Using FSL - STATS (First Level)
FILM General Linear Model
General linear modelling allows you to describe one or more stimulation types, and, for each voxel, a linear combination of the modelled response to these stimulation types is found which minimises the unmodelled noise in the fitting. If you are not familiar with the concepts of the GLM and contrasts of parameter estimates, then you should now read Appendix A.
For normal first-level time series analysis you should Use FILM prewhitening to make the statistics valid and maximally efficient. For other data - for example, very long TR (>30s) FMRI data, PET data or data with very few time points (<50) - this should be turned off.
You can setup FILM easily for simple designs by using the FILM "wizard" - press the Simple model setup button. Then choose whether to setup ABAB... or ABACABAC... designs (block or single-event). The A blocks will normally be rest (or control) conditions. Enter the timings (in seconds) for these periods and press Process; FILM will be automatically setup for you.
If you want to setup a more complex model, or adjust the setup created by the wizard, press Full model setup button. This is now described in detail.
EVs
First set the Number of original EVs (explanatory variables) - basic number of explanatory variables in the design matrix; this means the number of different effects that you wish to model - one for each modelled stimulation type, and one for each modelled confound. For first-level analyses, it is common for the final design matrix to have a greater number of real EVs than this original number; for example, when using basis functions, each original EV gives rise to several real EVs.
Now you need to setup each EV separately. Choose the basic shape of the waveform that describes the stimulus or confound that you wish to model. The basic waveform should be exactly in time with the applied stimulation, i.e., not lagged at all. This is because the measured (time-series) response will be delayed with respect to the stimulation, and this delay is modelled in the design matrix by convolution of the basic waveform with a suitable haemodynamic response function (see below).
For an on/off (or a regularly-spaced single-event) experiment choose a square wave. To model single-event experiments with this method, the On periods will probably be small - e.g., 1s or even less.
For sinusoidal modelling choose the Sinusoid option and select the number of Harmonics (or overtones) that you want to add to the fundamental frequency.
For a single-event experiment with irregular timing for the stimulations, a custom file can be used. With Custom (1 entry per volume), you specify a single value for each timepoint. The custom file should be a raw text file, and should be a list of numbers, separated by spaces or newlines, with one number for each volume (after subtracting the number of deleted images). These numbers can either all be 0s and 1s, or can take a range of values. The former case would be appropriate if the same stimulus was applied at varying time points; the latter would be appropriate, for example, if recorded subject responses are to be inserted as an effect to be modelled. Note that it may or may not be appropriate to convolve this particular waveform with an HRF - in the case of single-event, it is.
For even finer control over the input waveform, choose Custom (3 column format). In this case the custom file consists of triplets of numbers; you can have any number of triplets. Each triplet describes a short period of time and the value of the model during that time. The first number in each triplet is the onset (in seconds) of the period, the second number is the duration (in seconds) of the period, and the third number is the value of the input during that period. The same comments as above apply, about whether these numbers are 0s and 1s, or vary continuously. The start of the first non-deleted volume correpsonds to t=0.
Note that whilst ALL columns are demeaned before model fitting, neither custom format will get rescaled - it is up to you to make sure that relative scaling between different EVs is sensible. If you double the scaling of values in an EV you will halve the resulting parameter estimate, which will change contrasts of this EV against others.
If you select Interaction then you can set which EVs this EV models the interaction between. This EV is produced by multiplying together selected EVs, and allows the modelling of the non-additive interaction between the selected EVs. This requires that the EVs are sometimes on at the same time, and sometimes on separately.
If you have chosen a Square or Sinusoid basic shape, you then need to specify what the timings of this shape are. Skip is the initial period of zeros (in seconds) before the waveform commences. Off is the duration (seconds) of the "Off" periods in the square wave. On is the duration (seconds) of the "On" periods in the square wave. Period is the period (seconds) of the Sinusoid waveform. Phase is the phase shift (seconds) of the waveform; by default, after the Skip period, the square wave starts with a full Off period and the Sinusoid starts by falling from zero. However, the wave can be brought forward in time according to the phase shift. Thus to start with half of a normal Off period, enter the Phase as half of the Off period. To start with a full On period, enter the same as the Off period. Stop after is the total duration (seconds) of the waveform, starting after the Skip period. "-1" means do not stop. After stopping a waveform, all remaining values in the model are set to zero.
