Data Problems in SEM在扫描电子显微镜中的数据问题.docVIP

Data Problems in SEM Incomplete Data / Categorical Data The impact of incomplete data (and of any procedure for dealing with incomplete data) depends somewhat on the pattern of incompleteness: Missing Completely At Random (MCAR) The missing and observed distributions of Y are identical: Y1 Y2 1 1 2 2 3 3 4 4 5 5 6 6 P ( Y | incomplete ) = P ( Y | complete ) i.e., the missing values are literally a simple random sample excised from an otherwise complete data set So it follows that the complete cases (if any) are a random sampling from among the entire data set, i.e., the same model applies to both the complete cases and the total data set. Missing At Random (MAR) Y1 Y2 X 1 1 3 2 2 12 3 3 5 4 4 6 5 5 15 6 6 8 For variable Y, the missing and observed distributions are identical, conditional on some other set of variables: P ( Y | incomplete, X ) = P ( Y | complete ) But the missingness mechanism is not tied to the value of Y itself. On the positive side, the values of other variables may allow the researcher to statistically reconstruct the missing values of Y. Enders recommends using auxiliary variables to capitalize on MAR. Simply excluding the missing cases may truncate or alter the assessed relationship between Y and the other variables. However, the estimated mean and variance of Y in the complete cases will be an unbiased estimate of a complete sample. Nonignorable Missingness Y1 Y2 3 1 2 2 1 3 4 4 5 5 6 6 – the missing and observed values of Y are not the same, under any conditions: P ( Y | incomplete ) ≠ P ( Y | complete ) The reason that a given value is missing may have to do with the value itself. In other words, any model for the values of Y based only on the observed values will be wrong. Any estimate of statistics for Y, or for the relationships between Y and other variables, may be biased. The researcher cannot be sure of obtaining correct estimates, regardless of technique used. Resolving these questions requires new data collection. Procedure