningful discrepancies between SPSS RASCH and SPSS GENLIN/Winsetps. But, before I publicly present any results and draw any conclusions, I really need to carefully evaluate the algorithms underlying SPSS RASCH. I will write back with comparisons as soon as I feel confident enough that I fully understand SPSS RASCH. These discrepancies have piqued my interest, that's for certain! Ryan On Wed, Mar 27, 2013 at 4:49 PM, Alex Reutter <[hidden email]> wrote: > Hi Ryan, > > The SPSSINC RASCH command uses the R ltm package: > http://cran.r-project.org/web/packages/ltm/ltm.pdf. > > Alex > > > > From: R B <[hidden email]> > To: [hidden email], > Date: 03/27/2013 03:45 PM > Subject: SPSSINC RASCH - DOCUMENTATION? > Sent by: "SPSSX(r) Discussion" <[hidden email]> > ________________________________ > > > > Dear SPSS-L, > > With help from Jon Peck (Thanks Jon!), I have been able to install the > SPSSINC RASCH extension command and dialog box. > > Question: Does anybody know where I can find documentation/manual that > discusses the underlying algorithms, estimation method, etc. online? A link > or path to where I can find it would be most appreciated. Perhaps it was > automatically downloaded onto my machine and I didn't realize it? Whatever > the case may be, I can't find it. Any help locating it would be appreciated. > > Thanks, > > Ryan ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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Hello: I have read the R ltm documentation, and from what I understand, when fitting a "Rasch" model, the default is to estimate a discrimination parameter that is constant across all items. However, according to the documentation, it is possible to constrain the discrimination parameter to 1.0 by employing a "constraint argument."' I do not see this option in any of the sub-commands of SPSS INC RASCH. For those who have used the SPSS INC RASCH command, have you figured out a way to constrain the discrimination parameter to be 1.0? Ryan On Wed, Mar 27, 2013 at 9:07 PM, R B <[hidden email]> wrote: Thanks, Alex. I'm reading through the documentation now. Also, thanks |
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All,
I have made some conclusions:
1. Winsteps and GENLIN results should not be comared directly to the R ltm package, primarily because R ltm assumes that person abilities (theta) follow a normal distribution with a mean of 0 and sd of 1. Winsteps and GENLIN make no such distributional assumptions.
2. One could employ the GENLIMIXED procedure and treat subjects as random effects, since GENLINMIXED assumes that random effects follow a normal distribution with a mean of zero and estimated variance, AFAIA. However, GENLINMIXED uses pseudo-likelihood estimation methods, which has been shown to produce biased estimates, especially when modeling correlated binary data. I don't think comparing GENLINMIXED to SPSS RASCH is a useful endeavor. Integral approximation methods are far superior.
3. Since I could not think of another procedure in SPSS for comparison purposes, I employed the NLIMIXED procedure in SAS, treating subjects as random effects that follow a normal distribution with a variance to be estimated in the model rather than forcing it to be 1.0 (which is standard practice). As expected, the estimated sqrt(variance) or s.d. of the random intercept was very similar to the discrimination parameter estimated by the SPSS Rasch procedure. Moreover, the SAS NLMIXED estimated item difficulties were identical [to the second decimal place] when compared to the Rasch SPSS adjusted item difficulty estimates. I found this to be quite compelling because I hold the NLMIXED procedure in very high regard.
All in all, I would be comfortable using the SPSS Rasch procedure. One just has to keep in mind that (a) the discrimination parameter is not constrained to be 1.0, so an adjustment needs to be made to the item difficulties if that property is important to you, and (2) the SPSS Rasch procedure assumes that person abilities (thetas) follow a specific distribution. If one cannot make such an assumption regarding the distribution of the person abilities, then it would be better to use software and/or another procedure which does not make such an assumption.
Here's the NLMIXED code that produced identical estimated item difficulties [to at least the second decimal place] AFTER adjusting the SPSS Rasch estimated difficulties to account for the discrimination parameter not being constrained to be exactly 1.0 across all items.
proc nlmixed data=rasch.rasch
tech=trureg;
Hope this is of interest. Feedback, comments, etc. are welcome.
Ryan On Fri, Mar 29, 2013 at 8:21 PM, R B <[hidden email]> wrote:
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Re: SPSSINC RASCH - DOCUMENTATION?
