finding extreme values in a panel data set

Dear Matlab experts

I have

A={

    [1]    ' '              [NaN]     [NaN]     [NaN]     
    [1]    '30/11/08'    [11.1447]    [0.2117]    [463.1360]
    [1]    '28/12/08'    [11.7129]    [0.2209]    [436.6316]
    [1]    '25/01/09'    [11.5152]    [0.2212]    [441.5430]
    [1]    '22/02/09'    [11.4854]    [0.2201]    [453.7015]
    [1]    '22/03/09'    [NaN]       [0.2185]    [461.3925]
    [1]    '19/04/09'    [10.9700]    [0.2104]    [486.4095]
    [1]    '17/05/09'    [11.4846]    [0.2162]    [451.4833]
    [1]    '14/06/09'    [10.9967]    [0.2158]    [475.8620]
    [1]    '12/07/09'    [11.1990]    [0.2211]    [449.4574]
    [2]    ' '             [NaN]     [NaN]     [NaN]     
    [2]    '30/11/08'    [10.8638]    [0.2175]    [472.2659]
    [2]    '28/12/08'    [11.0897]    [0.2182]    [479.3408]
    [2]    '25/01/09'    [11.0996]    [0.2286]    [442.6719]
    [2]    '22/02/09'    [11.0473]    [0.2211]    [481.4548]
    [2]    '22/03/09'    [11.1151]    [0.2259]    [468.2757]
    [2]    '19/04/09'    [10.9865]    [0.2300]    [461.5581]
    [2]    '17/05/09'    [10.7931]    [0.2259]    [487.6257]
    [2]    '14/06/09'    [10.5845]    [0.2200]    [529.8777]
    [2]    '12/07/09'    [10.8926]    [0.2315]    [433.3039]
    [3]    ' '             [NaN]     [NaN]     [NaN]     
    [3]    '30/11/08'    [10.7658]    [0.2339]    [487.7729]
    [3]    '28/12/08'    [10.5227]    [0.2305]    [505.4553]
    [3]    '25/01/09'    [10.6700]    [0.2279]    [480.0745]
    [3]    '22/02/09'    [10.7632]    [NaN]    [518.5076]
    [3]    '22/03/09'    [10.5065]    [0.2271]    [470.0111]
    [3]    '19/04/09'    [10.6112]    [0.2215]    [483.5394]
    [3]    '17/05/09'    [10.5855]    [0.2190]    [497.3172]
    [3]    '14/06/09'    [10.3085]    [0.2158]    [515.7492]
    [3]    '12/07/09'    [10.4475]    [0.2211]    [482.3380]
}

A is a panel data set that shows the evolution of some variables (columns 3-5) over time (column 2) for 3 individuals (column 1).

I would like

1) to detect outliers (their position and their corresponding values) in columns 3, 4 and 5 where an outlier is defined as a “a value that it is larger than (or equal to) 3 standard deviations over the mean”.

2) plot a diagram for each of the columns 3, 4 and 5 where outliers will stand out with, say, a red color

Could I do that with some matlab code?

Thank you very much

just to mention that my real A is huge where I have 400 individuals.

That's far, far from huge. Do you want this done separately for each group listed in column 1? It looks complicated by the fact that not only do NaNs separate the groups listed in column 1, but there are random Nan's scattered about.

Answer 1

What have you tried so far? Did you try anything along the lines of

column3 = cell2mat(A(:,3))
goodIndexes = ~isnan(column3)
goodColumn3 = column3(goodIndexes)
mean3 = mean(goodColumn3)
std3 = std(goodColumn3)
lowerLimit = mean3 - std3
upperLimit = mean3 + std3
outliers = column3 < lowerLimit | column3 > upperLimit
outlierIndexes = find(outliers);
normalIndexes = find(~outliers);
x = (1:length(column3))';
stem(x(normalIndexes), column3(normalIndexes), 'b');
hold on;
grid on;
stem(x(outlierIndexes), column3(outlierIndexes), 'r');
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);

and so on for the other columns?

Hi imager.thank you for your reply. Yes it is almost ok apart from the fact that you code assumes that column 3 refers to one group. I want apply this for each group listed in column 1 (groups 1,2,3) and as I said in my initial question I have 400 such groups.

Thank you

Well you probably already did this but you could adapt it to find the groups, then process each group:

column3 = cell2mat(A(:, 3))
column4 = cell2mat(A(:, 4))
column5 = cell2mat(A(:, 5))
badIndexes3 = isnan(column3)
badIndexes4 = isnan(column4)
badIndexes5 = isnan(column5)
separatorIndexes = badIndexes3 & badIndexes4 & badIndexes5;
numberOfGroups = length(separatorIndexes)
% Tack on one more.
separatorIndexes = find([separatorIndexes; true]);
% Preallocate cells for outliers.
% Cells because there are different numbers of outliers for each group.
outliers = cell(1,1);
outlierIndexes = cell(1,1);
normalIndexes = cell(1,1);
outlierValues3 = cell(1,1);
for group = 1 : numberOfGroups
	% Go inbetween the separators.
	row1 = separatorIndexes(group)+1;
	row2 = separatorIndexes(group+1) - 1
	extractedGroup3 = column3(row1:row2);
	goodIndexes3 = ~isnan(extractedGroup3)
	goodColumn3 = extractedGroup3(goodIndexes3)
	mean3(group) = mean(extractedGroup3)
	std3(group) = std(extractedGroup3)
	lowerLimit(group) = mean3 - std3
	upperLimit(group) = mean3 + std3
	badLogicalIndexes = extractedGroup3 < lowerLimit | extractedGroup3 > upperLimit;
	outliers(group) = {badLogicalIndexes};
	outlierIndexes(group) = {find(badLogicalIndexes)};
	normalIndexes(group) = {find(~badLogicalIndexes)};
	outlierValues3(group) = extractedGroup3(badLogicalIndexes)
end

But you probably already know that mean+3*SD is not a good method for finding outliers for small groups because a single outlier could really affect the true mean A LOT. There are better methods, such as the Minimum Absolute Deviation (MAD, http://en.wikipedia.org/wiki/Median_absolute_deviation)

thanks imager very much for providing the code. What is the rule for an outlier based on "Minimum Absolute Deviation" ?

cheers

I searched on the internet but could not find a specific rule based on the MAD

You first calculate the MAD. Then you multiply that by a factor that says how many of those you need to consider something an outlier, just like you chose 3 for sigma to say that if it were more than 3 sigma away from the mean it's an outlier. Same thing except use MAD instead of the standard deviation sigma. Like, if that data point's value is more than 2 (or 3 or 4 or whatever suits your situation) MADs away from the mean, then that data point is an outlier.

thanks imager