195 lines
7.1 KiB
Plaintext
195 lines
7.1 KiB
Plaintext
{smcl}
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{* Mars 2012}{...}
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{hline}
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help for {hi:pcmodel}
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{hline}
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{title:Estimation of the parameters of a Partial Credit Model}
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{p 8 14 2}{cmd:pcmodel} (varlist) [{help if} {help in}],
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[{cmdab:cat:egorical}({it:varlist})
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{cmdab:cont:inuous}({it:varlist})
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{cmdab:dif:ficulties}({it:matrix list})
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{cmdab:it:erate}(#)
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{cmdab:ad:apt}
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{cmdab:ro:bust}
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{cmdab:f:rom}(matrix)
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{cmdab:rsm:}
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{cmdab:nip:}
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{cmdab:tr:ace}
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{cmdab:est:imateonly}
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{cmdab:l:evel}(#)]
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{title:Description}
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{p 8 14 2}{cmd:pcmodel} allows estimating the parameters of a random effect
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partial credit model or a random effect rating scale model
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(the item difficulties, and the covariates
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that may influence the considered latent trait are considered as fixed
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effects, and the individual latent traits are considered as a normally distributed
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random effect){p_end}
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{p 14 14 2}Two situations are possible:{p_end}
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{p 16 18 2}- The item difficulties can be considered as already known
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(for example provided by the scale developer).
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In this case, they do not have to be estimated during the analysis.{p_end}
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{p 16 18 2}- The difficulties are considered as unknowns and will
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be estimated during the analysis. {p_end}
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{p 14 14 2}{cmd:pcmodel} allows including covariates that
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can possibly influence the individual latent traits in the considered model
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(partial credit or rating scale). These covariates
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can either be categorical or continuous. {p_end}
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{p 14 14 2}{cmd:pcmodel} provides assistance for interpreting both the quality
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of model fit (by estimating the marginal McFadden's pseudo R2) and the
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contribution of covariates to the model
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(by estimating the the type III sum of squares, the percentage
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of variance explained with the introduction of each covariates and the percentage
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of McFadden's pseudo R2 explained with the introduction of each
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covariate). {p_end}
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{p 14 14 2}It is finally possible to test the fit using {cmd:pcmtest} after
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estimating parameters of the model with {cmd:pcmodel}
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{title:Options}
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{p 4 8 2}{cmd:categorical} List of the categorical covariates included in
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the Partial Credit model or the Rating Scale model.
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{p 4 8 2}{cmd:continuous} List of the continuous covariates included in
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the Partial Credit model or the Rating Scale model.
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{p 4 8 2}{cmd:difficulties} Row vectors containing the known values
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of each item difficulty (if they are known).
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A row vector must match with each item, and have the
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same name as the corresponding item. If the option {cmd:difficulties}
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is not filled, the item difficulties are
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considered as unknown, and they are estimated during the analysis.
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(this option cannot be used with the {cmd:rsm} option
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{p 4 8 2}{cmd:iterate} specifies the (maximum) number of iterations. With the
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adapt option, use of the iterate(#) option will cause pcmodel to skip the
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"Newton Raphson" iterations usually performed at the end without updating
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the quadrature locations.
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{p 4 8 2}{cmd:adapt} causes adaptive quadrature to be used instead of
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ordinary quadrature.
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{p 4 8 2}{cmd:robust} specifies that the Huber/White/sandwich estimator of the
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covariance matrix of the parameter estimates is to be used.
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{p 4 8 2}{cmd:from} specifies a row vector to be used for the initial values.
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It is not necessary to specify column-names or equation-names for this line vector,
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but this vector must have exactly the number of parameters to be estimated,
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starting with the difficulties parameters, the parameters associated
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with the covariates, and ending with the estimated standard deviation
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of the latent trait.
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{p 4 8 2}{cmd:rsm} performs a Rating Scale model instead of a Partial Credit model.
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{p 4 8 2}{cmd:estimateonly} Do not perform the Marginal McFadden's pseudo R2
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nor the type III sums of square computations
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{p 4 8 2}{cmd:nip} specifies the number of integration points to be used for each
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integral or summation. Only the following degrees are available: 5, 7, 9, 11, 15.