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In reply to this post by Ryan
I'm fairly certain that SPSSINC RASCH currently
does not surface the option to constrain the discrimination parameter,
but this would be a useful future update to the command.
Alex From: R B <[hidden email]> To: [hidden email], Date: 03/29/2013 07:50 PM Subject: Re: SPSSINC RASCH - DOCUMENTATION? Sent by: "SPSSX(r) Discussion" <[hidden email]> Hello: I have read the R ltm documentation, and from what I understand, when fitting a "Rasch" model, the default is to estimate a discrimination parameter that is constant across all items. However, according to the documentation, it is possible to constrain the discrimination parameter to 1.0 by employing a "constraint argument."' I do not see this option in any of the sub-commands of SPSS INC RASCH. For those who have used the SPSS INC RASCH command, have you figured out a way to constrain the discrimination parameter to be 1.0? Ryan On Wed, Mar 27, 2013 at 9:07 PM, R B <ryan.andrew.black@...> wrote: Thanks, Alex. I'm reading through the documentation now. Also, thanks to Jon for sending that information and pointing me in the right direction. Dear SPSS-L, If you recall, GENLIN and WINSTEPS produced nearly identical results (even when I didn't take into consideration rounding issues). Llittle doubt, those two are fitting the same model. OTOH, I'm finding some meaningful discrepancies between SPSS RASCH and SPSS GENLIN/Winsetps. But, before I publicly present any results and draw any conclusions, I really need to carefully evaluate the algorithms underlying SPSS RASCH. I will write back with comparisons as soon as I feel confident enough that I fully understand SPSS RASCH. These discrepancies have piqued my interest, that's for certain! Ryan On Wed, Mar 27, 2013 at 4:49 PM, Alex Reutter <areutter@...> wrote: > Hi Ryan, > > The SPSSINC RASCH command uses the R ltm package: > http://cran.r-project.org/web/packages/ltm/ltm.pdf. > > Alex > > > > From: R B <ryan.andrew.black@...> > To: [hidden email], > Date: 03/27/2013 03:45 PM > Subject: SPSSINC RASCH - DOCUMENTATION? > Sent by: "SPSSX(r) Discussion" <[hidden email]> > ________________________________ > > > > Dear SPSS-L, > > With help from Jon Peck (Thanks Jon!), I have been able to install the > SPSSINC RASCH extension command and dialog box. > > Question: Does anybody know where I can find documentation/manual that > discusses the underlying algorithms, estimation method, etc. online? A link > or path to where I can find it would be most appreciated. Perhaps it was > automatically downloaded onto my machine and I didn't realize it? Whatever > the case may be, I can't find it. Any help locating it would be appreciated. > > Thanks, > > Ryan |
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I hope SPSS is taking note of this request. It is common practice to set the common slope alpha=1.0 when fitting a Rasch model. In the meantime, for those interested, one can multiply the item difficulties by alpha, which is akin to obtaining an estimate of the item difficulties had alpha been constrained to 1.0.
To make this Rasch command even more useful, one should be permitted to "SAVE" the person estimates ("thetas"). Each person's estimate is an estimate of where he/she is placed along the continuum of the construct (in logits since the R ltm is based on the logistic ogive model).
In the educational setting, it is common practice to refer to a person's Rasch measure as an estimate of the person's "ability" level (e.g., Mary's math aptitude estimate is +2.3 logits), while in the clinical field, a person's Rasch measure is thought of as an estimate of the person's "severity" level (e.g., Mary's level of depression is +2.3 logits). Regardless, one should be able to obtain ("SAVE") each and every person's Rasch measure for future analyses.
Ryan On Mon, Apr 1, 2013 at 8:11 AM, Alex Reutter <[hidden email]> wrote: I'm fairly certain that SPSSINC RASCH currently does not surface the option to constrain the discrimination parameter, but this would be a useful future update to the command. |
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One point of clarification: In order to interpret the person measures in logits according to the traditional Rasch model in which alpha=1.0, the last point I made about person measures would obviously require a conversion be made accordingly as well.
Best, Ryan On Mon, Apr 1, 2013 at 10:01 PM, R B <[hidden email]> wrote:
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