Convolution sets the form of the HRF (haemodynamic response function) convolution that will be applied to the basic waveform. This blurs and delays the original waveform, in an attempt to match the difference between the input function (original waveform, i.e., stimulus waveform) and the output function (measured FMRI haemodynamic response). If the original waveform is already in an appropriate form, e.g., was sampled from the data itself, None should be selected. The next three options are all somewhat similar blurring and delaying functions. Gaussian is simply a Gaussian kernel, whose width and lag can be altered. Gamma is a Gamma variate (in fact a normalisation of the probability density function of the Gamma function); again, width and lag can be altered. Double-Gamma HRF is a preset function which is a mixture of two Gamma functions - a standard positive function at normal lag, and a small, delayed, inverted Gamma, which attempts to model the late undershoot.
The remaining convolution options setup different basis functions. This means that the original EV waveform will get convolved by a "basis set" of related but different convolution kernels. By default, an original EV will generate a set of real EVs, one for each basis function.
The Optimal/custom option allows you to use a customised set of basis functions, setup in a plain text file with one column for each basis function, sampled at the temporal resolution of 0.05s. The main point of this option is to allow the use of "FLOBS" (FMRIB's Linear Optimal Basis Set), which is a method for generating a set of basis functions that has optimal efficiency in covering the range of likely HRF shapes actually found in your data. You can either use the default FLOBS set, or use the Make_flobs GUI on the FEAT Utils menu to create your own customised set of FLOBS.
The other basis function options, which will not in general be as good at fitting the data as FLOBS, are a set of Gamma variates of different widths and lags, a set of Sine waves of differing frequencies or a set of FIR (finite-impulse-response) filters (with FIR the convolution kernel is represented as a set of discrete fixed-width "impulses").
You should normally apply the same temporal filtering to the model as you have applied to the data, as the model is designed to look like the data before temporal filtering was applied. In this way, long-time-scale components in the model will be dealt with correctly. This is set with the Apply temporal filtering option.
Adding a fraction of the temporal derivative of the blurred original waveform is equivalent to shifting the waveform slightly in time, in order to achieve a slightly better fit to the data. Thus adding in the temporal derivative of a waveform into the design matrix allows a better fit for the whole model, reducing unexplained noise, and increasing resulting statistical significances. Thus, setting Add temporal derivative produces a new waveform in the final design matrix (next to the waveform from which it was derived) This option is not available if you are using basis functions.
Orthogonalising an EV with respect to other EVs means that it is completely independent of the other EVs, i.e. contains no component related to them. Most sensible designs are already in this form - all EVs are at least close to being orthogonal to all others. However, this may not be the case; you can use this facility to force an EV to be orthogonal to some or all other EVs. This is achieved by subtracting from the EV that part which is related to the other EVs selected here. An example use would be if you had another EV which was a constant height spike train, and the current EV is derived from this other one, but with a linear increase in spike height imposed, to model an increase in response during the experiment for any reason. You would not want the current EV to contain any component of the constant height EV, so you would orthogonalise the current EV wrt the other.
Contrasts
Each EV (explanatory variable, i.e., waveform) in the design matrix results in a PE (parameter estimate) image. This estimate tells you how strongly that waveform fits the data at each voxel - the higher it is, the better the fit. For an unblurred square wave input (which will be scaled in the model from -0.5 to 0.5), the PE image is equivalent to the "mean difference image". To convert from a PE to a t statistic image, the PE is divided by its standard error, which is derived from the residual noise after the complete model has been fit. The t image is then transformed into a Z statistic via standard statistical transformation. As well as Z images arising from single EVs, it is possible to combine different EVs (waveforms) - for example, to see where one has a bigger effect than another. To do this, one PE is subtracted from another, a combined standard error is calculated, and a new Z image is created.
All of the above is controlled by you, by setting up contrasts. Each output Z statistic image is generated by setting up a contrast vector; thus set the number of outputs that you want, using Number of contrasts. To convert a single EV into a Z statistic image, set its contrast value to 1 and all others to 0. Thus the simplest design, with one EV only, has just one contrast vector, and only one entry in this contrast vector; 1. To add more contrast vectors, increase the Number of contrasts. To compare two EVs, for example, to subtract one stimulus type (EV1) from another type (EV2), set EV1's contrast value to -1 and EV2's to 1. A Z statistic image will be generated according to this request.