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{p 4 8 2}{cmd:trace} causes more output to be displayed. Before estimation begins,
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details of the specified model are displayed. In addition, a detailed iteration
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log is shown including parameter estimates and log-likelihood values for each iteration.
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{p 4 8 2}{cmd:level} set confidence level; default is level(95)
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{title:Outputs}
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{p 4 8 2}{cmd:e(ll)}: marginal log-likelihood
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{p 4 8 2}{cmd:e(cn)}: Condition number
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{p 4 8 2}{cmd:e(N)}: Number of observations
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{p 4 8 2}{cmd:e(Nit)}: Number of items
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{p 4 8 2}{cmd:e(Ncat)}: Number of categorical covariates
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{p 4 8 2}{cmd:e(Ncont)}: Number of continuous covariates
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{p 4 8 2}{cmd:e(sigma)}: Estimated standard deviation of the latent trait
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{p 4 8 2}{cmd:e(Varsigma)}: Variance of the estimated standard deviation of
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the latent trait
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{p 4 8 2}{cmd:e(theta)}: Coefficient vector of the parameters associated with the latent trait covariates (if no covariate is included in the model, value of the average latent trait)
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{p 4 8 2}{cmd:e(Vartheta)}: Covariance matrix for the latent trait covariates.
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{p 4 8 2}{cmd:e(delta)}: Estimated difficulty parameters
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{p 4 8 2}{cmd:e(Vardelta)}: Covariance matrix for the estimated difficulty parameters
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{p 4 8 2}{cmd:e(b)}: Overall estimated parameters of the PCM (or RSM)
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{p 4 8 2}{cmd:e(V)}: Covariance matrix for the overall estimated parameters
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{marker example}{...}
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{title:Example}
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{pstd}
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Simulation of the data (using {help simirt}):
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. {cmd:simirt, nbobs(200) dim(5) rsm1(0.2) group(0.5) deltagroup(0.4) clear}{right:(1) }
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{pstd}
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Estimating a Partial Credit Model with {cmd:pcmodel}:
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. {cmd:pcmodel item*}{right:(2) }
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{pstd}
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Estimating a Rating Sacle Model with {cmd:pcmodel}:
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. {cmd:pcmodel item*, rsm}{right:(3) }
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{pstd}
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Testing the fit of the previously performed model with {help pcmtest}:
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. {cmd:pcmtest, si }{right:(4) }
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{pstd}
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Estimating a Partial Credit Model with {cmd:pcmodel}, considering that the item difficulties
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are provided by the scale developer (-1 & -0.8 for item1, -0.5 & -0.3 for item2, 0 & 0.2 for
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item3, 0.5 & 0.7 for item4 and 1 & 1.2 for item5) and that the {it:group} covariate may
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influence the individual latent trait:
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{p 6 9 2}
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1/ Defining the row vectors containing the known values of each item difficulty, with the
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same name as the corresponding item:
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. {cmd:matrix item1=(-1,-0.8)}{right:(5) }
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. {cmd:matrix item2=(-0.5,-0.3)}{right:(6) }
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. {cmd:matrix item3=(0,0.2)}{right:(7) }
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. {cmd:matrix item4=(0.5,0.7)}{right:(8) }
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. {cmd:matrix item5=(1,1.2)}{right:(9) }
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{p 6 9 2}
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2/ Estimating the Partial Credit Model with item difficulties already known, including
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the {it:group} covariate as a categorical covariate:
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. {cmd:pcmodel item*, difficulties(item1 item2 item3 item4 item5) cat(group)}{right:(10) }
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{title:Author}
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{p 4 8 2}Jean-François Hamel{p_end}
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{p 4 8 2}Email:
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{browse "mailto:jeanfrancois.hamel@chu-angers.fr":jeanfrancois.hamel@chu-angers.fr}{p_end}
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{title:Also see}
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{p 4 13 2}Online: help for {help pcmtest}, {help gllamm}, {help simirt},
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{help raschtest}.{p_end}
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