Description Usage Arguments Details Author(s) Examples

This function computes the parameter estimates of a Rasch model for binary item responses by using weighted CML estimation. Input data should be a 0/1 matrix (1 = Yes). Residual correlation, fit statistics and corresponding standard errors, Rasch reliability and individual fit statistics are also reported.

1 |

`.data` |
Input 0/1 data matrix or data frame; affirmative responses must be coded as 1s. Rows represent individuals, columns represent items. Missing values are inserted as NA. |

`.w` |
Vector of sampling weights.
The length must be the same as the number of rows of |

`.d` |
Optional vector for the assumption on the extreme raw score parameters.
Default is |

`country` |
Optional (character) name of the dataset. |

`se.control` |
Are the extreme parameter standard errors fixed to the ones
corresponding to raw score |

`quantile.seq` |
Quantiles corresponding to the observed and the expected individual fit statistic distributions. |

`write.file` |
If |

The weighted CML method is used to estimate the item parameter. Respondent parameters are estimated post-hoc. Cases with missing responses to some items may be included, but will not be used to estimate the Rasch model.

As the parameters for the extreme raw scores (`0`

and `k`

), are undefined under the CML, some assumptions are needed unless the proportions of respondents with those raw scores are so small that they can be considered to be measured without error.
Vector `.d`

gives the possibility to include up to four alternative assumptions on each of the extreme parameters. More in detail, `.d`

can be a two, three or four element vector:

If

`length(.d) = 4`

, then the first two elements have to refer to the assumptions upon raw score 0, and the second two elements to raw score`k`

. For instance`.d = c(0.1, 0.7, 7.1, 7.6)`

, if the maximum raw score is 8.If

`length(.d) = 3`

, then the first two elements can either refer to the assumptions upon raw score`0`

or raw score`k`

, and the last one is defined accordingly. For instance`.d = c(0.1, 7.1, 7.6)`

or`.d = c(0.1, 0.7, 7.6)`

, if the maximum raw score is 8.If

`length(.d) = 2`

, then the first element have to refer to the assumption upon raw score`0`

, and the second element to raw score`k`

. For instance`.d = c(0.1, 7.6)`

, if the maximum raw score is 8.

Sara Viviani [email protected], Mark Nord [email protected]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | ```
## Not run:
data(data.FAO_country1)
# Questionnaire data and weights
XX.country1 = data.FAO_country1[,1:8]
wt.country1 = data.FAO_country1$wt
# Fit weighted Rasch
rr.country1 = RM.w(XX.country1, wt.country1)
# Fit unweighted Rasch
rr.country1.nw = RM.w(XX.country1)
# Item severity
rr.country1$b
# Item standard error
rr.country1$se.b
# Respondent severity for each raw score
rr.country1$a
# Respondent measurement error for each raw score
rr.country1$se.a
# Item infit
rr.country1$infit
# Item outfit
rr.country1$outfit
# Rasch reliability based on observed distribution of cases across raw scores
rr.country1$reliab
# Rasch reliability based on equal proportion of cases in each non-extreme raw score (more comparable across datasets)
rr.country1$reliab.fl
# Respondent infit distribution: observed and expected
quantile.seq = c(0,.01,.02,.05,.10,.25,.50,.75,.90,.95,
.98,.99,1)
q.infit = rr.country1$q.infit
q.infit.theor = rr.country1$q.infit.theor
plot(quantile.seq, q.infit, type = "b", xlab = "Quantiles",
ylab = "Observed infit", ylim = c(0, 6))
lines(quantile.seq, q.infit.theor, type = "b", col = 2)
# Checking conditional independence: residual correlation matrix
rr.country1$res.cor
# Save outputs to csv file with data name
rr.country1 = RM.w(XX.country1, wt.country1, country = "country1", write.file = T)
## End(Not run)
``` |

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