For first-level analyses, it is common for the final design matrix to have a greater number of real EVs than the original number; for example, when using basis functions, each original EV gives rise to several real EVs. Therefore it is possible in many cases for you to setup contrasts and F-tests with respect to the original EVs, and FEAT will work out for you what these will be for the final design matrix. For example, a single [1] contrast on an original EV for which basis function HRF convolutions have been chosen will result in a single [1] contrast for each resulting real EV, and then an F-test across these. In general you can switch between setting up contrasts and F-tests with respect to Original EVs and Real EVs; though of course if you fine-tune the contrasts for real EVs and then revert to original EV setup some settings may be lost. When you View the design matrix or press Done at the end of setting up the model, an Original EVs setup will get converted to the appropriate Real EVs settings.
An important point to note is that you should not test for differences between different conditions (or at higher-level, between sessions) by looking for differences between their separate individual analyses. One could be just above threshold and the other just below, and their difference might not be significant. The correct way to tell whether two conditions or session's analyses are significantly different is to run a differential contrast like [1 -1] between them (or, at higher-level, run a higher-level FEAT analysis to contrast lower-level analyses); this contrast will then get properly thresholded to test for significance.
There is another important point to note when interpreting differential (eg [1 -1]) contrasts. This is that you are quite likely to only want to check for A>B if both are positive. Don't forget that if both A and B are negative then this contrast could still come out significantly positive! In this case, the thing to do is to use the Contrast masking feature (see below); setup contrasts for the individual EVs and then mask the differential contrast with these.
F-tests
F-tests enable you to investigate several contrasts at the same time, for example to see whether any of them (or any combination of them) is significantly non-zero. Also, the F-test allows you to compare the contribution of each contrast to the model and decide on significant and non-significant ones. F-tests are non-directional (i.e. test for "positive" and "negative" activation).
One example of F-test usage is if a particular stimulation is to be represented by several EVs, each with the same input function (e.g. square wave or custom timing) but all with different HRF convolutions - i.e. several basis functions. Putting all relevant resulting parameter estimates together into an F-test allows the complete fit to be tested against zero without having to specify the relative weights of the basis functions (as one would need to do with a single contrast). So - if you had three basis functions (EVs 1,2 and 3) the wrong way of combining them is a single (T-test) contrast of [1 1 1]. The right way is to make three contrasts [1 0 0] [0 1 0] and [0 0 1] and enter all three contrasts into an F-test. As described above, FEAT will automatically do this for you if you set up contrasts for original EVs instead of real EVs.
You can carry out as many F-tests as you like. Each test includes the particular contrasts that you specify by clicking on the appropriate buttons.
Buttons
To view the current state of the design matrix, press View design. This is a graphical representation of the design matrix and parameter contrasts. The bar on the left is a representation of time, which starts at the top and points downwards. The white marks show the position of every 10th volume in time. The red bar shows the period of the longest temporal cycle which was passed by the highpass filtering. The main top part shows the design matrix; time is represented on the vertical axis and each column is a different (real) explanatory variable (e.g., stimulus type). Both the red lines and the black-white images represent the same thing - the variation of the waveform in time. Below this is shown the requested contrasts; each row is a different contrast vector and each column refers to the weighting of the relevant explanatory variable. Thus each row will result in a Z statistic image. If F-tests have been specified, these appear to the right of the contrasts; each column is a different F-test, with the inclusion of particular contrasts depicted by filled squares instead of empty ones.
If you have more than one EV and you press Covariance you will see a graphical representation of the covariance matrix of the design matrix. The first matrix shows the absolute value of the normalised correlation of each EV with each EV. If a design is well-conditioned (i.e. not approaching rank deficiency) then the diagonal elements should be white and all others darker. So - if there are any very bright elements off the diagonal, you can immediately tell which EVs are too similar to each other - for example, if element [1,3] (and [3,1]) is bright then columns 1 and 3 in the design matrix are possibly too similar. Note that this includes all real EVs, including any added temporal derivatives, basis functions, etc. The second matrix shows a similar thing after the design matrix has been run through SVD (singular value decomposition). All non-diagonal elements will be zero and the diagonal elements are given by the eigenvalues of the SVD, so that a poorly-conditioned design is obvious if any of the diagonal elements are black.
When you have finished setting up the design matrix, press Done. This will dismiss the GLM GUI, and will give you a final view of the design matrix.